DRYING OF MACADAMIA NUTS

By Mr.Chayapat Phusampao

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Program in Physics Graduate School, Silpakorn University

Academic Year 2014 Copyright of Graduate School, Silpakorn University

การอบแห้งแมคคาเดเมีย

โดย นายชยพทัธ์ ภูสําเภา

วทิยานิพนธ์นีเป็นส่วนหนึงของการศึกษาตามหลกัสูตรปริญญาปรัชญาดุษฎบีัณฑิต สาขาวชิาฟิสิกส์ ภาควชิาฟิสิกส์

บัณฑิตวทิยาลยั มหาวิทยาลัยศิลปากร ปีการศึกษา 2557

ลขิสิทธิของบัณฑิตวิทยาลยั มหาวทิยาลัยศิลปากร

DRYING OF MACADAMIA NUTS

By Mr.Chayapat Phusampao

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Program in Physics Graduate School, Silpakorn University

Academic Year 2014 Copyright of Graduate School, Silpakorn University

The Graduate School, Silpakorn University has approved and accredited the Thesis title of

“Drying of Macadamia Nuts” submitted by Mr.Chayapat Phusampao as a partial fulfillment of the

requirements for the degree of Doctor of Philosophy in Physics

............................................................................ (Assistant Professor Panjai Tantatsanawong, Ph.D.)

Dean of Graduate School ........../..................../..........

The Thesis Advisor Associate Professor Serm Janjai, Ph.D. The Thesis Examination Committee .................................................... Chairman (Professor Virulh Sa-yakanit, Ph.D.) ............/......................../.............. .................................................... Member (Associate Professor Sirichai Thepa, D.Sc.) ............/......................../.............. .................................................... Member (Associate Professor Serm Janjai, Ph.D.) ............/......................../..............

c

55306802: MAJOR: PHYSICS KEY WORDS: MACADAMIA NUTS/ DIFFUSIVITY/ FINITE ELEMENT MODELING/

MACADAMIA NUT DRYER CHAYAPAT PHUSAMPAO: DRYING OF MACADAMIA NUTS. THESIS ADVISOR: ASSOC. PROF. SERM JANJAI, Ph.D. 67 pp. In this work, drying characteristics of macadamia nuts and performance evaluation of a

solar greenhouse dryer for drying macadamia nuts has been carried out. The thin layer drying of

macadamia nuts was conducted under controlled condition of temperature and relative humidity. Drying

air temperature has great influence on the drying rate of macadamia nuts. The moisture content of

macadamia nuts was function of air temperature and relative humidity. The Modified Handerson and

Pabis model was found to be the best model to predict the moisture content of macadamia nuts during

drying. Moisture diffusivities of macadamia nuts have also determined. It was found that the diffusivity

of macadamia nuts increased with temperature. A two dimension finite element model has been

developed to simulate moisture diffusion in macadamia nuts using the diffusivities of macadamia nuts

obtained from this work. This finite element model satisfactorily predicted the moisture diffusion in

macadamia nuts.

The performance of a solar greenhouse dryer for drying macadamia nuts has been

evaluated. Six full-scale experimental runs were conducted and 730 kg of macadamia nuts was dried in

each experimental run. The drying time in this solar greenhouse dryer was 50 h for drying macadamia

nuts from an initial moisture content of 16% (wb) to a final moisture content of 3% (wb). A system of

partial differential equations describing heat and moisture transfer during drying of macadamia nuts in

this solar greenhouse dryer was also developed. The simulated results agreed well with the experimental

data. This model can be used to provide the design data and it is also essential for optimal design of the

dryer.

Department of Physics Graduate School, Silpakorn University Student's signature ........................................ Academic Year 2014 Thesis Advisor's signature ........................................

d

55306802: สาขาฟิสิกส์ คาํสาํคญั: แมคคาเดเมีย/ สมัประสิทธิการแพร่/ แบบจาํลองไฟไนตเ์อลิเมนต์/ เครืองอบแหง้แมคคาเดเมีย ชยพทัธ์ ภูสาํเภา: การอบแหง้แมคคาเดเมีย อาจารยที์ปรึกษาวิทยานิพนธ์: รศ. ดร. เสริม จนัทร์ฉาย 67 หนา้ ในงานวิจัยนี ผูวิ้จัยทาํการศึกษาการอบแห้งแมคคาเดเมีย และสมรรถนะของโรงอบพลงังานแสงอาทิตยแ์บบเรือนกระจกเพืออบแหง้แมคคาเดเมีย ผูว้ิจยัไดท้าํการทดลองอบแหง้แมคคาเดเมียแบบชันบาง โดยควบคุมอุณหภูมิและความชืนสัมพทัธ์ของอากาศ จากการทดลองพบว่าอุณหภูมิของอากาศมีอิทธิพลอยา่งมากต่ออตัราการอบแหง้ของแมคคาเดเมีย โดยความชืนของแมคคาเดเมียเป็นฟังกช์นัของอุณหภูมิและความชืนสัมพทัธ์ของอากาศ และพบว่าแบบจาํลองของ Modified Handerson and Pabis สามารถทีจะทาํนายการลดลงของความชืนของการอบแหง้แมคคาเดเมียไดดี้ทีสุด ในลาํดบัต่อไปผูวิ้จยัได้ทาํการหาค่าสัมประสิทธิการแพร่ของผลแมคคาเดเมีย ผลการศึกษาพบว่าค่าสัมประสิทธิการแพร่ของผลแมคคาเดเมียจะเพิมขึนตามอุณหภูมิ จากนนัผูวิ้จยัไดท้าํการพฒันาแบบจาํลองไฟไนตเ์อลิเมนต ์ มิติ ของการแพร่ความชืนในผลแมคคาเดเมีย โดยใชส้มัประสิทธิการแพร่ของผลแมคคาเดเมียขา้งตน้ ผลการศึกษาแบบจาํลองดงักล่าวสามารถทาํนายการแพร่ของความชืนในผลแมคคาเดเมียไดดี้ หลงัจากนันผูวิ้จยัไดท้าํการศึกษาสมรรถนะของโรงอบพลงังานแสงอาทิตยแ์บบเรือนกระจกในการอบแห้งแมคคาเดเมีย โดยทาํการอบแห้ง ครัง ๆ ละ กิโลกรัม ผลการทดลองพบว่าความชืนของผลแมคคาเดเมียลดลงจากความชืนเริมตน้ 16% (wb) จนถึงความชืนสุดทา้ย 3% (wb) โดยใช้เวลา ชวัโมง นอกจากนีผูท้าํวิจยัไดส้ร้างแบบจาํลองทางคณิตศาสตร์สาํหรับอธิบายการถ่ายเทมวลและความร้อนในโรงอบพลังงานแสงอาทิตย์แบบเรือนกระจก ผลการศึกษาพบว่า ผลการคํานวณจากแบบจาํลองสอดคลอ้งกบัผลการวดั ภาควิชาฟิสิกส์ บณัฑิตวิทยาลยั มหาวิทยาลยัศิลปากร ลายมือชือนกัศึกษา ……………………………………………. ปีการศึกษา 2557 ลายมือชืออาจารยที์ปรึกษาวิทยานิพนธ์ ……………………………………………………….

e

Acknowledgments This thesis is submitted in partial fulfillment of the requirements for the degree of Doctor of

Philosophy (Physics), Graduate School, Silpakorn University.

I would like to thank all the people who contributed in some ways to the work described in

this thesis. First and foremost, I thank my academic advisor, Associate Professor Serm Janjai, for his

helpful guidance and support throughout this study.

I would like to acknowledge the Department of Physics, Faculty of Science, Silpakorn

University. Additionally, I would like to thank. Prof. Dr.Virulh Sa-yakanit and Assoc. Prof. Dr.

Sirichai Thepa for examining this thesis.

Finally, I would like to acknowledge friends and family who supported me during my study at

Silpakorn University.

f

Table of Contents Page

Abstract ............................................................................................................................................ c

Abstract Thai .................................................................................................................................... d

Acknowledgments ............................................................................................................................ e

List of Tables ................................................................................................................................... h

List of Figures .................................................................................................................................. i

Chapter

1 Introduction .......................................................................................................................... 1

Rationale of this work .................................................................................................... 1

Objectives ....................................................................................................................... 2

Organization of the thesis ............................................................................................... 2

2 Thin layer drying of macadamia nuts .................................................................................... 3

Introduction .................................................................................................................... 3

Materials and methods ................................................................................................... 3

Drying experiments .......................................................................................... 3

Mathematical modeling ................................................................................... 4

Results and discussion.................................................................................................... 6

Drying characteristics of macadamia nuts and kernel nuts .............................. 6

Mathematical modeling of thin-layer drying .................................................................. 15

Conclusion ..................................................................................................................... 16

3 Sorption Isotherm of Macadamia nuts .................................................................................. 17

Introduction .................................................................................................................... 17

Materials and methods ................................................................................................... 17

Determination of the sorption isotherm of macadamia nuts ............................. 17

Selection of the sorption isotherm models ....................................................... 18

Results and discussion.................................................................................................... 19

Conclusion ..................................................................................................................... 21

4 Finite element simulation for macadamia nut drying ............................................................ 22

Introduction .................................................................................................................... 22

Material and method ...................................................................................................... 22

Diffusivities of components of macadamia nuts .............................................. 23

Finite element modeling of macadamia nuts drying ...................................................... 24

Results and discussions .................................................................................................. 32

Diffusivities of macadamia nuts ...................................................................... 32

Finite element simulated drying ...................................................................... 33

Conclusions .................................................................................................................... 34

g

5 Experimental performance and modeling of a greenhouse solar dryer

for drying macadamia nuts .................................................................................................... 35

Introduction .................................................................................................................... 35

Materials and methods .................................................................................................... 35

Experimental setup ........................................................................................... 35

Experimental procedure .................................................................................... 36

Modeling ........................................................................................................................ 39

Energy balance of the cover ............................................................................. 39

Energy balance of the air inside the dryer ........................................................ 40

Energy balance of the product .......................................................................... 41

Energy balance on the concrete floor ............................................................... 41

Mass balance equation ...................................................................................... 42

Heat transfer and heat loss coefficients ............................................................ 42

Thin layer drying equation ............................................................................... 44

Solution procedure ............................................................................................ 45

Colour measurement of dried macadamia nuts............................................................... 46

Economic analysis .......................................................................................................... 46

Results and discussion .................................................................................................... 48

Experimental results ......................................................................................... 48

Colour change ................................................................................................... 50

Food quality ...................................................................................................... 50

Economic result ................................................................................................ 51

Modeling result ................................................................................................. 52

Conclusions ..................................................................................................................... 53

6 Conclusions ........................................................................................................................... 54

References .................................................................................................................................. 56

Appendixes ................................................................................................................................... 60

Appendix 1 ............................................................................................................................ 61

Appendix 2 ............................................................................................................................ 62

Autobiography .................................................................................................................................. 67

h

List of Tables

Tables Page

2.1 The 7 selected thin-layer drying models................................................................... 6

2.2 Parameter value, coefficient of determination (R2) and

root mean square error (RMSE) value of the different models for in-shell nuts ...... 10

2.3 Parameter value, coefficient of determination (R2) and

root mean square error (RMSE) value of the different models for kernel nuts. ....... 14

3.1 Selected isotherm models ......................................................................................... 18

3.2 The coefficients of the selected models, standard error of estimate (RMSE)

and the coefficient of determination (R2) for macadamia nuts ................................. 20

4.1 Moisture diffusivities of kernel of macadamia nuts ................................................. 32

4.2 Moisture diffusivities of shell of macadamia nuts .................................................... 32

5.1 Comparison of the colour kernel of macadamia nuts dried using

the greenhouse solar dryer and that dried employing the box type dryer ................. 51

5.2 Data on cost and economic parameter ....................................................................... 51

i

List of Figures

Figures Page

2.1 Schematic diagram of the laboratory dryer. ................................................................... 4

2.2 Thin-layer drying of macadamia nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (10 %)................................................ 7

2.3 Thin-layer drying of macadamia nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (20 %)................................................ 7

2.4 Thin-layer drying of macadamia nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (30 %)................................................ 8

2.5 Predicted and observed moisture content of macadamia nuts

using modified Handerson and Pabis model at the temperatures of

40 ◦C, 50 ◦C and 60 ◦C and relative humidity of 10 %. .................................................... 8

2.6 Predicted and observed moisture content of macadamia nuts

using modified Handerson and Pabis model at the temperatures of

40 ◦C, 50 ◦C and 60 ◦C and relative humidity of 20 %. .................................................... 9

