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DRYING PHENOMENA

DRYING PHENOMENATHEORY AND APPLICATIONS

İbrahim DinccedilerandCalin ZamfirescuUniversity of Ontario Institute of Technology Oshawa ON Canada

This edition first published 2016copy 2016 John Wiley amp Sons Ltd

Registered OfficeJohn Wiley amp Sons Ltd The Atrium Southern Gate Chichester West Sussex PO19 8SQ United Kingdom

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

The right of the author to be identified as the author of this work has been asserted in accordance with the CopyrightDesigns and Patents Act 1988

All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted inany form or by anymeans electronic mechanical photocopying recording or otherwise except as permitted by the UKCopyright Designs and Patents Act 1988 without the prior permission of the publisher

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The publisher is not associated with any product or vendor mentioned in this book

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparing thisbook they make no representations or warranties with respect to the accuracy or completeness of the contents ofthis book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose It is soldon the understanding that the publisher is not engaged in rendering professional services and neither the publishernor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is requiredthe services of a competent professional should be sought

Library of Congress Cataloging-in-Publication Data

Dinccediler İbrahim 1964ndash authorDrying phenomena theory and applications İbrahim Dinccediler and Calin Zamfirescu

pages cmIncludes bibliographical references and indexISBN 978-1-119-97586-1 (cloth)

1 Drying I Zamfirescu Calin author II TitleTP363D48 2016664 0284ndashdc23

2015025655

A catalogue record for this book is available from the British Library

Set in 1012pt Times by SPi Global Pondicherry India

1 2016

DRYING PHENOMENA

DRYING PHENOMENATHEORY AND APPLICATIONS

İbrahim DinccedilerandCalin ZamfirescuUniversity of Ontario Institute of Technology Oshawa ON Canada

This edition first published 2016copy 2016 John Wiley amp Sons Ltd

Registered OfficeJohn Wiley amp Sons Ltd The Atrium Southern Gate Chichester West Sussex PO19 8SQ United Kingdom

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

The right of the author to be identified as the author of this work has been asserted in accordance with the CopyrightDesigns and Patents Act 1988

All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted inany form or by anymeans electronic mechanical photocopying recording or otherwise except as permitted by the UKCopyright Designs and Patents Act 1988 without the prior permission of the publisher

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The publisher is not associated with any product or vendor mentioned in this book

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparing thisbook they make no representations or warranties with respect to the accuracy or completeness of the contents ofthis book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose It is soldon the understanding that the publisher is not engaged in rendering professional services and neither the publishernor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is requiredthe services of a competent professional should be sought

Library of Congress Cataloging-in-Publication Data

Dinccediler İbrahim 1964ndash authorDrying phenomena theory and applications İbrahim Dinccediler and Calin Zamfirescu

pages cmIncludes bibliographical references and indexISBN 978-1-119-97586-1 (cloth)

1 Drying I Zamfirescu Calin author II TitleTP363D48 2016664 0284ndashdc23

2015025655

A catalogue record for this book is available from the British Library

Set in 1012pt Times by SPi Global Pondicherry India

1 2016

DRYING PHENOMENATHEORY AND APPLICATIONS

İbrahim DinccedilerandCalin ZamfirescuUniversity of Ontario Institute of Technology Oshawa ON Canada

This edition first published 2016copy 2016 John Wiley amp Sons Ltd

Registered OfficeJohn Wiley amp Sons Ltd The Atrium Southern Gate Chichester West Sussex PO19 8SQ United Kingdom

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

The right of the author to be identified as the author of this work has been asserted in accordance with the CopyrightDesigns and Patents Act 1988

All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted inany form or by anymeans electronic mechanical photocopying recording or otherwise except as permitted by the UKCopyright Designs and Patents Act 1988 without the prior permission of the publisher

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The publisher is not associated with any product or vendor mentioned in this book

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparing thisbook they make no representations or warranties with respect to the accuracy or completeness of the contents ofthis book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose It is soldon the understanding that the publisher is not engaged in rendering professional services and neither the publishernor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is requiredthe services of a competent professional should be sought

Library of Congress Cataloging-in-Publication Data

Dinccediler İbrahim 1964ndash authorDrying phenomena theory and applications İbrahim Dinccediler and Calin Zamfirescu

pages cmIncludes bibliographical references and indexISBN 978-1-119-97586-1 (cloth)

1 Drying I Zamfirescu Calin author II TitleTP363D48 2016664 0284ndashdc23

2015025655

A catalogue record for this book is available from the British Library

Set in 1012pt Times by SPi Global Pondicherry India

1 2016

This edition first published 2016copy 2016 John Wiley amp Sons Ltd

Registered OfficeJohn Wiley amp Sons Ltd The Atrium Southern Gate Chichester West Sussex PO19 8SQ United Kingdom

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

The right of the author to be identified as the author of this work has been asserted in accordance with the CopyrightDesigns and Patents Act 1988

All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted inany form or by anymeans electronic mechanical photocopying recording or otherwise except as permitted by the UKCopyright Designs and Patents Act 1988 without the prior permission of the publisher

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The publisher is not associated with any product or vendor mentioned in this book

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparing thisbook they make no representations or warranties with respect to the accuracy or completeness of the contents ofthis book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose It is soldon the understanding that the publisher is not engaged in rendering professional services and neither the publishernor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is requiredthe services of a competent professional should be sought

Library of Congress Cataloging-in-Publication Data

Dinccediler İbrahim 1964ndash authorDrying phenomena theory and applications İbrahim Dinccediler and Calin Zamfirescu

pages cmIncludes bibliographical references and indexISBN 978-1-119-97586-1 (cloth)

1 Drying I Zamfirescu Calin author II TitleTP363D48 2016664 0284ndashdc23

2015025655

A catalogue record for this book is available from the British Library

Set in 1012pt Times by SPi Global Pondicherry India

1 2016

Contents

Preface xi

Nomenclature xv

1 Fundamental Aspects 111 Introduction 112 Fundamental Properties and Quantities 213 Ideal Gas and Real Gas 1314 The Laws of Thermodynamics 1915 Thermodynamic Analysis Through Energy and Exergy 24

151 Exergy 24152 Balance Equations 27

16 Psychometrics 3617 Heat Transfer 45

171 General Aspects 45172 Heat Transfer Modes 48173 Transient Heat Transfer 54

18 Mass Transfer 5819 Concluding Remarks 63110 Study Problems 63References 65

2 Basics of Drying 6721 Introduction 6722 Drying Phases 6823 Basic Heat and Moisture Transfer Analysis 6924 Moist Material 76

25 Types of Moisture Diffusion 8126 Shrinkage 8227 Modeling of Packed-Bed Drying 8628 Diffusion in Porous Media with Low Moisture Content 8829 Modeling of Heterogeneous Diffusion in Moist Solids 90210 Conclusions 97211 Study Problems 97References 98

3 Drying Processes and Systems 9931 Introduction 9932 Drying Systems Classification 10033 Main Types of Drying Devices and Systems 105

331 Batch Tray Dryers 105332 Batch Through-Circulation Dryers 106333 Continuous Tunnel Dryers 108334 Rotary Dryers 110335 Agitated Dryers 114336 Direct-Heat Vibrating-Conveyor Dryers 116337 Gravity Dryers 117338 Dispersion Dryers 119339 Fluidized Bed Dryers 1283310 Drum Dryers 1303311 Solar Drying Systems 132

34 Processes in Drying Systems 137341 Natural Drying 137342 Forced Drying 145

35 Conclusions 15136 Study Problems 151References 152

4 Energy and Exergy Analyses of Drying Processes and Systems 15341 Introduction 15342 Balance Equations for a Drying Process 15443 Performance Assessment of Drying Systems 159

