selected topics in heat and mass transfer

8/10/2019 Selected Topics in Heat and Mass Transfer

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Selected Topics in heat and MassTransport

Jundika Candra KurniaAgus Pulung Sasmito

Sachin Vinayak Jangam

Hee Joo Poh

..A compilation of selected presentations

2011


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PREFACE

This e-book consists of selected topics to be covered as part of the postgraduate

course entitled ME6203 Mass Transport in the Mechanical Engineering Department ofthe National University of Singapore, given by Professor A. S. Mujumdar.

For the benefit of wider audience interested in the themes covered, this e-book is

being offered freely. It contains handouts of the PowerPoint presentations made by the

authors. We hope that this compilation will be useful to research students as well as

researchers in academia and industrial R&D. Professor Mujumdar recommended and

provided guidance to the authors of various chapters included in this e-book.

The authors would be happy to hear from readers about any related matter they

wish to discuss or seek clarification on.

Jundika Candra Kurnia

Agus Pulung Sasmito

Sachin Vinayak jangam

Hee Joo Poh

Singapore


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Index

Presentation

No

Title / Author names

01 Heat Transfer in Square duct

Jundika C. Kurnia

02 Computational Study of Energy-Efficient Thermal Drying Using

Intermittent Impinging Jets

Jundika C. Kurnia

03 Mass transport in a micro-channel T-Junction with coiled-base

channel design

Agus P. Sasmito

04 Mass Transport Considerations in PEM Fuel Cell ModelingHee Joo Poh

05 Heat Transfer in Fluidized Beds-An Overview

Sachin V. Jangam

06 Mass Transfer in Fluidized Beds - An Overview

Sachin V. Jangam


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Heat Transfer in

Square duct


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Heat Transfer in Square Duct

Prof. Arun S. Mujumdar

[email protected]

ME 6204: Convective Heat Transfer

Mathematical formulation

Governing equations:

Conservation of mass

Conservation of momentum

Conservation of energy

Constitutive equation (air)

Density Dynamic viscosity

Thermal conductivity

Specific heat

For water, properties are set

as constant

( ) 0 =u

( )( )( ) P = + + u u u u2

pc T k T = u

,absspecific

P

R T= ( )

6

2.67 10 ,MT

T

=

15 4 1,

4 15 3

pc MR

kM R

= +

.pR

cM

=

Pabs = Absolute pressure

Rspecific= Specific gas constant

cp = specific heat

= Collision diameter

= Collision integral

M = molecular weight

Nomenclature:

= fluid density

= fluid viscosity

u = fluid velocity

T = fluid temperature

kt = fluid thermal conductivity


10/196

Mathematical Formulation

Turbulent model used in this simulation is k-model

3

( )

( )2

12

2 2 22 2 2

,

,

2 ,

tt

k

t t

k

t

kk k G

t

C GC

t k k

u v w u v u w w vG

x y z y x z x y z

+ = + +

+ = + +

= + + + + + + + +

u

u

2

,

k

C =

C1= 1.44

C2= 1.92

C = 0.09

k = 1.0

= 1.0

Nomenclature:

u, v, w = component velocity

t= turbulent viscosityk = turbulent kinetic energy

= turbulent dissipationG = turbulent generation rate

Mathematical Formulation

Nusselt number calculation

4

= Nusselt number

= Hydraulic diameter

= Conductive heat transfer

= mixed mean velocity

Nomenclature:

= mixed mean temperature

= surface temperature

= cross-section area

= convective heat transfer

= heat flux

1,

1,

,

c

c

mean c

c A

cc A

surf ace m ean

T T dAVA

V dAA

Qh

T T

hDNu

k

=

=

=

=

u

u

&

meanT

surfaceT

cA

hQ

NuD

kV


11/196

Geometry

The flow configuration considered is full tubeflow inside square duct, as illustrated in figure

5

Schematic representation of flow in a) square duct and b) development

of a momentum boundary layer

Numerics

Finite-volume based solver: Fluent 6.3.