2.7 Predicted and observed moisture content of macadamia nuts

using modified Handerson and Pabis model at the temperatures of

40 ◦C, 50 ◦C and 60 ◦C and relative humidity of 30 %. ..................................................... 9

2.8 Thin-layer drying of kernel nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (10 %)................................................. 11

2.9 Thin-layer drying of kernel nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (20 %)................................................. 11

2.10 Thin-layer drying of kernel nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (30 %)................................................. 12

2.11 Predicted and observed moisture content of kernel nuts

using modified Handerson and Pabis model at the temperatures

of 40 ◦C, 50 ◦C and 60 ◦C and relative humidity of 10 % .................................................. 12

2.12 Predicted and observed moisture content of kernel nuts using

modified Handerson and Pabis model at the temperatures

of 40 ◦C, 50 ◦C and 60 ◦C and relative humidity of 20 % .................................................. 13

2.13 Predicted and observed moisture content of kernel nuts

using modified Handerson and Pabis model at the temperatures

of 40 ◦C, 50 ◦C and 60 ◦C and relative humidity of 30 % .................................................. 13

j

Figures Page

3.1 Predicted and measured sorption isotherms of macadamia nuts

at 40 ๐C, 50 ๐C and 60 ๐C (Modified Oswin model) ......................................................... 19

4.1 Macadamia nut comprising nut kernel and brow shell. ................................................... 31

4.2 Finite element grid for half of macadamia nut. ............................................................... 32

4.3 Variations of moisture diffusivity of kernel of macadamia nut as a function

of the reciprocal of absolute drying air temperature (Tab). ....................................... 33

4.4 Variations of moisture diffusivity of shell of macadamia nut as a function

of the reciprocal of absolute drying air temperature (Tab). ....................................... 33

4.5 Comparison of predicted moisture contents with the experiment

data at 60 ๐C and relative humidity 30 % ......................................................................... 33

5.1 The pictorial view of polycarbonate-covered greenhouse solar dryer,

from the front side .......................................................................................................... 37

5.2 Macadamia nuts inside the dryer .................................................................................... 38

5.3 Structure of the dryer and position of thermocouples, pyranometer,

solar radiation and product samples for moisture .......................................................... 38

5.4 The schematic diagram showing heat and mass transfers .............................................. 39

5.5 Variation of solar radiation with time of the day during drying of

macadamia nuts .............................................................................................................. 49

5.6 Variation of ambient temperature and the temperature at

different positions inside the greenhouse solar dryer

during drying of macadamia nuts ................................................................................... 49

5.7 Temporal variation of ambient relative humidity and relative humidity

inside the greenhouse dryer during drying of macadamia nuts ...................................... 49

5.8 Temporal variation of the moisture contents of macadamia nuts

at different positions inside the greenhouse dryer .......................................................... 50

5.9 Comparison between the simulated and observed moisture content

during drying macadamia nuts at the middle of the dryer for

a typical experimental run .............................................................................................. 52

5.10 Comparison between the simulated and observed temperatures

inside the greenhouse dryer at the middle position during drying

macadamia nuts for a typical experimental run .............................................................. 53

Chapter 1 Introduction

1.1 Rationale of this work

The macadamia (Macadamia integrifolia) is native to the rainforests of eastern

Australia (Storey and Hamilton, 1954). It was spread to grow in other parts of the

world. In Thailand, macadamia was introduced to grow in upland areas more than 40

years ago. Macadamia plantation areas are mainly located in northern and northeastern

Thailand with the annual production of 6,500 tons, worthing 500 million baths.

Macadamia nuts are rich in monosatuated fatty acids and are delicious. As the

productions of macadamia nuts are limited and there are high demands of the nuts, the

price of the nuts are high. Generally, fresh macadamia nuts have high moisture content

and are prone to deterioration. Thus, the moisture needs to be removed as quickly as

possible. Dried and roasted macadamia nuts have moisture content of around 1.5%

(db). High moisture contents will lead to fungal growth, reduction in shelf life, and

increased germination.

After harvesting, macadamia nuts need to be dried. To dry macadamia nuts,

efficiently, it is necessary to know drying characteristics and hygroscopic properties of

the nuts such as thin layer drying curves, moisture sorption isotherm and moisture

diffusivity. Due to the limited information available in literatures concerning drying of

macadamia nuts, research on the drying characteristics and hygroscopic properties of

macadamia nuts is still required. Therefore, this work aims to determine the drying

characteristics and hygroscopic properties of macadamia nuts. As drying of

macadamia nuts is an energy intensive process, the use of solar energy to dry

macadamia nuts is an interesting alternative to mechnical dryer used for drying

macadamia nuts. This research also aims to investigate the thermal performance of a

greenhouse solar dryer for drying macadamia nuts.

1

2

1.2 Objectives

1) To study the thin layer drying characteristics of macadamia nuts.

2) To determine moisture sorption isotherm of macadamia nuts.

3) To study moisture diffusivity of macadamia nuts.

4) To carry out a finite element simulation of macadamia nuts drying.

5) To investigate the performance of a greenhouse solar dryer for drying

macadamia nuts.

1.3 Organization of the thesis

This thesis composes of 6 chapters. Chapter 1 explains the rationale of the work and its

objectives. Chapter 2 presents the thin layer drying characteristics of macadamia nuts,

whereas the sorption isotherm of macadamia nuts is presented in chapter 3. Chapter 4

comprises the work on diffusivity and finite element simulation of macadamia nut drying.

Chapter 5 presents the Experimental performance and modeling of a greenhouse solar dryer

for drying macadamia nuts. Finally, chapter 6 presents the conclusion of the work. As

chapters 2 and 5 have been presented in conference and published in international journals,

the content of these chapters were written in the same way as that of the published papers.

Chapter 2

Thin layer drying of macadamia nuts

2.1 Introduction

Thin layer drying modeling is always used in order to understand and

estimate the drying characteristics of agricultural products (Hossain and Bala, 2002;

Akpinar et. al, 2003; Barrozo et. al, 2004; Ertekin and Yaldiz, 2004; Baini and

Langrish, 2006; Doymaz, 2009; Hacihafizoglu et. al, 2008). For proper understanding

of transfer processes during drying and production of quality dried macadamia nuts, it

is essential to know the thin-layer drying characteristics and the quality of the dried

products. This study aims to evaluate thin-layer drying characteristics of the

macadamia nuts obtained from macadamia plantation in northeastern Thailand.

2.2 Materials and methods

2.2.1 Drying experiments

The macadamia nuts used in this experiment come form Loei province in

northeastern Thailand. They had initial moisture content about 35-37% (db). The

average diameter of the macadamia nuts was 2.8 cm. The in-shell macadamia nuts

were placed on a tray in a thin-layer in a laboratory dryer and dried under controlled

conditions of temperature and relative humidity. The nuts were dried at the

temperature of 40 ๐C, 50 ๐C and 60 ๐C, the relative humidity of 10%, 20% and 30%

with the air speed of 1 ms-1.

A schematic diagram of this laboratory dryer is shown in Fig 2.1. The

laboratory dryer consists of a ceramic packed bed for producing saturated air at a given

temperature, an electrical heater, a blower, a drying section, measurement sensors data,

recording device and a controlling system. In this laboratory dryer, the blower forces

ambient air through a humid ceramic packed bed. The air absorbs moisture while it

passes through the packed bed. At the top of the packed bed, this air leaves in a

humidified condition. Then, this saturated air is heated by the air heater

*This part of the thesis has been published in the pproceedings of the 53th Annual Conference of

Kasetsart University, 3-6 February 2015, Bangkok, Thailand.

3

4

and passed across the product places in the tray. The relative humidity (rh) and

temperature of the drying air are controlled by adjusting the power supply to the air

heater and the water heater using a psychometric chart as a guideline.

Fig. 2.1 Schematic diagram of the laboratory dryer.

Prior to an experiment, the laboratory dryer was allowed to run for 30 min

to obtain a steady temperature. For each experiment in-shell macadamia nuts about

130 g were placed in the drying tray. The drying air temperatures were monitored

using thermocouples (K type, accuracy ±2%). These thermocouples were connected

to a digital data logger (Yokogawa, Model DC100). Voltage from the thermocouples

was converted into temperature by internal software of the data logger. The weights of

macadamia nuts were monitored by a load cell (accuracy ±1%). Electrical signal

obtained from the load cell was connected to a data logger (Wisco, Model ML21) in

which there is a software to convert the signal into weight.

The thin-layer drying tests were conducted in the temperature range of 40-

60 ๐C and the relative humidity of the drying air vary from 10% to 30%. Nine sets of

experiments were conducted for the macadamia nuts.

34

5

2.2.2 Mathematical modeling

There are three approaches to the modeling of thin-layer drying of agricultural

products (Bala, 1998). These are: (a) theoretical approach, (b) semi-theoretical

approach and (c) empirical approach. A theoretical equation gives a better

understanding of the transport processes but an empirical equation gives a better fit to

the experimental data without any understanding of the transport processes involved.

The semi-theoretical equation gives some understanding of the transport processes.

Thin-layer drying models of experimental data of the macadamia nuts are

expressed in the form of moisture content ratio of samples during drying, and it is

expressed as:

M - MeMR = M - Me0

(2.1)

where MR is the dimensionless moisture content or moisture ratio; and M, M0 and Me

are the moisture content at any given time, the initial moisture content and the

equilibrium moisture content, respectively.

In general, an agricultural moist product is composed of water and dried solid

mass. The moisture content (M) of the product in dry basis (% db.) can be calculated

from the following equation:

solid

solid

m - mM = × 100%

m (2.2)

where m is mass of the product and msolid is mass of dried solid mass of the product.

m can be obtained by using a balance or load cell. In order to obtain dried solid mass

(msolid), the water in the product must be totally removed by drying the product in an

oven at the temperature of 103 ๐C for 24 hours (Bala, 1998).

To select a suitable model for describing the drying process of macadamia

nuts, seven different thin-layer drying models were selected to fit the thin-layer

experimental data of macadamia nuts. The selected thin-layer drying models are

presented in Table 2.1.

6

The models were fitted to the experimental data by direct least square. The

coefficient of determination (R2) was one of the main criteria for selecting the best

equation. In addition to R2, the goodness of fit was determined by root mean square

error (RMSE). For the best fit, the R2 value should be high and RMSE values should

be low. RMSE and R2 are defined as:

model,i exp,i

exp

2n i=1

(MR - MR )NRMSE = × 100%

MR (2.3)

2 1 - Residual sum of squaresR = Corrected total of squares (2.4)

where MRexp,i and MRmodel,i are the moisture ratio derived from the experiment and the moisture ratio derived from the model.

expMR is mean moisture ratio obtained

from experiments. N is the number of observations.

Table 2.1 The 7 selected thin-layer drying models. No. Model equation Name of the model

1 MR=exp(-kt) Newton (Mujumdar, 1987)

2 MR=exp(-ktn) Page (Diamante and Munro, 1993)

3 MR=exp(ktn) Modified Page (Whith et al., 1978)

4 MR=a exp(-kt) Handerson and Pabis (Zhang and Litchfield, 1991)

5 MR=a exp(-kt)+c Logarithmic (Yangcioglu et al.,1999)

6 MR=a exp(-kt)+bexp(-gt) Two term (Henderson, 1978)

7 MR=a exp(-kt)+b exp(-gt)+c exp(-pt) Modifile Handerson and Pabis (Karathanos, 1999)

2.3 Results and discussion

2.3.1 Drying characteristics of in-shell macadamia nuts and kernel nuts

The changes in moisture contents with time for different drying air

temperatures are shown in Fig. 2.2, 2.3, 2.4 for in-shell nuts and show in Fig. 2.8, 2.9,

2.10 for kernel nuts. The final moisture content of samples dried under different

conditions ranged from 4% to 8% (db) for in-shell nuts and final moisture content

7

from 9% to 32% (db) for kernel nuts. The drying rate is higher for higher air

temperature. As a result, the time taken to reach the final moisture content is less, as

shown in Fig. 2.2, 2.3 and 2.4 for in-shell nuts and show in Fig. 2.8, 2.9 and 2.10 for

kernel nuts. Therefore, the drying air temperature has an important effect on the

drying of macadamia nuts. The variations of moisture contents with time for different

levels of relative humidity in the range of 10-30% can also be seen in Fig. 2.2, 2.3, 2.4

for in-shell nuts and show in Fig. 2.8, 2.9 and 2.10 for kernel nuts respectively.