431 Energy and Exergy Efficiencies 159432 Other Assessment Parameters 161

44 Case Study 1 Analysis of Continuous-Flow Direct Combustion Dryers 16245 Analysis of Heat Pump Dryers 16946 Analysis of Fluidized Bed Dryers 178

461 Hydrodynamics of Fluidized Beds 179462 Balance Equations 181463 Efficiency Formulations 183

47 Conclusions 18748 Study Problems 187References 188

vi Contents

5 Heat and Moisture Transfer 18951 Introduction 18952 Transient Moisture Transfer During Drying of Regularly Shaped Materials 190

521 Transient Diffusion in Infinite Slab 191522 Drying Time of an Infinite Slab Material 200523 Transient Diffusion in an Infinite Cylinder 202524 Transient Diffusion in Spherical-Shape Material 205525 Compact Analytical Solution or Time-Dependent Diffusion

in Basic Shapes 20853 Shape Factors for Drying Time 209

531 Infinite Rectangular Rod of Size 2Ltimes 2β1L 210532 Rectangular Rod of Size 2Ltimes 2β1L times 2β2L 210533 Long Cylinder of Diameter 2L and Length 2β1L 212534 Short Cylinder of Diameter 2β1L and Length 2L 213535 Infinite Elliptical Cylinder of Minor Axis 2L and Major Axis 2β1L 213536 Ellipsoid Having the Axes 2L 2β1L and 2β2L 213

54 Moisture Transfer Coefficient and Diffusivity Estimation from Drying Curve 21655 Simultaneous Heat and Moisture Transfer 21956 Models for Heat and Moisture Transfer in Drying 225

561 Theoretical Models 226562 Semitheoretical and Empirical Models for Drying 231

57 Conclusions 23258 Study Problems 233References 234

6 Numerical Heat and Moisture Transfer 23761 Introduction 23762 Numerical Methods for PDEs 239

621 The Finite Difference Method 240622 Weighted Residuals Methods Finite Element Finite Volume

Boundary Element 24663 One-Dimensional Problems 249

631 Decoupled Equations with Nonuniform Initial Conditionsand Variable Boundary Conditions 249

632 Partially Coupled Equations 253633 Fully Coupled Equations 256

64 Two-Dimensional Problems 261641 Cartesian Coordinates 261642 Cylindrical Coordinates with Axial Symmetry 271643 Polar Coordinates 276644 Spherical Coordinates 280

65 Three-Dimensional Problems 28466 Influence of the External Flow Field on Heat and Moisture Transfer 28867 Conclusions 29168 Study Problems 291References 292

viiContents

7 Drying Parameters and Correlations 29571 Introduction 29572 Drying Parameters 296

721 Moisture Transfer Parameters 296722 Drying Time Parameters 299

73 Drying Correlations 301731 Moisture Diffusivity Correlation with Temperature

and Moisture Content 301732 Correlation for the Shrinkage Ratio 304733 Biot NumberndashReynolds Number Correlations 305734 Sherwood NumberndashReynolds Number Correlations 307735 Biot NumberndashDincer Number Correlation 310736 Regression Correlations for μ1 Eigenvalues versus Lag Factor 312737 Biot NumberndashDrying Coefficient Correlation 313738 Moisture DiffusivityndashDrying Coefficient Correlation 315739 Biot NumberndashLag Factor Correlation 3167310 Graphical Determination of Moisture Transfer Parameters in Drying 3177311 Moisture Transfer Coefficient 318

74 Conclusions 32075 Study Problems 320References 321

8 Exergoeconomic and Exergoenvironmental Analyses of DryingProcesses and Systems 32381 Introduction 32382 The Economic Value of Exergy 32683 EXCEM Method 32984 SPECO Method 33785 Exergoenvironmental Analysis 34086 Conclusions 34587 Study Problems 345References 346

9 Optimization of Drying Processes and Systems 34991 Introduction 34992 Objective Functions for Drying Systems Optimization 351

921 Technical Objective Functions 351922 Environmental Objective Functions 359923 Economic Objective Functions 362

93 Single-Objective Optimization 363931 Trade-off Problems in Drying Systems 363932 Mathematical Formulation and Optimization Methods 366933 Parametric Single-Objective Optimization 371

94 Multiobjective Optimization 37595 Conclusions 37996 Study Problems 379References 380

viii Contents

10 Sustainability and Environmental Impact Assessment of Drying Systems 381101 Introduction 381102 Sustainability 383

1021 Sustainability Assessment Indicators 3831022 Exergy-Based Sustainability Assessment 391

103 Environmental Impact 3971031 Reference Environment Models 3991032 Anthropogenic Impact on the Environment 4011033 Exergy Destruction and Environmental Impact of Drying Systems 411

104 Case Study Exergo-Sustainability Assessment of a Heat Pump Dryer 4191041 Reference Dryer Description 4191042 Exergo-Sustainability Assessment for the Reference Drying System 4211043 Improved Dryer Description 4251044 Exergo-Sustainability Assessment for the Improved Drying System 4281045 Concluding Remarks 430

105 Conclusions 430106 Study Problems 430References 431

11 Novel Drying Systems and Applications 433111 Introduction 433112 Drying with Superheated Steam 436113 Chemical Heat Pump Dryers 438114 Advances on Spray Drying Systems 441

1141 Spray Drying of CuCl2(aq) 4411142 Spray Drying of Nanoparticles 4451143 Microencapsulation through Spray Drying 446

115 Membrane Air Drying for Enhanced Evaporative Cooling 448116 Ultrasound-Assisted Drying 449117 Conclusions 451118 Study Problems 451References 452

Appendix A Conversion Factors 455

Appendix B Thermophysical Properties of Water 457

Appendix C Thermophysical Properties of Some Foods and Solid Materials 461

Appendix D Psychometric Properties of Humid Air 463

Index 469

ixContents

Preface

Drying as an energy-intensive process plays a major role in various sectors ranging from foodindustry to wood industry and affects economies worldwide Drying applications consume anoticeable part of the worldrsquos produced energy and require a careful attention from microlevelto macrolevel applications to make them more efficient more cost effective and more envi-ronmentally benign Bringing all these dimensions into the designs analyses and assessmentsof drying systems for various practical applications is of paramount significanceThis book offers a unique coverage of the conventional and novel drying systems and appli-

cations while keeping a focus on the fundamentals of drying phenomena It includes recentresearch and contributions in sustainable drying systems and integration with renewableenergy The book is expected to serve the drying technology specialists by providing compre-hensive tools for system design analysis assessment and improvement This is essentially aresearch-oriented textbook with comprehensive coverage of the main concepts and drying sys-tems designs It includes practical features in a usable format for the design analysis multi-criteria assessment and improvement of drying processes and systems which are often notincluded in other solely academic textbooks Due to an extensive coverage practicing engi-neers researchers and graduate students in mainstream engineering fields of mechanicaland chemical engineering can find useful information in this bookThe book consists of 11 chapters which amalgamate drying technology aspects starting

from basic phenomena to advanced applications by considering energy exergy efficiencyenvironment economy and sustainability issues The first chapter covers in broad mannerintroductory topics of thermodynamics energy exergy and transient heat transfer and masstransfer so as to furnish the reader with sufficient background information necessary for therest of the bookChapter 2 covers the basics of drying introducing the drying phases and the related phenom-

ena of heat and moisture transfer The moist materials are characterized and classified (eghydroscopic nonhygroscopic capillary etc) in relation with the mechanisms of moisturediffusion and associated phenomena such as shrinkage Introduction to diffusion modelingthrough porous media and moist solids is provided