Mesh independence study ~10000 cells.

Pressure velocity coupling: SIMPLE (Semi-Implicit

Method for Pressure-Linked Equation).

Second-order upwind discretization.

Algebraic Multi-grid Method (AMG).

Relative residual ~10-6.

It took around one minute to converge in Quad-core 2.83

GHz with 8 GB RAM.

CFD analysis was carried out by Agus Pulung Sasmito

and Jundika Candra Kurnia (ME, NUS)

6


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7

LAMINAR FLOW

Boundary condition

Air Case 1: Constant heat flux at

wall

Inlet: air velocity = 1.6 m/s; T

air = 25 C.

Wall: no-slip; Q = 30 watt/m2.

Outlet: Pout = 1 atm; Q=0.

Re 1000.

Case 2: Constant wall

temperature


air = 25 C.

Wall: no-slip; T wall = 50 C.


Re 1000.

Water Case 3: Constant heat flux at

wall

Inlet: water velocity = 0.1 m/s;

T water = 25 C. Wall: no-slip; Q = 2870

watt/m2.


Re 1000.


temperature

Inlet: water velocity = 0.1 m/s;

T water = 25 C.



Re 1000.8


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Velocity in the middle channel

9

Water (Cases 3 and 4)

Air (Cases 1 and 2)

Temperature in the middle of the channel

10

Air (Case 1) Air (Case 2)

Water (Case 3) Water (Case 4)


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Temperature in the wall of the channel

11

Water (Case 3)

Air (Case 1)

Heat flux at the wall

12

Water (Case 4)

Air (Case 2)


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Nusselt Number

13

Water (Cases 3 and 4)Air (Cases 1 and 2)

Nusselt number asymptotic

Case 1: 2.8

Case 2: 2.7

Case 3: 2.7Case 4: 2.2

Wall and Mean temperature

14




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15

TURBULENT FLOW WITHRE=20000

Boundary condition


wall

Inlet: air velocity = 30 m/s; T

air = 25 C.



Re 20000.


temperature


air = 25 C.



Re 20000.


wall

Inlet: water velocity = 2 m/s; T

water = 25 C. Wall: no-slip; Q = 170370

watt/m2.


Re 20000.


temperature


water = 25 C.



Re 20000.16


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17


Air (Cases 1 and 2)


18




18/196


19

Water (Cases 3)

Air (Cases 1)


20

Water (Cases 4)

Air (Cases 2)


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Nusselt Number

21



Case 1: 45

Case 2: 34

Case 3: 623

Case 4: 127


22




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23

TURBULENT FLOW

WITH Re=60000

Boundary condition


wall


air = 25 C.

Wall: no-slip; Q = 1272

watt/m2.


Re 60000.


temperature


air = 25 C.



Re 60000.


wall


water = 25 C. Wall: no-slip; Q = 433879

watt/m2.


Re 60000.


temperature


water = 25 C.



Re 60000.24


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25


Air (Cases 1 and 2)


26




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27

Water (Cases 3)

Air (Cases 1)


28

Water (Cases 4)

Air (Cases 2)


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Nusselt Number

29



Case 1: 105

Case 2: 67

Case 3: 1700Case 4: 314


30




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Summary of heat transfer calculation

31

Air (Laminar) Water(Laminar)

Air (Turbulent Re 20000) Water (Turbulent Re 20000)

32

LAMINAR FLOW WITH VARIABLE T

and Q BOUNDARY condition


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Boundary conditions-Variable T,Q

33

Air Constant heat flux at wall


air = 25 C.



Re 1000.

Constant wall temperature


air = 25 C.


Outlet: Pout = 1 atm; Q=0. Re 1000.

Temperature distribution

34

Distance from entrance: 5 cm Distance from entrance: 25 cm


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Temperature distribution

35

Distance from entrance: 50 cm Distance from entrance: 100 cm

36

LAMINAR FLOW WITH

HEATING/COOLING


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Boundary condition

Case 1: Heating

Inlet: air velocity = 1.6 m/s; T air = 25 C.