Fig. 41 to 43 and Fig. 2.11 to 2.13 show the comparisons of the predicted and

experimental data of thin layer drying of in-shell nuts and kernel nuts for modified

Henderson and Pabis model, respectively.

0

5

10

15

20

25

30

35

40

1 8 15 22 29 36 43 50 57 64Time (hr)

Moi

sture

con

tent

(%, d

b).. 40 C

50 C

60 C

rh = 10 %

Fig. 2.2 Thin-layer drying of in-shell macadamia nuts at different temperatures (40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (10 %).

0

5

10

15

20

25

30

35

40

1 8 15 22 29 36 43 50 57 64

Time (hr)

Moi

sture

con

tent

(%, d

b)...

40 C

50 C

60 C

rh = 20 %

8

Fig. 2.3 Thin-layer drying of in-shell macadamia nuts at different temperatures (40 ๐C, 50 ๐C,and 60 ๐C) and relative humidities (20 %).

0

5

10

15

20

25

30

35

40

1 8 15 22 29 36 43 50 57 64Time (hr)

Moi

sture

con

tent

(%, d

b).. 40 C

50 C

60 C

rh = 30 %

Fig. 2.4 Thin-layer drying of in-shell macadamia nuts at different temperatures

(40 ๐C, 50 ๐C, and 60 ๐C) and relative humidities (30 %).

0

5

10

15

20

25

30

35

40

1 8 15 22 29 36 43 50 57 64Times (hr)

Moi

ture

con

tent

(%, d

b)...

Observed at 40 C

Predicted at 40 C

Observed at 50 C

Predicted at 50 C

Observed at 60 C

Predicted at 60 C

rh = 10 %

Fig. 2.5 Predicted and observed moisture content of in-shell macadamia nuts

using modified Handerson and Pabis model at the temperatures of 40

◦C, 50 ◦C and 60 ◦C and relative humidity of 10 %.

9

0

5

10

15

20

25

30

35

40

1 8 15 22 29 36 43 50 57 64Time (hr)

Moi

ture

con

tent

(%, d

b)..

Observed at 40 C

Predicted at 40 C

Observed at 50 C

Predicted at 50 C

Observed at 60 C

Predicted at 60 C

rh = 20 %

Fig. 2.6 Predicted and observed moisture content of in-shell macadamia nuts

using modified Handerson and Pabis model at the temperatures of 40

◦C, 50 ◦C and 60 ◦C and relative humidity of 20 %.

0

5

10

15

20

25

30

35

40

1 8 15 22 29 36 43 50 57 64Time (hr)

Moi

ture

con

tent

(%, d

b)..

Observed at 40 C

Predicted at 40 C

Observed at 50 C

Predicted at 50 C

Observed at 60 C

Predicted at 60 C

rh = 30 %

Fig. 2.7 Predicted and observed moisture content of in-shell macadamia nuts

using modified Handerson and Pabis model at the temperatures of 40

◦C, 50 ◦C and 60 ◦C and relative humidity of 30 %.

10

Table 2.2 Parameter value, coefficient of determination (R2) and root mean square

error (RMSE) value of the different models for in-shell macadamia nuts. Models T๐C rh

(%) k a b c n g p R2 RMSE

(%)

Newton

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1161 0.1524 0.1986 0.0952 0.1382 0.1887 0.0875 0.1214 0.1686

0.9913 0.9925 0.9937 0.9924 0.9881 0.9852 0.9893 0.9943 0.9878

2.0497 1.7382 1.4883 1.9728 2.2148 2.2576 2.3561 1.6201 2.1457

Page

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1554 0.2126 0.2593 0.1323 0.2094 0.2816 0.1321 0.1636 0.2352

0.8809 0.8438 0.8550 0.8740 0.8140 0.7879 0.8475 0.8740 0.8313

0.9959 0.9996 0.9985 0.9978 0.9992 0.9972 0.9982 0.9991 0.9947

1.4107 0.4229 0.7322 1.0713 0.5641 0.9730 0.9616 0.6586 1.4221

Modified Page

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

-0.1554 -0.2126 -0.2593 -0.1323 -0.2094 -0.2816 -0.1321 -0.1636 -0.2352

0.8809 0.8438 0.8550 0.8740 0.8140 0.7879 0.8475 0.8740 0.8313

0.9959 0.9996 0.9985 0.9978 0.9992 0.9972 0.9982 0.9991 0.9947

1.4107 0.4229 0.7322 1.0713 0.5641 0.9730 0.9616 0.6586 1.4221

Henderson and Pabis

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1077 0.1418 0.1891 0.0883 0.1260 0.1746 0.0798 0.1138 0.1607

0.9286 0.9348 0.9549 0.9299 0.9177 0.9326 0.9162 0.9397 0.9569

0.9956 0.9959 0.9952 0.9969 0.9937 0.9886 0.9961 0.9973 0.9892

1.4591 1.2938 1.2986 1.2584 1.6139 1.9757 1.4217 1.1115 2.0193

Logarithmic

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1059 0.1471 0.1976 0.0921 0.1332 0.1896 0.0836 0.1176 0.1756

0.9293 0.9338 0.9531 0.9282 0.9168 0.9315 0.9145 0.9386 0.9551

-0.0040 0.0084 0.0103 0.0101 0.0124 0.0180 0.0110 0.0078 0.0203

0.9957 0.9969 0.9973 0.9976 0.9957 0.9948 0.9968 0.9980 0.9961

1.4343 1.1231 0.9794 1.1012 1.3365 1.3339 1.2848 0.9687 1.2073

Two-term

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1021 0.5078 0.2467 0.0851 0.1069 0.2623 0.0755 1.0893 0.2107

0.8786 0.2327 0.8166 0.8957 0.7589 0.7723 0.8654 0.1192 0.8764

0.1218 0.7600 0.1683 0.1043 0.2353 0.2115 0.1344 0.8808 0.1209

1.5449 0.1201 0.0771 2.1726 0.5755 0.0679 1.1061 0.1070 0.0430

0.9981 0.9994 0.9971 0.9990 0.9989 0.9985 0.9992 0.9994 0.9992

0.9556 0.4862 0.5258 0.7330 0.6595 0.7074 0.6503 0.5253 0.5509

Modified Henderson and Pabis

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1020 0.1518 0.2198 0.2788 0.4287 0.4316 0.1357 0.2913 0.3430

0.4388 0.6153 0.8484 0.3968 0.5636 0.6704 0.6204 0.8885 1.1209

0.4388 0.6317 0.7051 0.0190 0.0292 0.0446 0.0242 0.2030 0.4380

0.1226 0.3067 0.5100 0.7001 0.8056 0.9283 0.8557 0.9009 1.4385

0.1020 0.1113 0.3374 0.0866 0.1265 0.2273 0.2386 0.3562 0.5107

0.4753 0.7596 0.9061 0.0355 0.1224 0.5191 0.0796 0.3111 0.2107

0.9981 0.9996 0.9995 0.9993 0.9994 0.9994 0.9993 0.9996 0.9992

0.9559 0.3893 0.3977 0.5850 0.4825 0.4650 0.5935 0.4213 0.5509

11

0

20

40

60

80

100

120

140

160

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61

Time (hr)

Moi

ture

con

tent

(%, d

b).. 40 C

50 C60 Crh = 10 %

Fig. 2.8 Thin-layer drying of kernel nuts at different temperatures (40 ๐C, 50

๐C, and 60 ๐C) and relative humidities (10 %).

0

20

40

60

80

100

120

140

160

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61

Time (hr)

Moi

ture

con

tent

(%, d

b)...

40 C50 C50 Crh = 20 %

Fig. 2.9 Thin-layer drying of kernel nuts at different temperatures (40 ๐C, 50

๐C, and 60 ๐C) and relative humidities (20 %).

12

0

20

40

60

80

100

120

140

160

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61

Time (hr)

Moi

ture

con

tent

(%, d

b)...

40 C50 C60 Crh = 30 %

Fig. 2.10 Thin-layer drying of kernel nuts at different temperatures (40 ๐C, 50

๐C, and 60 ๐C) and relative humidities (30 %).

0

20

40

60

80

100

120

140

160

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Time (hr)

Moi

ture

con

tent

(%, d

b)..

Observed at 40 CPredicted at 40 CObserved at 50 CPredicted at 50 CObserved at 60 CPredicted at 60 Crh = 10 %

Fig. 2.11 Predicted and observed moisture content of kernel nuts using

modifiedHanderson and Pabis model at the temperatures of 40 ◦C, 50

◦C and 60 ◦C and relative humidity of 10 %.

13

0

20

40

60

80

100

120

140

160

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Time (hr)

Moi

ture

con

tent

(%, d

b)...

Observed at 40 CPredicted at 40 CObserved at 50 CPredicted at 50 CObserved at 60 CPredicted at 60 Crh = 20 %

Fig. 2.12 Predicted and observed moisture content of kernel nuts using

modified Handerson and Pabis model at the temperatures of 40 ◦C,

50 ◦C and 60 ◦C and relative humidity of 20 %.

0

20

40

60

80

100

120

140

160

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Time (hr)

Moi

ture

con

tent

(%, d

b)….

Observed at 40 CPredicted at 40 CObserved at 50 CPredicted at 50 CObserved at 60 CPredicted at 60 Crh = 30 %

Fig. 2.13 Predicted and observed moisture content of kernel nuts using

modified Handerson and Pabis model at the temperatures of 40 ◦C, 50

◦C and 60 ◦C and relative humidity of 30 %.

14

Table 2.3 Parameter value, coefficient of determination (R2) and root mean square

error (RMSE) value of the different models for kernel nuts. Models T๐C rh

(%) k a b c n g p R2 RMSE

(%)

Newton

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1161 0.1524 0.1986 0.0952 0.1382 0.1887 0.0875 0.1214 0.1686

0.9988 0.9951 0.9873 0.9980 0.9933 0.9830 0.9946 0.9976 0.9910

0.7427 1.3796 0.6259 1.0352 1.7370 2.4193 1.9563 1.1708 1.9647

Page

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1770 0.1953 0.3649 0.1305 0.1938 0.3132 0.0555 0.1101 0.2037

20.9933 21.0610 0.7886 0.9399 0.8620 0.7757 1.0960 0.9727 0.8578

0.2811 0.4596 0.9987 0.9990 0.9989 0.9985 0.9969 0.9978 0.9969

18.5658 19.1713 0.6364 0.7218 0.6932 0.7192 1.4997 1.1190 1.1522

Modified Page

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

-0.1770 -0.1954 -0.3650 -0.1306 -0.1939 -0.3132 -0.0555 -0.1102 -0.2037

20.9931 21.0610 0.7886 0.9400 0.8620 0.7757 1.0960 0.9727 0.8579

0.2811 0.4596 0.9987 0.9990 0.9989 0.9985 0.9969 0.9978 0.9969

18.5658 14.4572 0.6364 0.7218 0.6932 0.7192 1.4997 1.1190 1.1522

Henderson and Pabis

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1425 0.1868 0.2425 0.1097 0.1343 0.1853 0.0759 0.1001 0.1380

0.9797 0.9644 0.9374 0.9722 0.9417 0.9069 1.0446 0.9733 0.9256

0.9992 0.9960 0.9903 0.9986 0.9960 0.9899 0.9964 0.9982 0.9956

0.6341 1.2420 1.7366 0.8570 1.3386 1.8613 0.5088 1.0142 1.3719

Logarithmic

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1417 0.1919 0.2520 0.1109 0.1389 0.1917 0.0785 0.0982 0.1404

0.9800 0.9633 0.9361 0.9717 0.9406 0.9060 1.0415 0.9746 0.9247

0.0013 0.0064 0.0085 0.0028 0.0079 0.0073 0.0102 0.0051 0.0042

0.9992 0.9967 0.9919 0.9987 0.9967 0.9909 0.9967 0.9984 0.9959

0.6261 1.1292 1.5792 0.8372 1.2090 1.7660 1.5257 0.9648 1.3359

Two-term

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1064 0.1474 0.6981 0.6450 0.6797 1.1804 0.0759 0.1001 0.1299

0.4398 0.6857 0.4023 0.0787 0.1818 0.2602 0.7978 0.3490 0.8711

0.4388 0.3244 0.6015 0.9252 0.8227 0.7405 0.2468 0.6243 0.1289

0.1407 0.4617 0.1701 0.1050 0.1194 0.1532 0.0759 0.1001 3.9235

0.9891 0.9993 0.9992 0.9993 0.9993 0.9996 0.9964 0.9982 0.9992

2.2880 0.5065 0.4881 0.6263 0.5584 0.3842 1.6114 1.0142 0.6028

Modified Henderson and Pabis

40 50 60 40 50 60 40 50 60

10 10 10 20 20 20 30 30 30

0.1331 0.4615 0.1701 0.1050 0.1195

25.1930 0.0759 0.1001 3.1889

0.3306 0.3245 0.3062 0.4620 0.4086 -0.182 0.3482 0.3245 0.1303

0.3299 0.3345 0.2953 0.0790 0.4141 0.4331 0.3482 0.3245 0.4366

0.3214 0.3511 0.4023 0.4629 0.1818 0.7492 0.3482 0.3244 0.4331

0.1328 0.1474 0.1702 0.6403 0.1194 1.7222 0.0759 0.1001 0.1297

0.1670 0.1473 0.6981 0.1050 0.6798 0.1543 0.0759 0.1001 0.1297

0.9992 0.9993 0.9992 0.9993 0.9993 0.9996 0.9964 0.9982 0.9992

0.6318 0.5065 0.4881 0.6263 0.5584 0.3682 1.6114 1.0142 0.6036

15

2.3 Mathematical modeling of thin-layer drying

Seven thin-layer drying model (Table 2.1) s were fitted to the experimental data

of moisture ratio of in shell nuts and kernel nuts dried at different temperatures and

relative humidity. The parameter values, R2 and RMSE, are also shown in Table 4 and

Table 5 of macadamia nuts and kernel nuts respectively. The Modified Handerson and

Pabis model was found to be the best, followed by the Two term model. The value of

R2 of the Modified Handerson and Pabis model was 0.9981-0.9992 and 0.9029-

0.9439 of in shell nuts and kernel nuts respectively, indicating good fit and RMSE

was 0.42-0.59% and 0.3682%-1.6114% of in-shell nuts and kernel nuts respectively.