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

25 Types of Moisture Diffusion 8126 Shrinkage 8227 Modeling of Packed-Bed Drying 8628 Diffusion in Porous Media with Low Moisture Content 8829 Modeling of Heterogeneous Diffusion in Moist Solids 90210 Conclusions 97211 Study Problems 97References 98

3 Drying Processes and Systems 9931 Introduction 9932 Drying Systems Classification 10033 Main Types of Drying Devices and Systems 105

331 Batch Tray Dryers 105332 Batch Through-Circulation Dryers 106333 Continuous Tunnel Dryers 108334 Rotary Dryers 110335 Agitated Dryers 114336 Direct-Heat Vibrating-Conveyor Dryers 116337 Gravity Dryers 117338 Dispersion Dryers 119339 Fluidized Bed Dryers 1283310 Drum Dryers 1303311 Solar Drying Systems 132

34 Processes in Drying Systems 137341 Natural Drying 137342 Forced Drying 145

35 Conclusions 15136 Study Problems 151References 152

4 Energy and Exergy Analyses of Drying Processes and Systems 15341 Introduction 15342 Balance Equations for a Drying Process 15443 Performance Assessment of Drying Systems 159

431 Energy and Exergy Efficiencies 159432 Other Assessment Parameters 161

44 Case Study 1 Analysis of Continuous-Flow Direct Combustion Dryers 16245 Analysis of Heat Pump Dryers 16946 Analysis of Fluidized Bed Dryers 178

461 Hydrodynamics of Fluidized Beds 179462 Balance Equations 181463 Efficiency Formulations 183

47 Conclusions 18748 Study Problems 187References 188

vi Contents

5 Heat and Moisture Transfer 18951 Introduction 18952 Transient Moisture Transfer During Drying of Regularly Shaped Materials 190

521 Transient Diffusion in Infinite Slab 191522 Drying Time of an Infinite Slab Material 200523 Transient Diffusion in an Infinite Cylinder 202524 Transient Diffusion in Spherical-Shape Material 205525 Compact Analytical Solution or Time-Dependent Diffusion

in Basic Shapes 20853 Shape Factors for Drying Time 209

531 Infinite Rectangular Rod of Size 2Ltimes 2β1L 210532 Rectangular Rod of Size 2Ltimes 2β1L times 2β2L 210533 Long Cylinder of Diameter 2L and Length 2β1L 212534 Short Cylinder of Diameter 2β1L and Length 2L 213535 Infinite Elliptical Cylinder of Minor Axis 2L and Major Axis 2β1L 213536 Ellipsoid Having the Axes 2L 2β1L and 2β2L 213

54 Moisture Transfer Coefficient and Diffusivity Estimation from Drying Curve 21655 Simultaneous Heat and Moisture Transfer 21956 Models for Heat and Moisture Transfer in Drying 225

561 Theoretical Models 226562 Semitheoretical and Empirical Models for Drying 231

57 Conclusions 23258 Study Problems 233References 234

6 Numerical Heat and Moisture Transfer 23761 Introduction 23762 Numerical Methods for PDEs 239

621 The Finite Difference Method 240622 Weighted Residuals Methods Finite Element Finite Volume

Boundary Element 24663 One-Dimensional Problems 249

631 Decoupled Equations with Nonuniform Initial Conditionsand Variable Boundary Conditions 249

632 Partially Coupled Equations 253633 Fully Coupled Equations 256

64 Two-Dimensional Problems 261641 Cartesian Coordinates 261642 Cylindrical Coordinates with Axial Symmetry 271643 Polar Coordinates 276644 Spherical Coordinates 280

65 Three-Dimensional Problems 28466 Influence of the External Flow Field on Heat and Moisture Transfer 28867 Conclusions 29168 Study Problems 291References 292

viiContents

7 Drying Parameters and Correlations 29571 Introduction 29572 Drying Parameters 296

721 Moisture Transfer Parameters 296722 Drying Time Parameters 299

73 Drying Correlations 301731 Moisture Diffusivity Correlation with Temperature

and Moisture Content 301732 Correlation for the Shrinkage Ratio 304733 Biot NumberndashReynolds Number Correlations 305734 Sherwood NumberndashReynolds Number Correlations 307735 Biot NumberndashDincer Number Correlation 310736 Regression Correlations for μ1 Eigenvalues versus Lag Factor 312737 Biot NumberndashDrying Coefficient Correlation 313738 Moisture DiffusivityndashDrying Coefficient Correlation 315739 Biot NumberndashLag Factor Correlation 3167310 Graphical Determination of Moisture Transfer Parameters in Drying 3177311 Moisture Transfer Coefficient 318

74 Conclusions 32075 Study Problems 320References 321

8 Exergoeconomic and Exergoenvironmental Analyses of DryingProcesses and Systems 32381 Introduction 32382 The Economic Value of Exergy 32683 EXCEM Method 32984 SPECO Method 33785 Exergoenvironmental Analysis 34086 Conclusions 34587 Study Problems 345References 346

9 Optimization of Drying Processes and Systems 34991 Introduction 34992 Objective Functions for Drying Systems Optimization 351

921 Technical Objective Functions 351922 Environmental Objective Functions 359923 Economic Objective Functions 362

93 Single-Objective Optimization 363931 Trade-off Problems in Drying Systems 363932 Mathematical Formulation and Optimization Methods 366933 Parametric Single-Objective Optimization 371

94 Multiobjective Optimization 37595 Conclusions 37996 Study Problems 379References 380

viii Contents

10 Sustainability and Environmental Impact Assessment of Drying Systems 381101 Introduction 381102 Sustainability 383

1021 Sustainability Assessment Indicators 3831022 Exergy-Based Sustainability Assessment 391

103 Environmental Impact 3971031 Reference Environment Models 3991032 Anthropogenic Impact on the Environment 4011033 Exergy Destruction and Environmental Impact of Drying Systems 411

104 Case Study Exergo-Sustainability Assessment of a Heat Pump Dryer 4191041 Reference Dryer Description 4191042 Exergo-Sustainability Assessment for the Reference Drying System 4211043 Improved Dryer Description 4251044 Exergo-Sustainability Assessment for the Improved Drying System 4281045 Concluding Remarks 430

105 Conclusions 430106 Study Problems 430References 431

11 Novel Drying Systems and Applications 433111 Introduction 433112 Drying with Superheated Steam 436113 Chemical Heat Pump Dryers 438114 Advances on Spray Drying Systems 441

1141 Spray Drying of CuCl2(aq) 4411142 Spray Drying of Nanoparticles 4451143 Microencapsulation through Spray Drying 446

115 Membrane Air Drying for Enhanced Evaporative Cooling 448116 Ultrasound-Assisted Drying 449117 Conclusions 451118 Study Problems 451References 452

Appendix A Conversion Factors 455

Appendix B Thermophysical Properties of Water 457

Appendix C Thermophysical Properties of Some Foods and Solid Materials 461

Appendix D Psychometric Properties of Humid Air 463

Index 469

ixContents

Preface

Drying as an energy-intensive process plays a major role in various sectors ranging from foodindustry to wood industry and affects economies worldwide Drying applications consume anoticeable part of the worldrsquos produced energy and require a careful attention from microlevelto macrolevel applications to make them more efficient more cost effective and more envi-ronmentally benign Bringing all these dimensions into the designs analyses and assessmentsof drying systems for various practical applications is of paramount significanceThis book offers a unique coverage of the conventional and novel drying systems and appli-

cations while keeping a focus on the fundamentals of drying phenomena It includes recentresearch and contributions in sustainable drying systems and integration with renewableenergy The book is expected to serve the drying technology specialists by providing compre-hensive tools for system design analysis assessment and improvement This is essentially aresearch-oriented textbook with comprehensive coverage of the main concepts and drying sys-tems designs It includes practical features in a usable format for the design analysis multi-criteria assessment and improvement of drying processes and systems which are often notincluded in other solely academic textbooks Due to an extensive coverage practicing engi-neers researchers and graduate students in mainstream engineering fields of mechanicaland chemical engineering can find useful information in this bookThe book consists of 11 chapters which amalgamate drying technology aspects starting

from basic phenomena to advanced applications by considering energy exergy efficiencyenvironment economy and sustainability issues The first chapter covers in broad mannerintroductory topics of thermodynamics energy exergy and transient heat transfer and masstransfer so as to furnish the reader with sufficient background information necessary for therest of the bookChapter 2 covers the basics of drying introducing the drying phases and the related phenom-

ena of heat and moisture transfer The moist materials are characterized and classified (eghydroscopic nonhygroscopic capillary etc) in relation with the mechanisms of moisturediffusion and associated phenomena such as shrinkage Introduction to diffusion modelingthrough porous media and moist solids is provided