Wall: no-slip; T wall = 50 C, 100 C, 200 C.


Re 1000.

Case 2: Cooling

Inlet: air velocity = 1.6 m/s; T air = 50 C, 100 C,200 C.

Wall: no-slip; T wall = 25 C. Outlet: Pout = 1 atm; Q=0.

Re 1000.

37

Nusselt number distribution in entry length

38

Heating Cooling


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39

LAMINAR FLOW WITH BOUYANCY

Boundary condition

Laminar flow (Air)

Boundary conditions

Inlet: air velocity = 0.15 m/s;

T air = 25 C.



Re 100.

Case 1: No gravity force

Case 2: Horizontal placement

Case 3: Tilted 45 Case 4: Vertical placement

Gravity force is applied for

case 2, 3 and 4.

40


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Velocity at entry region (z=2.5 cm)

41

Case 1 Case 2

Case 3 Case 4

Temperature at entry region (z=2.5 cm)

42

Case 1 Case 2

Case 3 Case 4


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Velocity at z= first 10 cm

43

Case 2

Case 1

Case 3

Case 4

Temperature at z= first 10 cm

44

Case 2

Case 1

Case 3

Case 4


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Nusselt number

45

46TAPERED DUCT


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Boundary condition

47

Laminar flow (Air)Case 1: Divergent duct

Inlet: air velocity = 16

m/s;

T air = 25 C. Wall: no-slip; T wall = 50

C. Outlet: Pout = 1 atm;

Q=0.

Re 1000.

Case 2: Convergent duct

Inlet: air velocity = 0.16

m/s; T air = 25 C. Wall: no-slip; T wall = 50

C. Outlet: Pout = 1 atm;

Q=0. Re 1000.


48

Convergent duct (Case 2)

Divergent duct (Case1)


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Temperature in the middle channel

49

Convergent duct (Case 2)

Divergent duct (Case1)

Nusselt number

50


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51

POWER LAW FLUID

Boundary condition

52

Power law fluid

1

1

eff

eff

where:

= flow consistency index ( )

= shear rate or the velocity gradient ( )

= flow behaviour index

= apparent or effective viscosity ( )

n

n

n

uK

y

K Pa s

us

y

n

uK

y

Pa s

=

=

Laminar flow (Air)

Case 1 (Pseudoplastic n=0.5)


air = 25 C.



Case 2 (Dilatant n=1.5)


air = 25 C.



n Type of fluid

1 Dilatant


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53

Dilatant (Case 2)

Pseudoplastic (Case1)


54

Dilatant (Case 2)

Pseudoplastic (Case1)


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Nusselt number

55

56

PULSATING FLOW


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Boundary condition

Case 1 (Frequency = 5 Hz)

Inlet: air velocity = Vin; T air =

25 C.



Re 1000.

Case 2 (Frequency = 10 Hz)

Inlet: air velocity = Vin; T air =

25 C.



Re 1000.

57


58

0 s 0.05 s

0.1 s 0.15 s

Case 1 (frequency 5 Hz)


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59

0 s 0.05 s

0.1 s 0.15 s



60

0 s 0.01 s

0.02 s 0.03 s



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61

0.04 s 0.05 s



62


0 s 0.01 s

0.02 s 0.03 s



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63


0.04 s 0.05 s


Average Nusselt number

64


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Summary

Flow inside square duct has been simulated for variety ofBCs and for buoyancy effect.

Several cases - laminar and turbulent flow are

considered

Cooling/heating, buoyancy effect, power law fluid,

tapered duct and pulsating inlet flow have also been

simulated; no analytical solution possible

Heat transfer distributions are calculated

65

References

W. Kays, M. Crawford, B. Weigand, Convective

heat and mass transfer 4th Edition, McGraw-Hill,

2005.