Empirical expressions were developed for the drying parameters of the Modified

Handerson and Pabis model and the drying parameters were found to be a function of

drying air temperature (T in ๐C) and relative humidity (rh in %):

k = - 1.52690+0.04227T + 0.06273rh + 0.00022Trh - 0.00039T2

- 0.00172rh2 (2.5)

a = 0.230723 + 0.021691T - 0.083943rh + 0.000227Trh - 0.000065T2

+ 0.002117rh2 (2.6)

b = 1.449237 + 0.014082T - 0.187288rh + 0.000369Trh - 0.000097T2

+ 0.003759rh2 (2.7)

c = 1.204763 - 0.077930T + 0.062076rh + 0.000488Trh + 0.000881T2

- 0.001223rh2 (2.8)

g = 1.306501 - 0.043473T - 0.047035rh + 0.000092Trh + 0.000524T2

+ 0.001292rh2 (2.9)

p = - 0.604983 + 0.059075T - 0.080746rh - 0.000750Trh - 0.000267T2

+ 0.002314rh2 (2.10)

16

The parameter values for kernel macadamia nuts.

k = - 48.294001 + 1.686829T - 0.035136rh + 0.003004Trh - 0.014543T2

- 0.003075rh2 (2.11)

a = - 4.764590 + 0.237951T - 0.205002rh + 0.001673Trh - 0.002313T2

+ 0.002800rh2 (2.12)

b = -1.897929 + 0.013931T + 0.229736rh - 0.002430Trh + 0.00273T2

- 0.002364rh2 (2.13)

c = 7.658853 - 0.251754T - 0.024804rh + 0.000756Trh + 0.002039T2

- 0.000433rh2 (2.14)

g = -1.635049 + 0.029858 + 0.088287rh - 0.001052Trh - 0.000010T2

- 0.000883rh2 (2.15)

p = - 219.148655 + 7.636277T - 0.940576rh - 0.001183Trh - 0.062994T2

+ 0.033341rh2 (2.16)

2.4 Conclusion

Thin-layer drying of macadamia nuts was investigated in this study and the

drying rate increases with the increase of air temperatures. The entire drying process

occurred in the falling rate period and constant rate period was not observed. Seven

thin-layer drying models were fitted to the experimental data of in-shell nuts and

kernel nuts to describe the drying characteristics of macadamia nuts. Drying

parameter of Modified Handerson and Pabis model were found to be a function of

drying air temperature and relative humidity. The Modified Handerson and Pabis

model was the best, followed by the Two term model. The Modified Handerson and

Pabis model can be used both to assess the drying behaviour of macadamia nuts and

for simulation and optimization of the dryer for efficient operation.

Chapter 3

Sorption Isotherm of Macadamia nuts

3.1 Introduction

Moisture sorption isotherms describe the relation between the equilibrium

moisture content of product and the relative humidity of air surrounding the product at

a constant temperature of the air. The moisture isotherm data of macadamia nuts is

also useful for predict shelf-life and determining packaging and storage characteristics

of dried macadamia nuts. In addition, the moisture isotherm is needed to calculate the

moisture exchanges that many occur during storage of the nuts (Bala, 1998). Moisture

sorption isotherms have been determined (Lomauro et. al, 1985; Mir and Nath, 1995;

Lahsasni et. al, 2004; Kaymak-Ertekin and Gedik, 2004). However, very few research

works on sorption isotherm of macadamia nuts was carried out. Therefore the

objective of this work is to experimentally determine the sorption isotherms of

macadamia nuts and to fit isotherm model to sorption isotherm data.

3.2 Materials and methods

3.2.1 Determination of the sorption isotherm of macadamia nuts

Equilibrium moisture contents of macadamia nuts were determined

experimentally using the gravimetric method. The sample box was essentially an

airtight plastic box containing saturated salt solution to maintain constant relative

humidity inside the sample box. The samples were placed inside the perforated

sample containers and the sample containers were placed on the perforated plastic

supports just above the salt solution. The selected temperatures for sorption isotherm

determination were 40 ◦C, 50 ◦C, and 60 ◦C and the relative humidity was 11–97%.

The values of the relative humidity were controlled by various saturated salt solutions

as described in Bala (1998). The final moisture contents of the product were

determined by the standard oven method (temperature of 103 ๐C for 24 hours).

17

18

3.2.2 Selection of the sorption isotherm models In Five isotherm models were tested to fit the sorption isotherm of macadamia

nuts. These models were selected because of effectiveness for describing isotherms of

many foods materials. These models are shown in Table 3.1.

Table 3.1 Selected isotherm models

No Model Mathematical expression

1 Day and Nelson Equation b3b b T1 2

w 0 ea = 1-exp(-b T M )

2 Modified Halsey Equation

2

0 1w b

e

exp(b +b T)a = exp -M

3 Modified Chung-Pfost Equation

0w 2 e

1

-ba = exp exp(-b M )T+b

4 Modified Oswin Equation

w2

0 1

e

1a b

b +b T1+

M

=

5 Kaleemullah Equation 3b

w 0 1 2 ea = b -b exp(-b TM )

Note Water activity (aw) in these models is equal to relative humidity in decimal.

The accuracy of the models in predicting equilibrium moisture content for

given values of relative humidity and temperature can be determined by coefficient of

determination (R2) and root mean square error (RMSE). For the best fit, the R2 value

should be high and the lowest RMSE. RMSE and R2 are defined as:

N

i=1

1/2

pre,i exp,i1RMSE (Me -Me )N (3.1)

2 Residual sum of squresR =1-

Corrected total sum of squares (3.2)

where Meexp,i is equilibrium moisture content from experiment (%, db), Mepre,i is

equilibrium moisture content from prediction (%, db), N is number of data to be

consider.

19

3.3 Results and discussion

Results from the experiment to find out sorption isotherm of macadamia nuts at

40 ๐C, 50 ๐C and 60 ๐C and water activity (aw) is in the range of 0.11 to 0.96 were

shown in Fig. 3.1. It could be seen that the isotherm curve was in the shape of

sigmoid. The equilibrium moisture content decreased when the temperature increased

at all levels of relative humidity. This could be explained as follows. The increasing

temperature made water molecule increase so much kinetic energy that it could break

attraction forces between molecules. The water in the product would evaporate to

surrounding air more than in the low temperature. The equilibrium moisture content,

therefore, decreases when the drying temperature increases. Besides, when the

temperature is constant, the equilibrium moisture content will increase when the

relative humidity in the surrounding air increases. This is due to the fact that high

relative humidity in the surrounding air will reduce the difference of vapor pressure

between the surrounding air and the product, resulting in water evaporation at the

surface of the product to the surrounding air in a little amount. Moreover, it takes

more time to reach equilibrium status.

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2Water activity

Equi

libriu

m m

oist

ure

cont

ent (

%,d

b)…. predit-40

predit-50

predit-60

40C

50C

60C

Fig. 3.1 Predicted (Modified Oswin model) and measured sorption isotherms

of macadamia nuts at 40 ๐C, 50 ๐C and 60 ๐C

20

The constant in the form of equation coefficient, the accuracy of the simulation

model (RMSE), the difference between the prediction result and the experiment result

(R2) for sorption isotherm of macadamia nuts were shown in Table 3.2. According to

the test through isotherm models to predict, the Modified Oswin model was the most

suitable method to predict the experiment result for isotherm of macadamia nuts at 40

๐C, 50 ๐C and 60 ๐C.

Table 3.2 The coefficients of the selected models, standard error of estimate (RMSE)

and the coefficient of determination (R2) for macadamia nuts.

Model Temperature (๐C) Coefficients

RMSE R2 b0 b1 b2 b3

Day and Nelson 40, 50, 60 0.00089 -4.27015 2.14672 0.29794 0.07 0.94

Modified Halsey 40, 50, 60 25.22471 -0.05623 6.71653 - 0.07 0.94

Modified Chung-

Pfost 40, 50, 60 3594.013 -26.624 0.184 - 0.07 0.94

Modified Oswin 40, 50, 60 42.18947 -0.24723 8.60964 - 0.06 0.95

Kaleemullah 40, 50, 60 0.520917 -0.000038 -0.006267 0.813293 0.26 0.21

Five models of the isotherm of macadamia nuts; the Modified Oswin model

fitted the best to the experimental data of macadamia nuts. The agreement between

the best-fitted models and experimental data was excellent. For simplicity and

consistency, effect of temperature i.e. equilibrium moisture content decreases with the

increase of moisture content, Modified Oswin was selected for use in this simulation.

Another advantage of Modified Oswin is that equilibrium moisture content can be

calculated directly as a function of temperature and water activity using only one set

of coefficient, thus facilitating the calculation. This equilibrium moisture content

model is written as:

w

1

8.6096442.18947+(-0.24723×T)

1Me

a (3.3)

21

where b0 = 42.18947, b1 = -0.24723, b2 = 8.60964. T is temperature (๐C), aw is water

activity (decimal) and Me is equilibrium moisture content (%, db). The water activity

is equal to the relative humidity (%) divided by 100.

3.4 Conclusion

The equilibrium moisture contents of macadamia nuts have been determined

experimentally using gravimetric method at the temperature levels of 40 ๐C, 50 ๐C, and

60 ๐C water activity (aw) in the range of 0.11-0.95. All the isotherms were sigmoid in

shape. The equilibrium moisture content decreases with increase in temperature at

constant water activity. Five sorption isotherm models were used to fit the

experimental data of macadamia nuts. Among them, modified Oswin model fitted the

best to the experimental data at the temperature levels of 40๐C, 50๐C, and 60 ๐C. This

model is suggested for use in drying of macadamia nuts

Chapter 4

Diffusivity of macadamia nuts and finite element simulation

for macadamia nut drying

4.1 Introduction

Several numerical methods available in simulation study, the finite element

method have been widely applied to model heat and mass transfer. The finite element

method assumes that any continuous quantity such as moisture content can be

approximated by a discrete model composed of a set of piecewise continuous

functions defined over a finite number of sub-domains or elements (Segerlind, 1984;

Janjai, 2008) Elements are connected at nodal points along the boundaries and their

equations are obtained by minimizing a function of the physical problem. The finite

element method has been extensively used to solve problems having irregular

geometrical configurations and material properties depending on the temperature and

moisture. This study aims to use the finite element method to simulate the drying of

macadamia nuts using experimentally determined diffusivities of macadamia nut

flesh.

4.2 Material and method

Macadamia nuts may be harvested directly from the tree or after they have

fallen to the ground and should be removed from the fleshy green husk. Macadamia

nuts were used for this study and the initial moisture content was 35% (db). It was

collected from Phurua Highland agricultural in northeast Thailand. The macadamia

nuts were stored at 5 ◦C temperature. Before starting any experiment,

the macadamia nuts were placed in room temperature in order to achieve equilibrium

condition with the room temperature. Thin layer drying of macadamia nuts was

conducted under controlled conditions of temperature and relative humidity in a

laboratory dryer. The details of the dryer is described in chapter 2.