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

5 Heat and Moisture Transfer 18951 Introduction 18952 Transient Moisture Transfer During Drying of Regularly Shaped Materials 190

521 Transient Diffusion in Infinite Slab 191522 Drying Time of an Infinite Slab Material 200523 Transient Diffusion in an Infinite Cylinder 202524 Transient Diffusion in Spherical-Shape Material 205525 Compact Analytical Solution or Time-Dependent Diffusion

in Basic Shapes 20853 Shape Factors for Drying Time 209

531 Infinite Rectangular Rod of Size 2Ltimes 2β1L 210532 Rectangular Rod of Size 2Ltimes 2β1L times 2β2L 210533 Long Cylinder of Diameter 2L and Length 2β1L 212534 Short Cylinder of Diameter 2β1L and Length 2L 213535 Infinite Elliptical Cylinder of Minor Axis 2L and Major Axis 2β1L 213536 Ellipsoid Having the Axes 2L 2β1L and 2β2L 213

54 Moisture Transfer Coefficient and Diffusivity Estimation from Drying Curve 21655 Simultaneous Heat and Moisture Transfer 21956 Models for Heat and Moisture Transfer in Drying 225

561 Theoretical Models 226562 Semitheoretical and Empirical Models for Drying 231

57 Conclusions 23258 Study Problems 233References 234

6 Numerical Heat and Moisture Transfer 23761 Introduction 23762 Numerical Methods for PDEs 239

621 The Finite Difference Method 240622 Weighted Residuals Methods Finite Element Finite Volume

Boundary Element 24663 One-Dimensional Problems 249

631 Decoupled Equations with Nonuniform Initial Conditionsand Variable Boundary Conditions 249

632 Partially Coupled Equations 253633 Fully Coupled Equations 256

64 Two-Dimensional Problems 261641 Cartesian Coordinates 261642 Cylindrical Coordinates with Axial Symmetry 271643 Polar Coordinates 276644 Spherical Coordinates 280

65 Three-Dimensional Problems 28466 Influence of the External Flow Field on Heat and Moisture Transfer 28867 Conclusions 29168 Study Problems 291References 292

viiContents

7 Drying Parameters and Correlations 29571 Introduction 29572 Drying Parameters 296

721 Moisture Transfer Parameters 296722 Drying Time Parameters 299

73 Drying Correlations 301731 Moisture Diffusivity Correlation with Temperature

and Moisture Content 301732 Correlation for the Shrinkage Ratio 304733 Biot NumberndashReynolds Number Correlations 305734 Sherwood NumberndashReynolds Number Correlations 307735 Biot NumberndashDincer Number Correlation 310736 Regression Correlations for μ1 Eigenvalues versus Lag Factor 312737 Biot NumberndashDrying Coefficient Correlation 313738 Moisture DiffusivityndashDrying Coefficient Correlation 315739 Biot NumberndashLag Factor Correlation 3167310 Graphical Determination of Moisture Transfer Parameters in Drying 3177311 Moisture Transfer Coefficient 318

74 Conclusions 32075 Study Problems 320References 321

8 Exergoeconomic and Exergoenvironmental Analyses of DryingProcesses and Systems 32381 Introduction 32382 The Economic Value of Exergy 32683 EXCEM Method 32984 SPECO Method 33785 Exergoenvironmental Analysis 34086 Conclusions 34587 Study Problems 345References 346

9 Optimization of Drying Processes and Systems 34991 Introduction 34992 Objective Functions for Drying Systems Optimization 351

921 Technical Objective Functions 351922 Environmental Objective Functions 359923 Economic Objective Functions 362

93 Single-Objective Optimization 363931 Trade-off Problems in Drying Systems 363932 Mathematical Formulation and Optimization Methods 366933 Parametric Single-Objective Optimization 371

94 Multiobjective Optimization 37595 Conclusions 37996 Study Problems 379References 380

viii Contents

10 Sustainability and Environmental Impact Assessment of Drying Systems 381101 Introduction 381102 Sustainability 383

1021 Sustainability Assessment Indicators 3831022 Exergy-Based Sustainability Assessment 391

103 Environmental Impact 3971031 Reference Environment Models 3991032 Anthropogenic Impact on the Environment 4011033 Exergy Destruction and Environmental Impact of Drying Systems 411

104 Case Study Exergo-Sustainability Assessment of a Heat Pump Dryer 4191041 Reference Dryer Description 4191042 Exergo-Sustainability Assessment for the Reference Drying System 4211043 Improved Dryer Description 4251044 Exergo-Sustainability Assessment for the Improved Drying System 4281045 Concluding Remarks 430

105 Conclusions 430106 Study Problems 430References 431

11 Novel Drying Systems and Applications 433111 Introduction 433112 Drying with Superheated Steam 436113 Chemical Heat Pump Dryers 438114 Advances on Spray Drying Systems 441

1141 Spray Drying of CuCl2(aq) 4411142 Spray Drying of Nanoparticles 4451143 Microencapsulation through Spray Drying 446

115 Membrane Air Drying for Enhanced Evaporative Cooling 448116 Ultrasound-Assisted Drying 449117 Conclusions 451118 Study Problems 451References 452

Appendix A Conversion Factors 455

Appendix B Thermophysical Properties of Water 457

Appendix C Thermophysical Properties of Some Foods and Solid Materials 461

Appendix D Psychometric Properties of Humid Air 463

Index 469

ixContents

Preface

Drying as an energy-intensive process plays a major role in various sectors ranging from foodindustry to wood industry and affects economies worldwide Drying applications consume anoticeable part of the worldrsquos produced energy and require a careful attention from microlevelto macrolevel applications to make them more efficient more cost effective and more envi-ronmentally benign Bringing all these dimensions into the designs analyses and assessmentsof drying systems for various practical applications is of paramount significanceThis book offers a unique coverage of the conventional and novel drying systems and appli-

cations while keeping a focus on the fundamentals of drying phenomena It includes recentresearch and contributions in sustainable drying systems and integration with renewableenergy The book is expected to serve the drying technology specialists by providing compre-hensive tools for system design analysis assessment and improvement This is essentially aresearch-oriented textbook with comprehensive coverage of the main concepts and drying sys-tems designs It includes practical features in a usable format for the design analysis multi-criteria assessment and improvement of drying processes and systems which are often notincluded in other solely academic textbooks Due to an extensive coverage practicing engi-neers researchers and graduate students in mainstream engineering fields of mechanicaland chemical engineering can find useful information in this bookThe book consists of 11 chapters which amalgamate drying technology aspects starting

from basic phenomena to advanced applications by considering energy exergy efficiencyenvironment economy and sustainability issues The first chapter covers in broad mannerintroductory topics of thermodynamics energy exergy and transient heat transfer and masstransfer so as to furnish the reader with sufficient background information necessary for therest of the bookChapter 2 covers the basics of drying introducing the drying phases and the related phenom-

ena of heat and moisture transfer The moist materials are characterized and classified (eghydroscopic nonhygroscopic capillary etc) in relation with the mechanisms of moisturediffusion and associated phenomena such as shrinkage Introduction to diffusion modelingthrough porous media and moist solids is provided