S. Kakac and Y. Yener, Convective Heat

Transfer, Hemisphere Pub, 1982.

A. Bejan, Convection heat transfer, Wiley, 2004.

F. P. Incropera and D. P. Dewitt,Fundamentals

of Heat and Mass Transfer, 5th Edition, Wiley,

2001.

J. H. Leinhard IV and J. H. Leinhard V,A Heat

Transfer Textbook, 3rd edition, 1980.66


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Computational Study ofEnergy-Efficient Thermal

Drying Using Intermittent

Impinging Jets


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1

Computational Study of Energy-Efficient

Thermal Drying Using Intermittent

ME 6203 Mass Transport

Impinging Jets

Prof. Arun S. Mujumdar

Email: [email protected]

Tel: +65-6516-4623, Fax: +65-6777-6235

2011

Guest lecturer

Jundika Candra Kurnia

Department of Mechanical Engineering

National University of Singapore

Outline

Overview of drying

Physical model

Problem description

Key assumptions

Numerical methodology Selected results

Case study

Velocit contours

Temperature contours

Drying kinetics

Summary

Q&A 2


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2

Drying Widely known as the most common way to preserve food

Essential operation in chemical, agricultural, biotechnology, food,

Overview

, , , ,

processing and wood processing industries

Involves simultaneous transport process

Transport processes in drying:

Mass transfer

Heat transfer

Flow

Occur simultaneously both internally and externally Induces deformation:

Shrinkage

Cracking

(Not modeled here) 3

Impinging jet drying

Various drying methods are available for

different material

One of this method is impinging jet drying

Offer high transport rate (mass and energy)

Effective for drying of continuous sheets (paperdrying); discrete flat/curved objects.

Impinging jets, however, have several

drawbacks

Non-uniform drying

High energy consumption compare to parallel flow

Further study in impinging jet drying is required

Pulsating jet is proposed to speed up drying kinetics

Not commonly used yet4


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3

Physical ModelAn orifice nozzle is used in this study- Axisymmetric case

55

Substrate dried is a potato chip. It is placed in a drying chamber under one

impinging jet. Pulsating and intermittent flow is applied on the inlet

Physical model

The aforementioned condition can be brought into computational domain as follows

6

Inlet

45

fixed pulsating and intermitent

17.5%

in

in

in

T C

V

RH

Drying chamber

0.4

0.02

L m

z m

Substrate dimension (chip)

30

0.5 and 5

s

s

L mm

H mm


48/196

4

What phenomena occur during drying?

Transport mechanism of mass? Energy?7

Physical model

moisture diffusion from the inner drying

Basic mechanisms

,

evaporates

conductive heat transfer within the drying

substrate

eva oration and convection of the va or

from the surface of the drying substrate

into the drying air

convection heat transfer from drying air to

the surface of the drying substrate 8


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5

Why do we need assumptions?

What are the key assumptions?

Comment on validity of assumptions?

9

Assumptions

The drying substrate is compact and homogeneous with uniform

initial tem erature and moisture content.

In developing the mathematical model, several assumptions are

made- some for simplicity

Within the drying substrate, the diffusivity of water vapor is 100

times larger than the diffusivity of liquid water.

The thermophysiscal properties of the drying substrate aretemperature and moisture content-dependent and isotropic (equal in

all directions).

Variations in dependent variables in span wise direction are

,

height (reduction in dimensionality from three to two dimensions).

The shape of the drying substrate remains constant. No shrinkage

or deformation is accounted for.

Newtonian fluid

10


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6

How to translate these physical phenomena intomathematical model?

What conservation equations do we need to model

e p ys ca p enomena

Do we need more information?