Before starting the experiments, the laboratory dryer is allowed to run for 1

hour to achieve steady state drying condition. For each experiment, about 130 g of

macadamia nuts was used for this study. Every experiment was conducted at an air

velocity of 1.0 ms-1. Drying temperatures were monitored by using a thermocouple (K

22

23

type) connected with a personal computer using an interface at an interval of 5 min.

The weights of macadamia nuts were recorded by electronic balance (accuracy ± 0.01

g) in an interval of 1 hour. The thin layer drying tests had been conducted in the

temperature range of 40 - 60◦C and the relative humidity value of 10%, 20% and 30%.

4.2.1 Diffusivities of the shell and kernel of macadamia nuts

Fick’s second law of the unsteady state diffusion, neglecting the effects of

temperature and total pressure gradient, can be used to describe the drying behavior of

fruits (Bala, 1997).

M . D Mt

(4.1)

This equation can be solved for different standard shapes of the drying

material. Mass transfer due to moisture migration takes place through the product so

as to reach moisture equilibrium between the product and the ambient environment.

The mechanisms involved can be commonly expressed by Fick’s second law of

diffusion for drying porous materials during the falling rate period (Zopas and

Maroulis, 1996). Assuming the kernel macadamia nuts being represented by a sphere

and the shell by a slab, assuming uniform initial moisture content distribution, one-

dimensional moisture diffusion, no shrinkage, negligible external resistance, and a

constant effective moisture diffusion coefficient throughout the drying period, the

analytical solutions of Eq. (4.2), for the nut samples are derived as follows (Crank,

1975).

For sphere

2

0

eff22

1n22

eo

e

rtDπnexp

n1

π6

MMMM (4.2)

24

For slab of half thickness z

2e eff2 2 2

n 1o e

M M D t8 4 exp (2n-1)M M π (2n-1) z

(4.3)

where Deff is effective moisture diffusion coefficient (square meter per minute), and r

is the spherical radius (metre) of the material, n is the number of terms of the Fourier

series and r is the average radius of the nuts, z is the average slab of half thickness. t is

time. Equations (4.2) can be fitted to the experimental data of the products if the

products have the shapes of sphere and the diffusivity can be determined minimizing

sum of squares of the deviations between the predicted and experimental data.

4.3 Finite element modeling of in-shell macadamia nut drying

Fick’s law of diffusion can be used to model the moisture movement within

fruit during drying (Bala, 1998). The general form of this law can be written as:

M . D Mt

(4.4)

In this work this diffusion equation is applied to describe the two-dimensional

movement of moisture (M) in a nut-in-shell (NIS).

In the Cartesian coordinates with constant diffusivity (D), this equation

becomes:

2 2

2 2M M MDt x y

(4.5)

with the initial conditions:

at t = 0, M = M0 and t > 0 (4.6)

25

and boundary conditions:

m s eMD h M Mn

(4.7)

where hm is the mass transfer coefficient, Me is the equilibrium moisture content on a

dry basis (db) and n is the magnitude of a normal vector to the surface. Finite element

equations are derived from an incorporation of Galerkin’s formulation of the weighted

residual method and using Galerkin’s method it can be expressed as:

2 2T

2 2M M M[N] D d 0.

tx y (4.8)

Since interpolation functions do not have continuous derivatives between

elements, the second derivatives in the Eq. (4.7) must be replaced by first derivatives.

By performing integrations by part, the first integral of Eq. (4.7) becomes:

T2

T T2

NM M MN D d N D d D d .x x x xx

(4.9)

Application of Gauss’ divergence theorem to the first integral on the right-hand side

of Eq. (4.6) yields:

TT

xΩ L

M MN D d D N n dL.x x x

(4.10)

Performing a similar operation for the second term, Eq. (4.7) can be written as:

T T

T

x yΩ L

N NM M M MD d D N n n dL.x x y y x y

(4.11)

26

The surface integral in Eq. (4.10) can be written in terms of flux M / n along the

boundary and n is the outward normal to the surface. Eq. (4.10) can now be expressed

as:

T T

T

Ω L

N NM M MD d D N dL.x x y y n

(4.12)

The unknown M in Eq. (4.11) can be defined as: (Segerlind, 1984)

M N M (4.13)

Hence, we can write:

NM Mx x

and NM M .y y

(4.14)

Substitution of these into Eq. (4.10) yields:

T T

T

Ω

N N N ND dΩ M D B B dΩ M

x x y y (4.15)

where:

31 2

1 2 3

NN Nx x xB

N N Ny y y

(4.16)

which is the gradient matrix of triangular elements in the finite element mesh. Using

Eq. (6), the right-hand side of Eq. (4.11) can be written as:

T T Tm m e

L L L

MD N dL -h N N M dL+ h N M dL.n

(4.17)

27

The gradient matrix [B] in Eq. (4.15) can be written as:

ji k

i kj

bb b1B =c cc2A

(4.18)

where A= area of the triangular element;

i j k

j k i

k i j

i k j

j i k

k j i

b =Y -Y

b =Y -Y

b =Y -Y

c =X -X

c =X -X

c =X -X

where (X, Y) are nodal coordinates of an element. Keeping {M} aside, the right-hand

side of Eq. (4.14) can be written as:

i iji k

j ji kjΩ

k k

b c bb b1D b c dΩ.c cc4A

b c

(4.19)

For a two-dimensional model, the thickness is assumed to be unity; thus,

dΩ can be replaced by dA. It is evident from Eq. (4.18) that all terms are constant for

any element.

Eq. (4.16) can therefore be expressed as:

T T

Ω Ω

D B B dΩ = D B B dA (4.20)

Eq. (4.19) is the element stiffness matrix [k]. The matrix obtained by integrating the

first term on the right-hand side of Eq. (4.16) should be added to matrix [k]. This

surface integral, keeping {M} aside as before, is expressed as:

28

i ji i i kT

m m j i j j j kL L

k i k j k k

N NN N N Nh N N dL h N N N N N N dL

N N N N N N

(4.21)

The suffixes i, j and k indicate the nodal points of a triangle to which the interpolation

function belongs. Assuming that L1 is measured from opposite node i, we can replace

the Ns in the coordinate system as:

L1 = Ni, L2 = Nj and L3 = Nk.

Now there are two types of products in Eq. (4.20) and these are

2 2 21 2 3 1 2 1 3L , L , L , L L , L L and 2 3L L

If we consider, for example nodes j and k on the surface, the integrals of the square

products are:

jk jk

jk jk2 22 3

L L

2!0!L LL dL = L dL =

2+0+1 ! 3 (4.22)

where Ljk is the length of the side between nodes j and k of the surface element under

consideration. Integration of the cross-product yields:

jk

jkj k jk

L

L0!1!1!L L dL = L .0+1+1+1 ! 6

(4.23)

However, for an integration over an element, Eqs. (4.21) and (4.22) can be modified

as:

2 2 0 01 i j k

A A

2!0!0! AL dA = L L L dA = 2A = 2+0+0+2 ! 6

(4.24)

29

0 1 1i k i j k

A A

0!1!1! AL L dA = L L L dA = 2A = 0+1+1+2 ! 12

(4.25)

where A is the area of the triangular element. Eqs. (4.23) and (4.24) are used later.

The second term in Eq. (4.16) is the mass transfer term and is a load vector. This can

be expressed as:

i 1T

m e m j e m 2 eL L L

k 3

N Lh N M dL h N M dL h L M dL.

N L (4.26)

The solution of this equation is:

12

1m e

m 2 e 23L

3

31

1L 1

0

L 0h M

h L M dL L 1 .2

L 1

1L 0

1

(4.27)

Only one or two of the three column vectors on the right-hand side of Eq. (4.26) can

be active at a time depending on the side facing the ambient air. The last term in Eq.

(4.7) can be expressed as:

T T MMN d N N dt t

(4.28)

The time derivative of moisture inside the kernel macadamia nuts, the first M / t is

independent of the coordinates of the fruit domain . Hence, Eq. (4.27) can be written

as:

T TM MN N d N N d .t t

(4.29)

30

The integral within the bracket on the right-hand side of Eq. (4.28) is the element

capacitance matrix [c], which can be solved using Eqs. (4.23) and (4.24). By

combining the approximate terms in Eq. (4.16), (4.19) and (4.28), and replacing the

notation d with two-dimensional space dA, the following first-order differential

equation can be obtained:

d Mc + k M = f .

dt (4.30)

The direct stiffness method is the name given to the procedure for incorporating the element matrixes into the final system of equations. The method is simple and straightforward and when [c] is combined with the element matrices using the direct stiffness procedure, the final result is a system of first-order differential equations.

MC K M F 0.t

(4.31)

Mathematically we can write:

t+Δt tM Md M

dt t (4.32)

t+Δt tM θ M 1 θ M (4.33)

where θ 1,0

The finite difference equation for each value of θ is as follows: θ = 0 forward

difference method

t+Δt t tC M C Δt K M Δt F . (4.34)

θ = 1/2 Central difference method

t+Δt t t t+Δt

Δt Δt ΔtC K M C K M F F .2 2 2

(4.35)

31

θ = 2/3 Galerkin’s method

t+Δt t t+Δt t

2Δt Δt ΔtC + K M C K M + F +2 F3 3 3

(4.36)

θ = 1 backward difference method

t+Δt t t+ΔtC +Δt K M C M +Δt F . (4.37)

Regardless of the value of θ , the final system of equations has the following form:

*t+Δt tA M P M + F . (4.38)

Nut kernel

Brow shell

Macadamia nut

Fig. 4.1 macadamia nut comprising nut kernel and brow shell.

macadamia nut used in this experiment is shown in Fig. 4.1. Moisture moves

from inside of the kernel macadamia nut and shell macadamia nut to the outer surface

and passes through two different sections of the macadamia nut that have different

diffusivities. To analyze the problem, a two dimensional central axis symmetric finite

element triangular grid is used to model for the macadamia nut and half of the

section of the domain in two dimensions is solely taken into account because of the

geometric and transfer symmetries. The domain consists of kernel macadamia nut and

shell macadamia nut. Fig. 4.2 shows finite element discretization for half of a two

dimensional central axis symmetry section of in-shell Macadamia nut consisting of

202 grids and 350 triangular elements.

32

0.0 4 8 12 16 200.0

2

4

6

8

10

y (mm)

x (mm)

Fig. 4.2 Finite element grid for half of in-shell macadamia nut.

4.3 Results and discussions

4.3.1. Diffusivities of kernel and shell of macadamia nut

The moisture diffusivities of kernel and shell of macadamia nut are presented in

table 4.1 and 4.2 respectively. The diffusivities of kernel of shell of macadamia nut

were found to be dependent on temperatures and can be expressed as function of

temperature by using the Arrhenius-type equations as follows:

For kernel

-2938.81/T6ker

abD 5.190 10 enel (4.39)

For shell

-2776.97/T6 abD 5.850 10 eshell (4.40)

Table 4.1 Moisture diffusivities of kernel of macadamia nut. Relative

humidity (%)

Diffusivity (m2s-1) at temperature Mean Diffusivity (m2s-1)

40 ◦C 50 ◦C 60 ◦C

10

20

30

8.33×10-10 1.13×10-09 1.48×10-09 1.15×10-09

6.52×10-10 8.16×10-10 1.13×10-09 8.65×10-10

4.61×10-10 5.77×10-10 8.25×10-10 6.21×10-10

Table 4.2 Moisture diffusivities of shell of macadamia nut. Relative

humidity (%)

Diffusivity (m2s-1) at temperature Mean Diffusivity (m2s-1)

40 ◦C 50 ◦C 60 ◦C

10

20

30

1.88×10-10 1.94×10-10 2.30×10-10 2.04×10-10

2.24×10-10 2.54×10-10 3.02×10-10 2.60×10-10

1.68×10-10 1.89×10-10 2.05×10-10 1.87×10-10

33

Fig. 4.3 and 4.4 present the variations of moisture diffusivities of kernel and

shell of macadamia nut respectively as functions of the reciprocal of absolute drying

air temperature. The mean diffusivities of kernel and shell of macadamia nuts in the

range of 6.21×10−10 to 1.15 ×10−09 m2/s and 2.04×10-10 to 1.87×10-10 respectively are

found in this study.