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

7 Drying Parameters and Correlations 29571 Introduction 29572 Drying Parameters 296

721 Moisture Transfer Parameters 296722 Drying Time Parameters 299

73 Drying Correlations 301731 Moisture Diffusivity Correlation with Temperature

and Moisture Content 301732 Correlation for the Shrinkage Ratio 304733 Biot NumberndashReynolds Number Correlations 305734 Sherwood NumberndashReynolds Number Correlations 307735 Biot NumberndashDincer Number Correlation 310736 Regression Correlations for μ1 Eigenvalues versus Lag Factor 312737 Biot NumberndashDrying Coefficient Correlation 313738 Moisture DiffusivityndashDrying Coefficient Correlation 315739 Biot NumberndashLag Factor Correlation 3167310 Graphical Determination of Moisture Transfer Parameters in Drying 3177311 Moisture Transfer Coefficient 318

74 Conclusions 32075 Study Problems 320References 321

8 Exergoeconomic and Exergoenvironmental Analyses of DryingProcesses and Systems 32381 Introduction 32382 The Economic Value of Exergy 32683 EXCEM Method 32984 SPECO Method 33785 Exergoenvironmental Analysis 34086 Conclusions 34587 Study Problems 345References 346

9 Optimization of Drying Processes and Systems 34991 Introduction 34992 Objective Functions for Drying Systems Optimization 351

921 Technical Objective Functions 351922 Environmental Objective Functions 359923 Economic Objective Functions 362

93 Single-Objective Optimization 363931 Trade-off Problems in Drying Systems 363932 Mathematical Formulation and Optimization Methods 366933 Parametric Single-Objective Optimization 371

94 Multiobjective Optimization 37595 Conclusions 37996 Study Problems 379References 380

viii Contents

10 Sustainability and Environmental Impact Assessment of Drying Systems 381101 Introduction 381102 Sustainability 383

1021 Sustainability Assessment Indicators 3831022 Exergy-Based Sustainability Assessment 391

103 Environmental Impact 3971031 Reference Environment Models 3991032 Anthropogenic Impact on the Environment 4011033 Exergy Destruction and Environmental Impact of Drying Systems 411

104 Case Study Exergo-Sustainability Assessment of a Heat Pump Dryer 4191041 Reference Dryer Description 4191042 Exergo-Sustainability Assessment for the Reference Drying System 4211043 Improved Dryer Description 4251044 Exergo-Sustainability Assessment for the Improved Drying System 4281045 Concluding Remarks 430

105 Conclusions 430106 Study Problems 430References 431

11 Novel Drying Systems and Applications 433111 Introduction 433112 Drying with Superheated Steam 436113 Chemical Heat Pump Dryers 438114 Advances on Spray Drying Systems 441

1141 Spray Drying of CuCl2(aq) 4411142 Spray Drying of Nanoparticles 4451143 Microencapsulation through Spray Drying 446

115 Membrane Air Drying for Enhanced Evaporative Cooling 448116 Ultrasound-Assisted Drying 449117 Conclusions 451118 Study Problems 451References 452

Appendix A Conversion Factors 455

Appendix B Thermophysical Properties of Water 457

Appendix C Thermophysical Properties of Some Foods and Solid Materials 461

Appendix D Psychometric Properties of Humid Air 463

Index 469

ixContents

Preface

Drying as an energy-intensive process plays a major role in various sectors ranging from foodindustry to wood industry and affects economies worldwide Drying applications consume anoticeable part of the worldrsquos produced energy and require a careful attention from microlevelto macrolevel applications to make them more efficient more cost effective and more envi-ronmentally benign Bringing all these dimensions into the designs analyses and assessmentsof drying systems for various practical applications is of paramount significanceThis book offers a unique coverage of the conventional and novel drying systems and appli-

cations while keeping a focus on the fundamentals of drying phenomena It includes recentresearch and contributions in sustainable drying systems and integration with renewableenergy The book is expected to serve the drying technology specialists by providing compre-hensive tools for system design analysis assessment and improvement This is essentially aresearch-oriented textbook with comprehensive coverage of the main concepts and drying sys-tems designs It includes practical features in a usable format for the design analysis multi-criteria assessment and improvement of drying processes and systems which are often notincluded in other solely academic textbooks Due to an extensive coverage practicing engi-neers researchers and graduate students in mainstream engineering fields of mechanicaland chemical engineering can find useful information in this bookThe book consists of 11 chapters which amalgamate drying technology aspects starting

from basic phenomena to advanced applications by considering energy exergy efficiencyenvironment economy and sustainability issues The first chapter covers in broad mannerintroductory topics of thermodynamics energy exergy and transient heat transfer and masstransfer so as to furnish the reader with sufficient background information necessary for therest of the bookChapter 2 covers the basics of drying introducing the drying phases and the related phenom-

ena of heat and moisture transfer The moist materials are characterized and classified (eghydroscopic nonhygroscopic capillary etc) in relation with the mechanisms of moisturediffusion and associated phenomena such as shrinkage Introduction to diffusion modelingthrough porous media and moist solids is provided

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

10 Sustainability and Environmental Impact Assessment of Drying Systems 381101 Introduction 381102 Sustainability 383

1021 Sustainability Assessment Indicators 3831022 Exergy-Based Sustainability Assessment 391

103 Environmental Impact 3971031 Reference Environment Models 3991032 Anthropogenic Impact on the Environment 4011033 Exergy Destruction and Environmental Impact of Drying Systems 411

104 Case Study Exergo-Sustainability Assessment of a Heat Pump Dryer 4191041 Reference Dryer Description 4191042 Exergo-Sustainability Assessment for the Reference Drying System 4211043 Improved Dryer Description 4251044 Exergo-Sustainability Assessment for the Improved Drying System 4281045 Concluding Remarks 430

105 Conclusions 430106 Study Problems 430References 431

11 Novel Drying Systems and Applications 433111 Introduction 433112 Drying with Superheated Steam 436113 Chemical Heat Pump Dryers 438114 Advances on Spray Drying Systems 441

1141 Spray Drying of CuCl2(aq) 4411142 Spray Drying of Nanoparticles 4451143 Microencapsulation through Spray Drying 446

115 Membrane Air Drying for Enhanced Evaporative Cooling 448116 Ultrasound-Assisted Drying 449117 Conclusions 451118 Study Problems 451References 452

Appendix A Conversion Factors 455

Appendix B Thermophysical Properties of Water 457

Appendix C Thermophysical Properties of Some Foods and Solid Materials 461

Appendix D Psychometric Properties of Humid Air 463

Index 469

ixContents

Preface

Drying as an energy-intensive process plays a major role in various sectors ranging from foodindustry to wood industry and affects economies worldwide Drying applications consume anoticeable part of the worldrsquos produced energy and require a careful attention from microlevelto macrolevel applications to make them more efficient more cost effective and more envi-ronmentally benign Bringing all these dimensions into the designs analyses and assessmentsof drying systems for various practical applications is of paramount significanceThis book offers a unique coverage of the conventional and novel drying systems and appli-

cations while keeping a focus on the fundamentals of drying phenomena It includes recentresearch and contributions in sustainable drying systems and integration with renewableenergy The book is expected to serve the drying technology specialists by providing compre-hensive tools for system design analysis assessment and improvement This is essentially aresearch-oriented textbook with comprehensive coverage of the main concepts and drying sys-tems designs It includes practical features in a usable format for the design analysis multi-criteria assessment and improvement of drying processes and systems which are often notincluded in other solely academic textbooks Due to an extensive coverage practicing engi-neers researchers and graduate students in mainstream engineering fields of mechanicaland chemical engineering can find useful information in this bookThe book consists of 11 chapters which amalgamate drying technology aspects starting

from basic phenomena to advanced applications by considering energy exergy efficiencyenvironment economy and sustainability issues The first chapter covers in broad mannerintroductory topics of thermodynamics energy exergy and transient heat transfer and masstransfer so as to furnish the reader with sufficient background information necessary for therest of the bookChapter 2 covers the basics of drying introducing the drying phases and the related phenom-

ena of heat and moisture transfer The moist materials are characterized and classified (eghydroscopic nonhygroscopic capillary etc) in relation with the mechanisms of moisturediffusion and associated phenomena such as shrinkage Introduction to diffusion modelingthrough porous media and moist solids is provided