11

Conservation equations

Conservation of

For drying substrate (chip)

lc

Transient term (time dependent)

Diffusion

Liquid water

Water vapor

,

,

lb l l

vvb v l

t

c

D c Kct

Evaporation

Transient term (time dependent)

Diffusion

energy

12

b pb bT

c k T qt

Transient term (time dependence; heat capacity)

Conduction

Cooling due toevaporation


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7

Conservation equation

Mass

For drying air (Impinging jet) unsteady case

0, u For incompressible fluidInertia/net rate Viscous

Momentum

Energy

' ,a apt

uu u u - u

' ' ,a pa a a paT

c T k T c T t

u u

Pressure gradient

ass o

water vapor

13

,v va v vc

D c ct

u

Convection

Transient term (storage) Diffusion

Advection/bulk motion Conduction ur u en

heating

What is a turbulence model?Why do we need one?

What is Reynolds averaging?

Basic /popular turbulence models

14


52/196

8

Turbulence model

A turbulence model is a model which is used to approximates thephysical behavior of turbulent flows*

Turbulence model are necessary in numerical simulation due to

impracticality in computing all scales of turbulent motion. Therefore,

approx mate met o s tur u ence mo e s are ntro uce to s mp y

and reduce computational cost.

Reynolds averaging refers to the process of averaging a variable or

an equation in time. For example, if we have time dependent

variable , we can decompose this variable into an average partand fluctuating part in the following way:

'1

where T has to be long enough to phase out fluctuation part on (t).

Aside from time averaging, Reynolds averaging also deals with

space averaging and Ensemble averaging**

15*J.J. Bertin, J. Periaux, J. Ballmann, 1992, Advances in hypersonics v2: Modeling hypersonic flows, Birkhauser, Cambridge**J. Sodja, 2007, Turbulence model in CFD, Ljubljana, Slovenia (http://www-f1.ijs.si/~rudi/sola/Turbulence-models-in-CFD.pdf)

, .

T

T

Turbulence model

Various turbulence models have been developed. They

can be categorized as*:

Algebraic/Zero-equation models

One equation models

Two equation models

Second-order closure models

Among these models,

k-, k-, LES (Large Eddy Simulation), RSM (ReynoldsStress Model) are among the most popular turbulence

model used in computational fluid dynamics.

In this study, Reynolds Stress Model (RSM) is used as it

has been shown to be superior to k-and k-turbulence

models in steady impinging jets

16*D. C. Wilcox, 2006, Turbulence modeling for CFD, DCW Industries, La Canada, Clifornia** P. Xu, B. Yu, S. Qiu, H. J. Poh and A. S. Mujumdar. Turbulent impinging jet heat transfer enhancement due to intermittent pulsation. International Journal of

Thermal Science, 49 (7): 1247-1252, 2010.


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9

Turbulence model for impinging jet drying

ij

ij ij ij ij ij ij

RC P D

t

' 'u u

Reynolds stress model (5 equations)