01

234

567

89

0.002950 0.003000 0.003050 0.003100 0.003150 0.003200 0.003250

1/Tab(k-1)

Diff

usiv

ity(1

0-11 m

2 s-1) Experiment Predicted

Fig. 4.3 Variations of moisture diffusivity of kernel of macadamia nut as a

function of the reciprocal of absolute drying air temperature (Tab).

0

0.5

1

1.5

2

2.5

0.00295 0.003 0.00305 0.0031 0.00315 0.0032 0.00325

1/Tab(k-1)

Diff

usiv

ity(1

0-10 m

2 s-1)

Experiment Predicted

Fig. 4.4 Variations of moisture diffusivity of shell of macadamia nut as a

function of the reciprocal of absolute drying air temperature (Tab).

4.3.3. Finite element simulated drying

Finite element model for in-shell macadamia nut drying was simulated to

predict the moisture content and it was programmed in Compaq Visual FORTRAN

version 6.5. The simulated moisture contents were compared with the experimented

34

values in order to validate the model. Fig. 4.5 shows the comparison of moisture

contents between the predicted values and the experimental without shrinkage for

drying temperature of 60◦C. The root mean square errors between the predicted values

and the experimental values of moisture contents for drying temperature of 60◦C is

10.42502%.

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35Time (hr)

Moi

sture

cont

ent (

%,d

b)... Experiment

Model with diffusivity

T=60°Crh=30%

Fig.4.5 Comparison of predicted moisture contents with the experiment data at

60 ๐C and relative humidity 30 %

4.4. Conclusions

Moisture diffusivities of in-shell macadamia nuts have been determined

experimentally and moisture diffusivities were found to increase with the increase in

drying air temperature. Moisture diffusivities of macadamia nuts can be explained

using an Arrhenius-type equation. The mean diffusivity values of macadamia nuts in

this study are 9.57×10−10 m2/s.

A two-dimensional finite element model of macadamia nuts was developed for

drying and it was programmed in Compaq Visual FORTRAN version 6.5. The finite

element model using macadamia nut diffusivities is sufficient in the moisture content

predictions during drying process. The finite element model predicts the moisture

contents very well during drying. This model can be used to provide information on

the dynamics of moisture movement without the need for measurements and design

data. Furthermore, the model provides a better understanding of the transport

processes inside the macadamia nuts.

Chapter 5

Experimental performance and modeling of a greenhouse solar dryer for drying

macadamia nuts

5.1 Introduction

In general, box-type dryers using LPG (liquefied petroleum gas) are usually

used to dry macadamia nuts in Thailand. As the price of LPG increases, drying cost of

macadamia is consequently in creases. Other drying equipment is needed to reduce

the drying cost.

Situated in the tropics, Thailand receives abundant solar radiation (Janjai et. al,

2005). Consequently, the use of solar dryers is a good alternative solution of the

problem of macadamia nut drying. Although several types of solar dryers have been

developed in the last 50 years (Janjai et. al, 2012); Sharma et. al, 2009; Murthy et. al,

2009; Funholi et. al, 2009; Oueslati et. al, 2012; Adeniyi et. al, 2012), most of them

have small loading capacity which could not meet the demand of macadamia drying.

Having realized this demand, a polycarbonate sheet-covered greenhouse solar dryer

has been developed at the department of physics, Silpakorn University (Janjai et. al,

2004; Janjai et. al, 2007; Janjai et. al, 2009; Janjai et. al, 2010). In this work, the dryer

was used to dry macadamia nuts and its performance is reported. In addition, a

simulation model of this dryer for drying macadamia nuts was also developed and the

experimental results were used to validate the performance of the model.

5.2 Materials and methods

5.2.1 Experimental setup

The greenhouse solar dryer was installed at Loei province (17.37, 101.43),

Thailand. The dryer consists of a parabolic roof structure made from polycarbonate

sheets on a concrete floor. Dimension of the dryer is 9 m in width, 12.4 m in length

*This chapter has been published in International Journal of Scientific & Engineering Research.

Volume 5, Issue 6, 1155-1161, 2014.

35

36

and 3.45 m in height. To ventilate the dryer, six DC fans operated by two 50-W solar

cell modules were installed in the wall opposite to the air inlet. The pictorial view of the

dryer is shown in Fig. 5.1. The product dried inside the dryer is shown in Fig. 5.2.

Solar radiation passing through the polycarbonate roof heats the product in the

dryer and the concrete floor. Ambient air is drawn in through an air-inlet at the bottom

of the front side of the dryer and is heated by the floor and the products exposed to

solar radiation. Direct exposure to solar radiation of the products and the heated air

enhance the drying rate of the products. Moist air passing through and over the

products is sucked from the dryer by the fans at the top of the rear side of the dryer.

Due to the utilization of the PV ventilated system, this type of greenhouse solar dryer

can be used in rural areas without electricity grids.

5.2.2 Experimental procedure

In this study, macadamia nuts were dried in the greenhouse solar dryer to

investigate the dryer potential. The experimental runs were conducted during June,

2013 - February, 2014. Solar radiation was measured by a pyranometer (Kipp&Zonen,

model CM 11) placed on the roof of the dryer. Thermocouples (K type) were used to

measure air temperatures in the different positions of the dryer. A hot wire anemometer

(airflow, model TA5) was used to monitor the air speed inside the dryer. The relative

humidity of ambient air and drying air were periodically measured by hygrometers

(Electronnik, model EE23). The positions of all measurements are shown in Fig. 5.3.

Measured data from the pyranometer, hygrometers and thermocouples were

automatically recorded every 10 minutes by a multi-channel data logger (Yokogawa,

model DC100). The air speed at the inlet and outlet of the dryer were recorded during

the drying experiments.

Six batches of drying test were carried out. For each batch, 730 kg of in-

shell macadamia nuts was placed on the trays inside the dryer. Each day, the

experiment was started at 8:00 am and lasted until 6:00 pm. The drying was continued

on subsequent days until the desired moisture content was reached. Product samples

were placed at various positions in the dryer and were weighed periodically at two

hour intervals using a digital balance (Kern, model 474 – 42). Product samples about

130 g from the dryer were weighed at two hour intervals. At the end of the

37

experimental drying, the exact dry solid weight of the product samples was

determined by the oven method (103๐C for 24 hours). The moisture content during

drying was estimated from the weight of the product samples and the estimated dried

solid mass of the samples.

Fig. 5.1 The pictorial view of polycarbonate-covered greenhouse solar dryer,

from the front side

38

Fig. 5.2 Macadamia nuts inside the dryer

9m

12.4m

Air inletConcrete floor

Solar cell moduleFans (air outlet)

Polycarbonate roof

M1

M2

M3 M6

M5

M4

T_ambientT1

T2 T3 T4

T5 T6 T7 T8

T9T10 T11 T12

T13 T14 T15 T16

T17T18 T19 T20

T21 T22 T23 T24

M_natural sundrying

Rh_ambient

T_outletRh_inside

3.45m

Rh_outlet It

Fig. 5.3 Structure of the dryer and position of thermocouples ( T), hygrometer

( rh), pyranometer ( It) and product samples for moisture ( M).

39

5.3 Modeling

To facilitate the modeling of the dryer, the following assumptions are made.

These are: 1) there is no stratification of air inside the dryer; 2) drying calculation is

based on a thin layer drying model and 3) specific heat of air, cover and product is

constant.

Heat and mass transfer is schematically shown in Fig. 5.4 and heat and mass

balances are formulated as follows.

ConvectionRadiationConduction

Vout

Vin Vin

Polycarbonatecover

hr,c-s

hr,p-c

hw

hc,c-a Tahc,p-a

hc,f-a

product

Concrete floor

Fan

Mass transfer

Mass transfer

Fig. 5.4 The schematic diagram showing heat and mass transfers

1) Energy balance of the cover

The balance of energy on the polycarbonate cover is considered as: Rate of

accumulation of thermal energy in the cover = Rate of thermal energy transfer

between the air inside the dryer and the cover due to convection + Rate of thermal

energy transfer between the sky and the cover due to radiation + Rate of thermal

energy transfer between the cover and ambient air due to convection + Rate of

thermal energy transfer between the product and the cover due to radiation + Rate of

solar radiation absorbed by the cover. The energy balance of the cover gives:

40

cc pc c c,c-a a c c r,c-s s c

c w am c p r,p-c p c c c t

dTm C =A h (T -T )+A h (T -T )

dt + A h (T -T )+A h (T -T )+A α I

(5.1)

where mc is mass of the cover (kg), Ac is the cover area (m2), Ap is the product area

(m2), hc,c–a is convective heat transfer coefficient between the cover and the air in the

greenhouse dryer (Wm-2K-1), hr,c–s is radiative heat transfer coefficient between the

cover and the sky (Wm-2K-1), hw is convective heat transfer coefficient between the

cover and ambient air due to wind (Wm-2K-1), hr,p–c is radiative heat transfer

coefficient between the product and cover (Wm-2K-1). Cpc is specific heat of cover

(Jkg-1K-1), Ta is the drying air temperature (K), Tc is the cover temperature (K), Ts is

the sky temperature (K), Tam is the ambient temperature (K), Tp is the temperature of

the product (K), It is the solar radiation (Wm-2), αc is the absorptance of the cover

(decimal).

2) Energy balance of the air inside the dryer

This energy balance can be written as: Rate of accumulation of thermal energy

in the air inside the dryer = Rate of thermal energy transfer between the product and

the air due to convection + Rate of thermal energy transfer between the floor and the

air due to convection + Rate of thermal energy gain of the air from the product due to

sensible heat transfer from the product to the air + Rate of thermal energy gained in

the air chamber due to inflow and outflow of the air in the chamber + Rate of over all

heat loss from the air in the dryer to the ambient air + Rate of energy absorbed by the

air inside dryer from solar radiation. The energy balance of the air inside the

greenhouse chamber gives:

aa pa p c,p-a p a f c,f-a f a

pp p pv p p a a out pa out a in pa in

c c am a

dTm C = A h T -T + A h T -T

dtdM

+ D A C α T -T + ρ v C T -ρ v C Tdt

+ U A T -T 1-F 1-α + 1-α F I A τp p p c ctf+

(5.2)

41

where ma is mass of the polycarbonate cover (kg), Cpa is specific heat of air in the

product (Jkg-1K-1), Af is floor area (m2), Ap is product area (m2), Mp is the moisture

content of product in the dryer model (db, decimal), ρa is density of air (kgm-3), vin is

inlet air flow rate (m3s-1), vout is outlet air flow rate (m3s-1), hc,p–a is convective heat

transfer coefficient between the product and the drying air (Wm-2K-1), hc,f–a is

convective heat transfer coefficient between the floor and the drying air (Wm-2K-1), Tf

is temperature of the floor (K), Tin is temperature of the air at the inlet air of the dryer

(K), Tout is temperature of the air at the outlet of the dryer (K), Cpv is the specific heat

of water vapour (Jkg-1K-1), Dp is the average distance between the cover and the

product (m), Fp is fraction of solar radiation falling on the product (decimal), Uc is

overall heat loss coefficient from the cover to ambient air (Wm-2K-1), τc is

transmittance of the cover (decimal), αp is absorptance of the product (decimal), αf is

absorptance of the floor (decimal).

3) Energy balance of the product

Rate of accumulation of thermal energy in the product = Rate of thermal

energy transfer between air and product due to convection + Rate of thermal energy

transfer between cover and product due to radiation + Rate of thermal energy lost

from the product due to sensible and latent heat loss from the product + Rate of solar

energy absorbed by the product. The energy balance on the product gives:

pp pg pl p p c,p-a a p p r,p-c c p

pp p p p pv a p p p t c c

dTm C + C M = A h T -T + A h T -T

dtdM

+ D A ρ L + C T -T + F α I A τdt

(5.3)

where mp is mass of product (macadamia nuts) (kg), Cpg is the specific heat of air in

the dryer (Jkg-1K-1), Cpl is the specific heat of liquid in the product (Jkg-1K-1), ρp is

density of product (kgm-3), Lp is the latent heat of evaporation of the product (Jkg-1).

4) Energy balance on the concrete floor

Rate of accumulation of thermal energy in the floor = Rate of convection heat

transfer between air in the dryer and the floor + Rate of conduction heat transfer

42

between the floor and the ground + Rate of solar radiation absorption on the floor.

The energy balance of the floor can be written as:

f

f pf f c,f-a a f f D,f-g g f p f t f cdT

m C = A h T -T + A h T -T + 1-F α I A τdt

(5.4)

where mf is mass of floor (kg), hD,f–g is conductive heat transfer between the floor and

the underground (Wm-2K-1), Cpf is specific heat of floor (Jkg-1K-1), Tg is ground

temperature (K).