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

Preface

Drying as an energy-intensive process plays a major role in various sectors ranging from foodindustry to wood industry and affects economies worldwide Drying applications consume anoticeable part of the worldrsquos produced energy and require a careful attention from microlevelto macrolevel applications to make them more efficient more cost effective and more envi-ronmentally benign Bringing all these dimensions into the designs analyses and assessmentsof drying systems for various practical applications is of paramount significanceThis book offers a unique coverage of the conventional and novel drying systems and appli-

cations while keeping a focus on the fundamentals of drying phenomena It includes recentresearch and contributions in sustainable drying systems and integration with renewableenergy The book is expected to serve the drying technology specialists by providing compre-hensive tools for system design analysis assessment and improvement This is essentially aresearch-oriented textbook with comprehensive coverage of the main concepts and drying sys-tems designs It includes practical features in a usable format for the design analysis multi-criteria assessment and improvement of drying processes and systems which are often notincluded in other solely academic textbooks Due to an extensive coverage practicing engi-neers researchers and graduate students in mainstream engineering fields of mechanicaland chemical engineering can find useful information in this bookThe book consists of 11 chapters which amalgamate drying technology aspects starting

from basic phenomena to advanced applications by considering energy exergy efficiencyenvironment economy and sustainability issues The first chapter covers in broad mannerintroductory topics of thermodynamics energy exergy and transient heat transfer and masstransfer so as to furnish the reader with sufficient background information necessary for therest of the bookChapter 2 covers the basics of drying introducing the drying phases and the related phenom-

ena of heat and moisture transfer The moist materials are characterized and classified (eghydroscopic nonhygroscopic capillary etc) in relation with the mechanisms of moisturediffusion and associated phenomena such as shrinkage Introduction to diffusion modelingthrough porous media and moist solids is provided

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

Chapter 3 comprehensively classifies and describes drying devices systems Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation The mostrelevant processes occurring in drying systems and devices are presented for natural and forceddryingChapter 4 introduced the energy and exergy analyses for drying processes and systems

There are only few studies in the literature that treat the exergy analysis of drying processesand system most of the published research limit to energy analyses only Therefore this chap-ter aims to fill this gap and provides a comprehensive method for irreversibility analysis ofdrying using exergy as a true method to identify the potentials for system improvement Per-formance assessment of drying systems based on energy and exergy efficiency is explained indetail Some relevant drying systems are analyzed in detail such as direct combustion dryersfluidized bed dryers and heat pump dryersChapter 5 focuses on analytical methods for heat and moisture transfer The solutions for

moisture transfer in basic geometries such as infinite slab infinite cylinder and sphere aregiven Parameters such as drying coefficient and lag factor which are essential for analyticalmodeling of the processes are introduced The chapter also teaches about the analytical expres-sions for drying time of object with regular and irregular geometry and the so-called shape fac-tors for drying time One important aspect is represented by determination of moisture transferdiffusivity and moisture transfer coefficient in drying operation A comprehensive method todetermine these parameters based on the experimental drying curve is introduced Also thechapter allocates sufficient space to the analytical formulation and treatment of the processof simultaneous heat and moisture transfer In this respect the Luikov equations and other for-mulations for simultaneous heat and moisture transfer are presented and the impact of sorptionndashdesorption isotherms is explained A summary of drying curve equations and models is givenNumerical heat and moisture transfer is treated extensively in Chapter 6 Finite difference

schemes and three types of weighted residual numerical methods (finite element finite volumeand boundary element) are introduced in sufficient detail The subsequent part of the chapter isstructured in three sections corresponding to one- two- and three-dimensional numerical anal-ysis of heat and moisture transfer covering Cartesian cylindrical polar and spherical coordi-nate systems The influence of external flow field on heat and moisture transfer inside the moistmaterial is also discussedDrying parameters and correlations are presented in Chapter 7 Selected correlations are

introduced for quick firsthand calculation of essential drying parameters such as drying timemoisture diffusivity moisture transfer coefficient binary diffusion coefficient drying coeffi-cient and lag factor An interesting and useful graphical method for moisture transfer para-meters determination in drying processes is givenChapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying pro-

cesses and systems Here the economic value of exergy is emphasized together with its role ineconomic analysis and environmental impact assessment of drying technologies Two exergoe-conomic methods and their application to drying are presented namely the energyndashcostndashexergyndashmass and the specific exergy cost methods The use of exergy and exergy destructionfor environmental impact assessment of drying systems is explainedChapter 9 concentrates on optimization of drying processes and system Optimization is cru-

cial for the design of better systems with improved efficiency effectiveness more economi-cally attractive and sustainable and having a reduced environmental impact It is importantto formulate technical economic and environmental objective functions and this aspect is

xii Preface

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

extensively explained in the chapter Single-objective and multiobjective optimizations arediscussedChapter 10 is about sustainability and environmental impact assessment of drying systems

Here sustainability as a multidimensional parameter is defined and the most important sustain-ability indicators are introduced An exergy-based sustainability assessment method is pro-posed which accounts for energy environment and sustainable development Variousaspects are discussed such as reference environment models and environmental impacts andthe role of exergy destruction-based assessment of environmental impact of drying systemsA case study is treated comprehensively regarding the life cycle exergo-sustainability assess-ment of a heat pump dryerSome selected novel drying systems and applications are presented in Chapter 11 based on a

literature review The use of superheated steam as drying medium appears very promising andconsists of a novel development trend on drying technology Chemical heat pump-assisteddryers emerged as a technology push Very impressive developments in spray drying arereported to cover drying and production of nanoparticles and microcapsules These emergingtechnologies are relevant in medicine for nanotherapeutics in pharmaceutical industry for drugdelivery and in food industry for foodstuff encapsulation Other emerging technologies andapplications such as ultrasonic drying and membrane-assisted air conditioning are reviewedThe book comprises a large number of numerical examples and case studies which provide

the reader with a substantial learning experience in analysis assessment and design of practicalapplications Included at the end of each chapter is the list of references which provides the trulycurious reader with additional information on the topics yet not fully covered in the textWe hope that this book brings a new dimension to drying technology teaching and learning

promoting up-to-date practices and methods and helping the community implement better solu-tions for a better more sustainable futureWe acknowledge the assistance provided by Dr Rasim Ovali for drawing various illustra-

tions of the bookWe also acknowledge the support provided by the Natural Sciences and Engineering

Research Council of Canada and Turkish Academy of SciencesLast but not least we warmly thank our wives Gulsen Dincer and Iuliana Zamfirescu and

our children Meliha Miray Ibrahim Eren Zeynep and Ibrahim Emir Dincer and Ioana andCosmin Zamfirescu They have been a great source of support and motivation and theirpatience and understanding throughout this book have been most appreciated