ccumu a on

Convective

Production

Rotation

Diffusion

ij

t t

' 'ij a i jC u u Uj i

ij im jm

m m

U UP R R

x x

' ' ' '2ij k j m ikm i m jkmu u e u u e 2

with 0.09 and 1.0t k

D R C C

17

Dissipation

Pressure strain

interaction

tk

23

ij ij

1 2

1 2

2 2

3 3

with 1.8 and 0.6

ij ij ij ij ijC R k C P P k

C C

To solve this model, k- turbulence model is required

Governing equations

k- turbulence model

,t tk

k k G

u

2

12

2 2 22 2 2

,

2 ,

k

t t

k

C GC

t k k

u v w u v u w w vG

x y z y x z x y z

u

2k

18

t ,

C1= 1.44

C2= 1.92

C = 0.09

k = 1.0

= 1.0

Nomenclature:u, v, w = component velocity

t= turbulent viscosityk = turbulent kinetic energy

= turbulent dissipation

G = turbulent generation rate


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10

Constitutive relations

Density air

Dynamic viscosity of air

5 2 21.076 10 1.039 10 3.326air air air T T

15 3 11 2 8 75.21 10 4.077 10 7.039 10 9.19 10air air air air

T T T

Conductivity of air

Specific heat of air

Heat evaporation

Density of substrate

10 3 7 2 44.084 10 4.519 10 2.35 10 0.0147air air air air k T T T

1000 2.394( 273.15) 2502.1fgh T

, 1

1

b ref

b

X

SbX

6 3 3 2

, 4.647 10 4.837 10 1.599 1175

p air air air airc T T T

19

on uc v y o su s ra e

Specific heat of substrate

Diffusivity of water vapor and

liquid water inside substrate

3

. .exp

1 8.3143 10 273.15 335.15 1

b

s

k

T X

6 0.0725 20441.29 10 exp exp273.15

vb lb

s

D DX T

, 1750 2345

1p b

Xc


Heat of wetting (heat to evaporate

bound water)

Total heat of evaporation

6 4 6 3 5 2

4

8.207 10 4.000 10 6.161 10

2.368 10 1163for 0.01 0.2

wH X X X

X X

evap fg wh h H

Moisture content

Dry basis

Wet basis

Equilibrium moisture content

(GAB model)

mass of water

mass of dry product

mass of watermass of wet product 1

l

s

l l

s l b

X

XWX

,

1

0.0209, 0.976, 4.416

m we

w w w

m

X CKAX

KA KA CKA

X K C

20

Free moisture content

Cooling rate due to evaporation

Rate of water evaporation

Diffusivity of water vapor in air

evap l l q h M Kc

0

Ea

RTK K e

6 8 10 22.775 10 4.479 10 1.656 10va

D T T

free eX X X (free to be removed)


55/196

11


Relation of moisture content to concentration of water inside substrate

,

,

1,

1 1

w b

b ref

w

W

XX

X SbX

,

2

,2 2

, ,2

,1

1 1 ,

1 1 0,

can be solved analytically for X and by neglecting wrong root th

b ref

w w

b ref

w w

b ref b ref

w w w w

X XM c

SbX X SbX

SbX Sb X X X M c

Sb X Sb X M c M c

2

e solution is

21

,

,

,2

,

1 ,

1.

b ref

w w

b ref

w w

Xa

where

a SbM c

b SbM c

c

Correlations

Local Nusselt number

Calculation of h, Nu, Nu distributions in impinging jets

( , ) x jet

luid

h DNu x t

k

Local heat transfer

coefficient

Local heat transfer flux

xx

jet wall

qh

T T

0

( )x fluid

y

T xq k

y

me average oca

Nusselt number

Time averaged Nusselt

number 22

0

1( ) ( , )avgNu x Nu x t dt

t

0 0

1 1( , )

x t

avgNu Nu x t dtdxx t


56/196

12

Nomenclature

cl concentration of liquid water [mol m-3

] p Pressure [Pa]

cv concentration of water vapor [mol m-3

] Dva diffusivity of vapor on the drying air [m2s]

Dlb diffusivity of liquid inside the drying substrate [m2s] dynamic viscosity of the drying air [Pa s]

Dvb diffusivity of vapor inside the drying substrate [m2s] a density of the drying air [kg m

-3]

T temperature [K] cpa specific heat of the drying air [J kg-1

K-1

]

q cooling rate due to evaporation [W m-3

] ka thermal conductivity of the drying air [W m-2

K-1

]

K production of water vapor mass per unit volume Ea activation energy [kJ mol-1

]

b density of the drying substrate [kg m-3

] R universal gas constant [J K1

mol1

]

cpb specific heat of the drying substrate [J kg-1

K-1

] Ml molecular weight of water [kg kmol-1

]

23

kb thermal conductivity of the drying substrate [W m-

K-

] hevap total heat of evaporation [J g-

]

u mean velocity [m s-1] X moisture content (dry basis) [kg kg-1]

u fluctuate velocity [m s-1

] W moisture content (wet basis) [kg kg-1

]

Initial and boundary conditions

Substrate

Initial conditions:

,0

0.

where

,b

l b

l

Wc

M

0 0, 0,, , ,l l b v v bT T c c c c

Drying chamber inlet

Boundary conditions:

0,

0.