5) Mass balance equation

The accumulation rate of moisture in the air inside dryer = Rate of moisture

inflow into the dryer due to entry of ambient air – Rate of moisture outflow from the

dryer due to exit of air from the dryer + Rate of moisture removed from the product

inside the dryer. The mass balance inside dryer chamber gives:

p

a in a in in out a out out p p ddMdHρ V = A ρ H v - A ρ H v + D A ρ

dt dt (5.5)

where ρd is density of the dried product (kgm-3), V is speed of the air (ms-1), Ain is

total cross-sectional area of the air inlets (m2), Aout is total cross-sectional area of the

air outlets (m2), H is humidity ratio (kgkg-1), Hin is humidity ratio of air entering the

dryer (kgkg-1), Hout is humidity ratio of the air leaving the dryer (kgkg-1).

5.4 Heat transfer and heat loss coefficients

Radiative heat transfer coefficient from the cover to the sky (hr,c-s) is calculated

as (Duffie and Beckman, 1991):

2 2

r,c-s c c s ch = ε σ(T + T )(T + T) (5.6)

43

where σ is Stefan-Boltzmann’s constant (Wm-2K-4), εc is the emittance of cover

(decimal). Radiative heat transfer coefficient between the product and the cover (hr,p-c)

is computed as (Duffie and Beckman, 1991)

2 2r,p-c p p c p ch = ε σ T + T T + T (5.7)

where εp is emissivity of the product (decimal). Convective heat transfer coefficient

from the cover to ambient due to wind (hw) is computed as (Watmuff et. al, 1977):

w wh = 2.8 + 3.0V (5.8)

where Vw is wind speed (ms-1). Convective heat transfer coefficient inside the solar

greenhouse dryer for either the cover or product and floor is computed from the

following relationship (Kays and Crawford, 1980):

a

c,f-a c,c-a c,p-ah

Nu Kh = h = h =

D (5.9)

Ka is thermal conductivity of air (Wm-1K-1). Dh is hydraulic diameter of the dryer (m).

Nusselt number (Nu) is computed from the Reynolds number (Re) by using the

following relationship (Duffie and Beckman, 1991):

0.8Nu = 0.0158Re (5.10)

The overall heat loss coefficient from the greenhouse cover (Uc) is computed from the

following relation:

cc

c

KU =

δ (5.11)

44

where Kc is thermal conductivity of insulation material (Wm-1K-1), δc is thickness of

the cover (m).

5.5 Thin layer drying equation

We conducted thin layer experiments in a laboratory dryer under controlled

conditions of temperature and relative humidity as described in chapter 2 and the

following thin layer drying equation was used for thin layer drying of macadamia

nuts:

e

0 e

M - M= Aexp(-Kt) + Bexp(-Gt) + Cexp(-Pt)

M - M (5.12)

where M(decimal, db) is the product moisture content at time t (hour), M0 (decimal,

db) is initial moisture content, Me(decimal, db) is the equilibrium moisture content.

The drying parameters k, a, b, c, g and p are given as:

k = - 1.52690+0.04227T + 0.06273rh + 0.00022Trh - 0.00039T2

- 0.00172rh2 (5.13)

a = 0.230723 + 0.021691T - 0.083943rh + 0.000227Trh - 0.000065T2

+ 0.002117rh2 (5.14)

b = 1.449237 + 0.014082T - 0.187288rh + 0.000369Trh - 0.000097T2

+ 0.003759rh2 (5.15)

c = 1.204763 - 0.077930T + 0.062076rh + 0.000488Trh + 0.000881T2

- 0.001223rh2 (5.16)

g = 1.306501 - 0.043473T - 0.047035rh + 0.000092Trh + 0.000524T2

+ 0.001292rh2 (5.17)

p = - 0.604983 + 0.059075T - 0.080746rh - 0.000750Trh - 0.000267T2

+ 0.002314rh2 (5.18)

45

where T is temperature (°C) and rh is relative humidity (%).We also conducted

experiments to determine the equilibrium moisture content (Me) under controlled

conditions of temperature and relative humidity as explained in chapter3. The result is

written as:

w 8.60964

e

1a = 42.18947 - 0.24723T1 +

M

(5.19)

where T is temperature (°C) and aw is water activity (decimal). The water activity is

equal to the relative humidity in percent divided by 100.

5.6 Solution procedure

The system of (5.1-5.5) is solved numerically using the finite difference

technique. On the basis of the drying air temperature and relative humidity inside the

drying chamber, the drying parameters k, a, b, c, g, and p and the equilibrium

moisture content (Me) of the product are computed. Using the k, a, b, c, g, p and Me

values, the change in moisture content of the product, ∆M for a time interval ∆t are

calculated using (5.12). Next, the system of equations consisting of (5.1-5.4) is

expressed in the following form for the interval ∆t:

c11 12 13 14 1

a21 22 23 24 2

p31 32 33 34 3

41 42 43 44 4f

Ta a a a bTa a a a b

=Ta a a a b

a a a a bT

(5.20)

This system of equations is a set of implicit calculations for the time interval ∆t.

These are solved by the Gauss–Jordan elimination method using the recorded values

for the drying air temperature and relative humidity, the change in moisture content of

the product (∆M) for the given time interval. The process is repeated until the final

time is reached. The numerical solution was programmed in Compaq Visual

FORTRAN version 6.5.

46

5.7 Colour measurement of dried macadamia nuts (Janjai et. al, 2011)

The colour of dried macadamia nut samples was measured by a chromometer

(CR-400, Minolta Co., Ltd., Japan) in Commission Internationale d’Eclairage (CIE)

chromaticity coordinates. The instrument was standardized each time with a white

ceramic plate. Three readings in term of lightness (L*), a* (green to red), and b* (blue

to yellow) were taken at each place on the surface of samples and then the mean

values of L*, a* and b* were averaged. The different colour parameters were

calculated using the following equations (Camelo and Gomez, 2004). Hue angle (h)

indicating colour combination is defined as:

-1 * *

o -1 * *

tan (b /a ) (when a* > 0)h =

180 + tan (b /a ) (when a* < 0) (5.21)

and chroma (C*) indicating colour saturation is defined as:

2 2* * * 1/2C = (a + b ) (5.22)

The colour of macadamia kernel from greenhouse solar dryer was measured for

comparison with dried kernel using box type dryer, heated by Liquefied Petroleum

Gas (LPG). The box type dryer is usually used by dried macadamia nut producers in

Thailand.

5.8 Economic analysis (Janjai, 2012 )

The total capital cost for the solar dryer (CT) is given by the following

equation:

T m lC = C + C (5.23)

where Cm is the material cost of the dryer and Cl is the labour cost for the

construction. The annual cost calculation method proposed by Audsley and Wheeler

47

(Audsley and Wheeler, 1978) was used. According to this method, the annual cost can

be expressed as:

N

iannual T maint,i op,i N

i=1

- 1C = C + C + C -1

(5.24)

where Cannual is the annual cost of the system. Cmaint,i and Cop,i are the maintenance cost

and the operating cost of the year i, respectively. is expressed as:

in f = 100 + i 100 + i (5.25)

where iin and are if the interest rate and the inflation rate in percent, respectively. The

operating cost (Cop) is the labour cost for operating the dryer (Clabour,op).

The maintenance cost of the first year was assumed to be 1% of the capital cost.

The annual cost per unit of dried product is called the drying cost (Z, USDkg-1). It can

be written as:

annual

dry

CZ =

M (5.26)

where Mdry is the dried product obtained from this dryer per year.

The payback period was calculated from the following equation:

T

dry d f f dry

CPayback period = M P - M P - M Z

(5.27)

where Mdry is annual production of dry product (kg), Mf is the amount of fresh

product per year (kg). Pd is the price of the dried product (USDkg-1) and Pf is the

price of the fresh product (USDkg-1).

48

5.9 Results and discussion

5.9.1 Experimental results

Six experiment batches were carried out during June, 2013 - February, 2014,

each season. The typical results are shown in Fig. 5.5 – Fig. 5.8.

Solar radiation was strongly fluctuated in the experimental days shown in Figure

5.5. Air temperature at three different locations inside the dryer and the outside

ambient air temperature have different amplitudes of their fluctuation shown in Fig.

5.6. The pattern of temperature inside the dryer at different positions was comparable

for all locations. Temperatures in these three positions varied between 30-65 °C.

Temperatures at each of the locations inside the dryer differed significantly from the

ambient air temperature.

Relative humidity at two different positions inside the dryer is lower than the

outside ambient air relative humidity with the same pattern of variation (Fig. 5.7).

Relative humidity decreased over time at different locations inside the dryer during

the first half of the day while the opposite is true for the other half of the day. No

significant difference was found between relative humidity of different positions

inside the dryer. However, there was a significant difference in relative humidity for

all locations inside the dryer compared to relative humidity of the ambient air. The

relative humidity of the air inside the dryer was lower than that of the outside ambient

air. Hence, the air leaving the dryer had lower relative humidity than that of the

ambient air. This indicated that the exhaust air from the dryer still had drying

potential for recirculation to dry the product. The moisture content of macadamia nuts

in the solar dryer was reduced from an initial value of 14-16% (wb) to a final value of

2-3% (wb) in 5 days (Fig. 5.8).

49

0

200

400

600

800

1000

1200

1400

8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:0016:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00

Time(hr)

Sola

r rad

iatio

n(W

/m2 )

28/06/2013 29/06/2013 30/06/2013 02/07/201301/07/2013

Fig. 5.5 Variation of solar radiation with time of the day during drying of

macadamia nuts

0

10

20

30

40

50

60

70

8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00

Time(hr)

Tem

pera

ture

( o C)

T3T11T19Ambient

28/06/2013 29/06/2013 30/06/2013 02/07/201301/07/2013

Fig. 5.6 Variation of ambient temperature and the temperature at different

positions inside the greenhouse solar dryer during drying of

macadamia nuts

0

10

20

30

40

50

60

70

80

90

100

8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00 8:00 10:00 12:00 14:00 16:00 18:00

Time (hr)

Rel

ativ

e hu

mid

ity (%

).

AmbientInsideOutlet

28/06/2013 29/06/2013 30/06/201302/07/201301/07/2013

Fig. 5.7 Temporal variation of ambient relative humidity and relative humidity

inside the greenhouse dryer during drying of macadamia nuts

50

0

2

4

6

8

10

12

14

16

18

8:00 10:00 12:00 14:00 16:00 18:00 9:00 11:00 13:00 15:00 17:00 8:00 10:00 12:00 14:00 16:00 18:00 9:00 11:00 13:00 15:00 17:00 8:00 10:00 12:00 14:00 16:00 18:00

Time (hr)

Moi

sture

con

tent

(%,w

b).. M1

M2M3M4M5M6

28/06/2013 29/06/2013 30/06/2013 01/07/2013 02/07/2013

Fig. 5.8 Temporal variation of the moisture contents of macadamia nuts at

different positions inside the greenhouse dryer

5.9.2 Colour change

The colour of dried macadamia kernels was measured using the chromometer

(CR-400, Minolta Co. Ltd, Japan). The colour of the kernel of macadamia nuts dried

using the greenhouse solar dryer was compared with that of the kernel of macadamia

nuts dried employing the box type dryer (Table 1). The colour of macadamia kernels

changed from white to lightcream(L*=71.61) after having dried using the greenhouse

dryer. The colour of the kernels dried using the box type dryer is dark-yellow-brown

(L*=58.76). This comparison indicated that macadamia nuts dried using the

greenhouse dryer has better colour than that dried employing the box type dryer.

5.9.3 Food quality

In general, the total fat is the most important parameter indicating food quality

of macadamia nuts and the good quality macadamia nuts have to have a total fat in the

range of 72.0-78.0 g (100g)-1 (Salwin, 1959) and (Borompichaichartkul at el., 2009).

The total fat of the macadamia nuts dried by using the greenhouse solar dryer is 75.2

g(100g)-1 which implies that these macadamia nuts are in good quality .

51

Table 5.1 Comparison of the colour kernel of macadamia nuts dried using the

greenhouse solar dryer and that dried employing the box type dryer

Drying method Colour value

L* a* b* C* h

Greenhouse solar dryer 71.61 0.13 20.23 20.23 1.56

Box type dryer 58.76 0.17 17.23 17.23 1.56

5.9.4 Economic result

As there are now several units of this type of dryer being used for production of

dried macadamia nuts, information used for economic evaluation is based on the field

level data and recent prices of the materials used for construction of the dryers. Data

on costs involved and economic parameters are shown in Table 5.2.