İbrahim Dinccediler and Calin ZamfirescuOshawa September 2015

xiiiPreface

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

Nomenclature

a empirical constanta acceleration ms2

a general parametera thermal diffusivity m2sa regression coefficienta1 a2 constantsaw water activityA area (general or area normal to the flow of heat or mass) m2

A discretization parameterA factor in Eq (78)

discretization matrixAC annual consumptionAI annual income $An factor in Eq (510)AP annual production unitsAr Archimedes numberAR aspect ratioASI aggregated sustainability indexb general parameterb regression coefficientb numerical scheme parameterB driving forceB discretization parameterBi Biot numberBim Biot number for moisture transferBn factor in Eq (510)c speed of light in vacuum msC specific heat Jkg KC coefficients for numerical schemes

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

C molar concentration mollcost $cost rate $h

CEF consumed energy fractionex exergy price $

CExF consumed exergy fractionCIEx exergy based capital investment effectivenessCm moisture (or mass) concentration kgm3

COP coefficient of performanceCp specific heat Jkg KCP capital productivityCRF capital recovery factorCSF capital salvage factorCv specific heat at constant volume kJkg Kd diameter md constantD diffusion coefficient m2sD moisture diffusivity m2sDc binary diffusion coefficient for water vapor in air m2sDDTOF dimensionless drying time objective functionDE drying effectivenessDeff effective diffusion coefficient m2sDEI dryer emission indicatorDh hydraulic diameter mDi Dincer numberDim Dincer number for mass transferDPV drying product valueDQ drying qualityDT Soret coefficient for thermal diffusion kgm s Ke specific energy kJkge elementary charge Ce mass specific energy kJkgE shape factorE energy JE energy rate WEcI eco-indicatorEE embodied energy GJtEEOF energy efficiency objective functionEF ecological footprintEI environmental impactEinOF energy input objective functionEPC environmental pollution cost $kgEPCex exergetic environmental pollution cost $GJex specific exergy kJkgEx exergy amount kJ

xvi Nomenclature

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

Ex exergy rate kWExCI specific exegetic capital investmentExCDR construction exergy expenditure to lifecycle exergy destruction ratioExIE exergetic investment efficiencyExEOF exergy efficiency objective functionEUR energy utilization ratiof friction coefficientf functionf r distribution of pores radiusF force NF Faraday constant CmolF functionF radiative forcing Wm2

dimensionless parameterF1 F2 series expansions for shape factorsFo Fourier numberFobj objective functionFom Fourier number for mass transfer (dimensionless time)g gravity constant (= 981 ms2)g specific Gibbs free energy kJkgG basis weightGC generated capital $GEI grid emission indicator gkW hGF greenization factorGr Grashof numberGu Gukhman numberGWP global warming potentialGz Graetz numberh specific enthalpy kJkgh Planck constant kJ sH enthalpy kJhm moisture transfer coefficient msHR Hausner ratioHT halving timehtr or h heat transfer coefficient Wm2 Ki inflation rateI irradiation Wm2

I electric current AInd indicatorIv luminous intensity cdj diffusive mass flux kgm2 sj mass flux kgm2 sJ0 zeroth-order J Bessel functionJ1 first-order J Bessel functionJm mass flux kgm2 s

xviiNomenclature

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

m q boundary intervalsk thermal conductivity Wm Kk drying rate sminus1

K12 parametersk constant coefficient or parameterkB Boltzmann constant JKkm mass transfer coefficient sminus1

l (characteristic) length mL length characteristic length or thickness mL bed height mLc (characteristic) dimension mLCC levelized cost of consumables $unitLCEIex Life cycle exergetic emission indicator gkW hLCSI lifecycle sustainability indexLe Lewis numberLF lag factorLHV lower heating value MJkgLPP levelized product price $LPPOF levelized product price objective functionLT life cycle time yearsm indexm mass kgm mass ratiom mass flow rate kgsm mass flux kgm2 sm n p number of elements (vector)M molecular weight kgkmolMa relative molecular mass of air kgkmolMEPC molar environmental pollution cost $kmolMv molecular mass of vapor kgmoln index exponent numbern empiric exponentn mole number kmoln adiabatic exponentn system lifetimen normal to surfaceN number of particlesNA Avogadrorsquos numberNH number of halving timesnhour number of hours of operation hNI net income $NSI normalized sustainability indexNu Nusselt numberP pressure kPaPa partial pressure of air Pa

xviii Nomenclature

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

Pam mean of partial pressures of air over the product surface and in drying air PaPBP payback period yearsPe Peacuteclet numberPoI point of impingementPP performance parameterPr Prandtl numberPv partial pressure of vapor PaPva partial pressure of vapor in drying air PaPlowastv saturated vapor pressure Pa

PVF present value factorPvm mean of partial vapor pressures of vapor over the product surface and in drying

air PaPvo vapor pressure over the product surface PaPWI present worth income $PWF present worth factorq heat rate per unit area Wm2 flow rate per unit width or depthq heat flux Wm2

q heat flux Wm2

Q heat flux J or kJQ quantity (amount)Q heat transfer rate W

Q heat flux per unit of surface Wm2

QP quality parameterr radial coordinate radius mr aerodynamic resistance msr real discount rater latent heat Jkgr particle coordinate mr distance normal to the flow of heat mr mesh parameterR loss ratioR radius radius of a single particle m

universal gas constant kJkg KRa Rayleigh numberRC specific resource consumptionRD relative dryingRe Reynolds numberRI relative irreversibilityrealn residual functionRpai practical application impact ratioRPC removal pollution costRsi sectorial impact ratioRti technological impact ratioRv gas constant for water vapor JkgKs specific entropy kJkg

xixNomenclature

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

S entropy rate kWKS entropy kJKS drying coefficient sndash1

S surface m2

S entropy rate WKSc Schmidt numberSE specific GHG emissions kgGHGGJSEI sustainability efficiency indicatorSg gas phase saturationSh Sherwood numberSI exergetic sustainability indexSIOF sustainability index objective functionSP spanSPI sustainable process indexSRW specific reversible workSR shrinkage ratioSt Stanton numberSV salvage value $t time st tortuosity factorT temperature K

temperature function Kt05 halftime htc tax creditTCD tax credit deduction $TExDOF total exergy destruction objective functionti tax on incomeTI taxable income $Tm mean temperatures of product surface and drying air CTma mean absolute temperatures of product surface and drying air KTo surface temperature KTOI tax on income $top operational time hTOP tax on property $tp tax on propertyts tax on salvageu specific internal energy kJkgu velocity in x directionu displacement mU internal energy kJU flow velocity of drying air msU economic utilityv specific volume m3kgv velocity in y directionv velocity ms

xx Nomenclature

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

V volume m3

V velocity msV volumetric flow rate m3sV0 standard ideal gas volume m3kmolu velocity (speed) msw mass specific work kJkgw weighting factorsW work kJW work rate kW

moisture content function kgkg dry basisW moisture content kg waterkg dry materialW average moisture content kgkgx quality kgkgx Cartesian coordinate mxs degree of saturationXv volumetric moisture content m3m3

y mole fractiony Cartesian coordinate my dimensional coordinate mY characteristic dimension (length) spatial dimension mz Cartesian coordinate mz axial coordinate thickness mZ compressibility factor

Greek Lettersα volume fraction of airβ enhancement factorβ volume-shrinkage coefficientβ length ratioγ parameterγ quality factorγ climate sensitivity factorδ thickness length coordinate mδ space increment mδ thermal gradient coefficient Kminus1