,0

0,

,

0,

1000 .1

v b

l a

a

v a

l

c

c

RHc

RH M

0,0, , , , .in in in v v au v v T T RH RH c c

0 0, 0,, , , 0,

l l a v v aT T c c c c u v

24

Drying chamber outlet

Drying chamber wall

, 0, 0.out vp p D c k T n n

0, 0, ( ) 0.v vu v D c c k T n u n


57/196

13

Boundary conditions and parameters

Inlet velocity for various cases Steady laminar jet

vin = 2 m s-1

Pulsating laminar jet

Parameters needed to solvethe model are

3

, 1420 ,b ref kg m

vin = 1+1sin(2ft) m s-1

Intermitent laminar jet

vin= 2 m s-1(on),0 m s-1(off)

Steady turbulent jet

vin = 20 m s-1

Pulsating turbulent jet

1

0

3

,45

5 1 1

,45

1 1

,

0.018 ,

4.6,

1.110 ,

1.934 10

8.314 ,

in

l

a C

a C

M kg mol

X

kg m

kg m s

R J K mol

vin = + s n m s-

Intermitent laminar jet vin= 2 m s-1(on),0 m s-1(off)

25

1

48.7 ,1.4

1

120

Ea kJ molSb

f Hz

Numerics

Gambit: creating geometry, meshing,

labeling boundary condition

Fluent: solver based on finite volume

method

Domain is discretized onto a finite set of

control volumes (or cells).

General conservation (transport)equationsfor mass, momentum, energy, species, etc.

are solved on this set of control volumes.

V A A V

dV V dA dA S dV t

Partial differential equations are discretized

into a system of algebraic equations.

All algebraic equations are then solved

numerically to render the solution field.26

Convection Di ffusionUnsteady Generation


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14

Numerics

Flow chart of computational fluid dynamics (CFD)*

27

*http://progdata.umflint.edu/MAZUMDER/Fluent/Intro%20Training/L-1%20Introduction%20to%20CFD.pdf

Numerics

User Defined Scalars: solving for water liquid and vapor

User Defined Funct ions Macros

DEFINE_SOURCE, DEFINE_DIFUSIVITY, DEFINE_FLUX,

_ , _ ,

Three different mesh sizes of 2000, 4000, 8000 elements

were implemented and compared in terms of velocity,temperature and moisture content to ensure a mesh-

independent. We found that the result from the mesh

size 2000 deviates 5% and 4000 deviates 1% from 8000

28

. ,

chosen.

Relative residual 10-6 for all dependent variable.

It took around 30-50 min to converge in Quadcore 1.8

GHz with 8 GB RAM for 5 to 8 h drying time


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15

SELECTED RESULTS

29

Contours of velocity

Laminar steady jet

Turbulent steady jet

30


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16

Contours of temperature

Laminar steady jet

Turbulent steady jet

31

Temperature contours in substrate

32


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17

Moisture profile in substrate

33

Drying kinetics (0.5 mm substrate)

Impinging jet is not recomended

especially when drying cost is

considered (energy cost).

Effect of the pulsating and

intermittent flow can be seen on this

case Frequency and velocity have no

effect on this case, most likely due

to the thin substrate 34


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18

Drying kinetics (5 mm substrate)

Velocity slightly affect drying

kinetics. It is clearer compare to

that for thin substrate.