Table 5.2 Data on cost and economic parameter

Items costs and economic parameters

Polycarbonate sheets Solar modules and fans Materials of constructions Labour costs for constructions Repair and maintenance cost Operating cost Price of fresh in shell macadamia nuts Price of dried macadamia kernels Expected life of the dryer Interest rate Inflation rate

2,257 USD 450 USD 1,285 USD 571 USD 1% of capital cost per year 171 USD per year 2.03 USD per kg 26.59 USD per kg 15 years 7.3% 2.5%

The dryer can be used for 6 months per year for drying macadamia nuts and

approximately 3,250 kg of dried macadamia kernel is annually obtained. Based on

this production and the capital and operating costs of the dryer (Table 5.2), the drying

cost (Z) is estimated to be 0.367 USDkg-1 and the payback period is calculated to be

approximately 1 year.

52

5.9.5 Modeling result

The model predicts well the variation of the moisture content during the drying

(Fig. 5.9). Predicted temperature shows plausible behavior, and the predicted and the

observed values are in good agreement (Fig. 5.10).

The model predictions for drying macadamia nuts were evaluated using root

mean square difference (RMSD). The RMSD from overall comparison of the

simulated temperature in the dryer is 11.8%. The RMSD from overall comparison of

the simulated moisture contents is 1.9%. These comparisons indicate that the

simulation model can predict the moisture content and the temperature with a

reasonable accuracy.

0

2

4

6

8

10

12

14

16

8:00 11:00 14:00 17:00 9:00 12:00 15:00 18:00 10:00 13:00 16:00 8:00 11:00 14:00 17:00 9:00 12:00 15:00 18:00

Time (hr)

Moi

ture

con

tent

(%,w

b)..

ExperimentSimulation

28/06/2013 29/06/2013 30/06/2013 01/07/2013 02/07/2013

Fig. 5.9 Comparison between the simulated and observed moisture content

during drying macadamia nuts at the middle of the dryer for a typical

experimental run.

53

0

10

20

30

40

50

60

70

8:00 12:00 16:00 8:00 12:00 16:00 8:00 12:00 16:00 8:00 12:00 16:00 8:00 12:00 16:00Time (hr)

Tem

pera

ture

(๐C

)

ExperimentSimulation

28/06/2013 29/06/2013 30/06/2013 01/07/2013 02/07/2013

Fig. 5.10 Comparison between the simulated and observed temperatures inside

the greenhouse dryer at the middle position during drying macadamia

nuts for a typical experimental run.

5.10 Conclusions

The system of partial differential equations for heat and moisture transfer has

been used for simulation of solar drying of macadamia nuts in the solar greenhouse

dryer. From the validation, the simulated air temperature inside the dryer reasonably

agreed with the measured temperature. Good agreement was found between the

experimental and simulated moisture contents. Simulation using this method is useful

for providing data for further design of solar greenhouse dryers.

Solar radiation has high variation through the experiment days. Sinusoidal-like

around the peak at noon, the solar radiation influences other ambient parameters of

the macadamia. Inside the greenhouse dryer, air temperature variation follows the

variation of the solar radiation. The ambient relative humidity varies almost the

inverse pattern with the solar radiation. The dried macadamia nuts using the solar

greenhouse dryer are high-quality product. The estimated payback periods for drying

macadamia nuts using this greenhouse solar dryer is about 1 year.

Chapter 6

Conclusions In this work, thin layer drying, sorption isotherm, diffusivity and finite

element simulation of macadamia nuts were investigated. In addition, the performance

of a greenhouse solar dryer for drying macadamia nuts was also examined. The results

of the investigation are as follows.

1) Thin-layer drying of macadamia nuts was investigated in this study and the

drying rate increases with the increase of air temperatures. Seven thin-layer

drying models were fitted to the experimental data of in shell nuts and kernel

nuts to describe the drying characteristics of macadamia nuts. In addition,

Modified Handerson and Pabis model was found to be the best model to

predict the moisture content of thin layer drying macadamia nuts.

2) The equilibrium moisture contents of macadamia nuts have been determined

experimentally using the gravimetric method. Five sorption isotherm models

were used to fit the experimental data of macadamia nuts. Among them,

modified Oswin model fitted the best to the experimental data. This model is

suggested for use in drying of macadamia nuts.

3) Diffusivity of macadamia nut has been experimentally determined. It was

found that the diffusivity of the nuts increased with temperature.

4) A two-dimensional finite element model has been developed to simulate

moisture diffusion in macadamia nuts during drying. The simulation results

revealed the moisture content inside the macadamia nut. This model can be

used to provide information on the dynamics of moisture movement without

the need for measurements and design data. Furthermore, the model provides a

better understanding of the transport processes inside the macadamia nuts.

5) The performance of greenhouse solar dryer for drying macadamia nuts has

been evaluated. The experimental results showed that the drying time of

macadamia nuts in this greenhouse solar dryer is significantly shorter than that

of the natural sun drying and good quality dried product was obtained.

54

55

Additionally, a system of partial differential equations describing heat and

moisture transfer during drying of macadamia nuts was developed and the

simulated results agreed well with the experimental data. Simulation using this

method is useful for providing data for further design of solar greenhouse

dryers.

For the future work, it is recommended that moisture distribution in side the

macadamia nut be measured with advanced instruments to validate the finite element

simulation.

56

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Appendixes

61

Appendix 1

Parts of this thesis have been published international journals and conference

proceedings as follows:

1. Phusampao C.; Nilnont W.; Janjai S. (2014). Performance of a Greenhouse Solar

Dryer for Drying Macadamia Nuts. Proceedings of the International Conference

and Utility Exhibition 2014 on Green Energy for Sustainable Development, 19-21

March 2014, Pattaya city, Thailand.

2. Janjai S.; Phusampao C.; Nilnont W.; Pankaew P. (2014). Experimental

performance and modeling of a greenhouse solar dryer for drying macadamia nuts.

International Journal of Scientific & Engineering Research, Volume 5, Issue 6,

115-1161, (impact factor 3.2).

3. Janjai S.; Phusampao C.; Nilnont W.; Boonrod Y.; Mahayothee B. (2014).

Modeling a large scale greenhouse solar dryer for drying macadamia nuts.

Proceeding of the International Drying Symposium. 24-27 August 2014, Lyon,

France.

4. Phusampao C.; Pankaew P.; Nilnont W.; Janjai. Thin layer drying of macadamia

nut. (2015). Proceeding of the 53th Annual Conference of Kasetsart University, 3-6

February 2015, Bangkok, Thailand.

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Appendix 2

Nomenclature

A parameter of thin layer equation (-)

Ac collector area (m2)

[A] intermediate parameter matrix (-)

a* parameter in the colour measurements (-)

a parameter in thin layer drying models (-)

aw water activity (-)

B parameter of thin layer equation (-)

b parameter in thin layer drying models (-)

b0, b1, b2 parameter in equilibrium moisture content models (-)

C* colour parameter for chroma (-)

Ca specific heat of air (J/kg –K)

Cannual annual cost of the system (USD/year)

Cb specific heat of absorber material (J/kg –K)

Cf specific heat of air (J/kg –K)

C1 labour cost for the construction (USD)

Clabour ,op labour cost for operating the dryer (USD/year)

Cm material cost of the dryer (USD)

Cmant maintenance cost (USD/year)

Cop,i operating cost (USD/year)

Cp specific heat of peeled longan (J/kg –K)

Cv specific heat of water vapour (J/kg –K)

CT the total capital cost for the solar dryer (USD)

Cv specific heat of water vapour (J/kg –K)

Cw specific heat of water (J/kg –K)

[C] global capacitance matrix (-)

[c] element capacitance matrix (-)

c parameter in thin layer drying models (-)

D diffusivity of macadamia nut (m2/s)

Dh hydraulic diameter of the collector (m)

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Deff effective diffusivity (m2/s)

Dflesh diffusivity of flesh (m2/s)

d diameter of macadamia nut (m)

Dair diffusivity of air (m2/s)

{F} global load force vector (-)

{F*} intermediate parameter vector (-)

{f} element load force vector (-)

Gmass flow rate of air (kg/s –m2)

g parameter in thin layer drying models (h-1)

H humidity ratio (kg/kg)

h colour parameter for hue angle (degree)

hfg latent heat of vaporization of moisture from macadamia nut (J/kg)

hr,b-c radiative heat transfer coefficient between the cover and the absorber

(W/m2 –K)

hc,b-f convective heat transfer coefficient between the absorber and the air

(W/m2 –K)

hc,c-f convective heat transfer coefficient between the cover and the air (W/m2 –K)

hc,p-f convective heat transfer coefficient between the product and the air (W/m2 –K)

hm mass transfer coefficient (m/s)

hr,c-s radiative heat transfer coefficient between the cover and the sky (W/m2 –K)

hr,p-c radiative heat transfer coefficient between the cover and the product

(W/m2 –K)

hv volumetric heat transfer coefficient (W/m3 –K)

hw convective heat transfer coefficient between the cover and the ambient due to

wind (W/m2 –K)

It incident solar radiation (W/m2)

[K] global stiffness matrix (-)

[k] element stiffness matrix (-)

k drying rate constant (h-1)

k1 drying rate constant in Page model (h-n)

ka thermal conductivity of air (W/m –K)

kb thermal conductivity of back insulator (W/m –K)

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ini interest rate (%)

fi inflation rate (%)

L* parameter in the colour measurements (-)

Lp latent heat of evaporation of product (J/kg)

Lb thickness of back insulator (m)

M moisture content of macadamia nut (%, db)

Mo initial moisture content of the components of macadamia nut (%, db)

Mdry annual production of dry product (kg)

Me equilibrium moisture contents of macadamia nut (%, db)

Mf amount of fresh product per year (kg)

Mi initial moisture content of longan on a dry basis (%, db)

Mobs observed or experimental moisture content (%, db)

Mpre predicted moisture content (%, db)

MR moisture content ratio (-)

Ms surface moisture content on a dry basis (%, db)

ma mass flow rate of air (kg/m2 –s)

[N] matrix of interpolating function (-)

Nu Nusselt number (-)

n magnitude of the outward normal vector to the surface (-)

n integer number of the infinite series, n=1, 2, 3,……..

n empirical constant in Page and modified Page model (-)

[P] intermediate parameter matrix (-)

Pd price of the dry product (USD/kg)

Pf price of the fresh product (USD/kg)

p parameter in thin layer drying models (h-1)

R2 coefficient of determination (-)

R coefficient of determination (%)

R0 universal gas constant (J/mol-K)

Re Reynolds number (-)

RMSE root mean square error (%)

r radius of the cylindrical seed stalk (m)

rh relative humidity (%)

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rl2 norm radius of macadamia nut (m)

ro radius of seed (m)

S cross sectional area (m2)

Sc Schmidt number (-)

T temperature (ºC)

Tab absolute temperature (K)

Ta ambient temperature (K)

Tb temperature of the absorber (K)

Tc temperature of the collector cover (K)

Tc1 temperature of the cover of the drying unit (K)

Tp product temperature (K)

Ts sky temperature (K)

t time (h)

u air velocity (m/s)

Va wind velocity (m/s)

Z drying cost (USD/kg)

z half thickness of the slab ( shell, flesh and seed coat ) (m)

∆t time step (s)

μ viscosity of air (kg/m/s)

Ω fruit domain (-)

operatorx y z

αb absorbtance of the absorber (-)

αc absorbtance of the cover material (-)

αn roots of the Bessel function of zero order, n= 1, 2, 3,……

αp absorbtance of macadamia nut (-)

δb thickness of the absorber (m)

δc thickness of the cover (m)

ρb density of the absorber material (kg/m3)

ρair density of air (kg/m3)

ρc density of the cover material (kg/m3)

ρs,p density of the macadamia nut (kg/m2)

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σ Stefan Boltzmann’s constant (W/m2-K4)

τc transmittance of the cover material (-)

(τα) transmittance-absorptance product of the system composing of the cover and

absorber (-)

εc emissivity of the cover material (-)

εb emissivity of the absorber material (-)

υ viscosity of air (m2/s)

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Autobiography

Name : Chayapat Phusampao

Sex : Male

Date of birth : 25 October 1980

Address : 102 M. 5 T. Nakam A. Muang, Loei, 42100

Education

2003 Bachelor of Science (Physics) Mahasarakham University,

Mahasarakham, Thailand

2009 Master of Engineering (Energy), Graduate School

Chaingmai University, Thailand