Δhlv latent heat of vaporization JkgΔt time step sε void fractionε phase conversionε volumetric fraction of vaporζ dimensionless coordinateη energy efficiencyη dynamic viscosity Pasη dimensionless space variableθ total specific energy of flowing matter kJkg

xxiNomenclature

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

θ dimensionless temperatureμ dynamic viscosity kgmsμ chemical potential kJkgμ diffusion resistance factor root of the transcendental characteristic equationμ1 first eigenvalueμn nth eigenvalueν kinematic viscosity m2sξM specific mass capacity (kg molkJ)ξT specific temperature coefficient (kgkg K)ρ density kgm3

ρdr bone dry density kgm3

σ StefanndashBoltzmann constant Wmsup2 K4

σ surface tension Nmσ standard averageτ time constant sτ residence time sτ atmospheric lifetime sϑcontact contact angleϕ relative humidityϕ Φ dimensionless moisture contentΦs sphericityφ total specific exergy kJkgφ porosity m3m3

φ relative humidityφ zenith angleφ trial functionψ exergy efficiencyψ test functionω humidity ratioΩ domain of decision variables

Subscripts0 reference state0 dry material05 1 frac12 frac14⅛ 2 indices05 half timeinfin bulka (dry) air medium surroundingsact activationacum accumulatedair airam air mixerap air penetration processAP air pollutionavg averageb boundary dry bulb bulk

xxii Nomenclature

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

b fluidized bedbw bounded moisturec characteristic critical convectionc cyclonecap capitalch chemicalCIE capital investment effectivenesscmp compressorcomb combustorcond condenserconc concentrationCO carbon monoxidecons consumedcsteel carbon steelcv control volumecyl cylinderd destroyed dew point dryingda drying airdissip dissipationdr dryerdeliv deliverede equilibriumEef effective effusionef effectiveen energeticex exergy exergeticevap evaporatorf fluid final flow force formation fuelfa fanfc feederconveyorfg liquidndashvapor equilibriumfi filterg gas global generationgen generatedgt gas turbine generatorH high-temperatureha humid airhp heat pumpi j k indicesi in initialin inputint internalk conductionke kinetic energyl liquid laterallam laminar

xxiiiNomenclature

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

lc lifecycleliq liquidloss lost lostlv liquidndashvaporL low-temperaturem mass environment material moisture moist material marketm monolayerma material-to-air (binary coefficient)mat materialsmf minimum fluidizationmm moist materialmr moisture removaln normal directionnf nonflowoc other costocc other cost creationoampm operation and maintenanceopt optimumout outputp particlep prod productpe potential energyph physicalpr pollutant removalpw pollutant wasteQ heatr reducedr refrigerantr removed moistureR radiusrec recoveredref referencerev reversiblerf recirculation flaps surface solid saturation dry solid surfacesat saturationsc supplementary combustorsep separatorshape shapeslab slabsph spheressteel stainless steelsurface surfacesys systemtot total

xxiv Nomenclature

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

tr heat transferturb turbulenttv throttling valveused utilized or usedv vaporw wet bulb water wind moisture vaporwb wet bulbwm wet materialx x directiony y direction

Superscriptsaverage valuesaturation condition

0 reference state with respect to dry airch chemicalq discretized time indexQ heat

xxvNomenclature

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

1Fundamental Aspects

11 Introduction

Drying is a key industrial process of great practical importance in chemical and pharmaceuticalindustries agriculture and food processing pulp and paper wood and minerals processingsolid fuels preparation (eg biomass or coal drying) It consists of a mass transfer processaimed at removing a solvent ndash in general water (or moisture) ndash from a solid liquid or a semi-solid (a highly viscous liquid) Thence drying is a thermally driven separation process andtypically occurs by evaporation of the solvent (the moisture) or by sublimation or by a super-critical process that avoids solidndashliquid boundary or by reverse osmosisThe process of drying is recognized as one of the most energy intensive process among the

separation technologies For example according to Mujumdar (2006) drying energy sector inNorth America is just responsible of ~15 energy consumption It requires a source of heat andsometimes it necessitates maintaining deep vacuum for effective moisture removal Drying canbe also applied in some cases followed by heat addition and moisture removal by sublimationIn addition the method can be integrated with other types of separation technologies such ascentrifugal draining which require the application of strong centrifugal forcesIn the drying sector it is aimed to make drying processes more efficient more cost effective

more environmentally benign and more sustainable Thus this requires optimization methodsto be applied to these processes Furthermore there is large panoply of materials spanning fromthick slabs to nano-powders which require specific methods of dryingUnderstanding drying processes requires the application of analysis methods from thermo-

dynamics heat mass and momentum transfer psychometrics porous media materials scienceand sometimes chemical kinetics altogether Some specific processes that occur during dryingand must be considered in the analysis are crystallization and allotropic transition or shrinkagetexture change porosity change and fracture Drying is a transient process therefore changing

Drying Phenomena Theory and Applications First Edition İbrahim Dinccediler and Calin Zamfirescucopy 2016 John Wiley amp Sons Ltd Published 2016 by John Wiley amp Sons Ltd

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena

of moisture removal rate must be accounted for Depending on the drying material (eg samplesize porosity tortuosity) and drying conditions drying can extend from milliseconds to coupleof monthsIn this chapter fundamental aspects on drying are reviewed First some general physical

notions and basic properties and quantities are presented Thermodynamics fundamentalsare introduced The name ldquothermodynamicsrdquo is meaningful it came from the Greek wordsldquothermerdquo which means ldquoheatrdquo and ldquodynamisrdquo which means power Therefore ldquothermody-namicsrdquo suggests a science of conversion of thermal energy into mechanical energy In varioussources thermodynamics is defined as the science of energy and entropy In this book wedefine thermodynamics as the science of energy and exergy This definition is more correctsince both energy and exergy are given in the same units and can be used for performanceassessment through energy and exergy efficiencies Furthermore this makes both first-lawand second-law of thermodynamics very significant concepts as energy comes from the firstlaw and exergy from the second law These two laws essentially govern thermodynamicsystemsThermodynamics differentiates two categories of energies (i) organized (such as mechan-

ical electrical or electromagnetic photonic gravitational) and (ii) disorganized (which is ther-mal energy or ldquoheatrdquo) According to the second law of thermodynamics (SLT) which will bedetailed further in this chapter the organized forms of energy can be completely converted inany other forms of energy However thermal energy cannot be fully converted in organizedforms of energy due to the intrinsic irreversibilities In separation technologies ndash such asdrying ndash Gibbs free energy is an important parameter that quantifies the required work (organ-ized energy) to drive the process Irreversibilities within the system can be determined accord-ing to the SLT In this chapter exergy analysis is expanded as a method to quantify theirreversibilities which helps in design improvement The advantage of exergy method springsfrom the fact that it relates the thermodynamic analysis to the reference environment

Exergy analysis is useful in identifying the causes locations and magnitudes of processinefficiencies and irreversibility The exergy is a quantitative assessment of energy usefulnessor quality Exergy analysis acknowledges that although energy cannot be created or destroyedit can be degraded in quality eventually reaching a state in which it is in complete equilibriumwith the surroundings and hence of no further use for performing tasks (ie doing work)Besides thermodynamics a good amount of this chapter is dedicated to heat and mass trans-

fer with emphasis on moisture diffusion in steady state and transient regime In addition porousmedia are analyzed and characterized based on their porosity tortuosity and other parameterswhich affect moisture transfer Psychometrics and most air modeling though energy and exergymethods is analyzed in detail

12 Fundamental Properties and Quantities

In this section several thermodynamics properties and other physical quantities are covered toprovide adequate preparation for the study of drying processes systems and applicationsAdoption of a system of units is an important step in the analyses There are two main systemsof units the International System of Units which is normally referred to as SI units and theEnglish System of Units (sometimes referred as Imperial) The SI units are used most widelythroughout the world although the English System is traditional in the United States In this

2 Drying Phenomena