Effect of the pulsating andintermittent flow can be seen in this

case Frequency has no effect

35

Conclusion

Simple physical model to show how one

can use a math model consisting of

conservation equations and relevant

boundary conditions For gas-side, we use continuity,

momentum, energy and species equations

simple diffusion model for both water and

vapor. For low temperature only liquid

diffusion model is adequate.36


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19

References

[1] M. V. De Bonis, G. Ruocco, 2008, A Generalized Conjugate Model for

Forced Convection Drying Based on An Evaporative Kinetics, Journal of

Food Engineering, Vol. 89, pp: 232-240

2 M. R. Islam J. C. Ho A. S. Mu umdar 2003 Convective Dr in with Time-

Varying Heat Input, Drying Technology, Vol. 21(7), pp: 1333-1356

[3] J. Srikiatden a, J. S. Roberts, 2008, Predicting moisture profiles in potato

and carrot during convective hot air drying using isothermally measured

effective diffusivity, Journal of Food Engineering, Vol. 84, pp: 516-525

[4] W. Kays, M. Crawford, B. Weigand, 2005, Convective Heat and Mass

Transfer 4th ed., McGraw Hill, Singapore

[5] F. P. Incropera and D. P. Dewitt , 2001, Fundamentals of Heat and Mass

, ,

[6] P. Xu, B. Yu, S. Qiu, H. J. Poh, A. S. Mujumdar, 2010, Turbulent ImpingingJet Heat Transfer Enhancement Due to Intermittent Pulsation, International

Journal of Thermal Sciences. doi:10.1016/j.ijthermalsci.2010.01.020

[7] H. J. Poh, K. Kumar, A. S. Mujumdar, 2005, Heat transfer from a pulsed

laminar impinging jet, International Communications in Heat and Mass

Transfer, Vol. 32, pp:13171324 37

For Self-Study

How would you model

Case where jet temperature is 200 C?

The jet is superheated steam at atmospheric

pressure and 200 C?

The drying chamber is at very low (but finite)

pressure and dried by superheated steam

Will drying time be reduced if the slab is

flipped after some time? Why?

38


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65/196

Mass transport in a micro-

channel T-Junction with

coiled-base channel design


66/196


67/196

Mass transport in a micro-channel

T-Junction with coiled-base channel design

ME 6203 Mass Transport Guest Lecture

Prof. Arun S. MUJUMDAR

Email: [email protected]

Tel: +65-6516-4623, Fax: +65-6777-6235

Guest lecturer

Agus Pulung SASMITO

Minerals Metals Materials Technology Center

National University of Singapore

2011

Outline

Overview of micro-channel T-Junction

Physical model

Problem description

Key assumptions

Numerical methodology

Selected results

Mass transport enhancement

Concluding remarks

2


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Micro-channel T-Junction Widely used in industry, especially pharmaceutical, for mixing

and reaction processes

Relatively easy to control the reactions, especially for highly

exothermic reaction

Involves simultaneous transport process

Transport process in T-Junction:

Momentum transfer

Mass transfer

Heat transfer

Occur simultaneously

Main phenomena:

Mixing

Surface reactions

Overview

3

Micro-Channel T-Junction

Passive mixing for various chemical reaction; it

does not require additional energy for mixing

processes

Micro-channel T-Junction, however, has several

drawbacks

Poor mixing, especially at short channel and high

Reynolds number

High pressure drop due to impingement effect

Various innovative designs are proposed to

improve mixing and reactions

Coiled channel

Channel with fins

Impinging jet channel4


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Typical geometry

5

Inlet

300

Re500

in

in

T K

V

=

Micro-channel T-junction

120 mm

1 mm

L

h

=

=

A typical micro-channel T-

junction is used to mix methane

and air; the channel surface iscoated with catalyst (platinum)

Example case of mixing and reaction of

methane oxidation in platinum surface

CH4H2T = 300K

O2N2T = 300K

CO

CO2H2O

Pt

surface;

T

1290K

Ptsurface;T1290K

L

h

4 2 2 2

2 2 2

2 3

2

Gas species: CH , O , H ,H O,

CO , HO , N

Surface species: Pt(s), H(s), O(s),OH(s), H O(s), H (s),

CH (s), CH(s), C(s),

CO( 2s), CO (s)

Solid species: Pt(b)

Innovative coiled-base design

6

Conical T-junctionTypical straight T-junction

In-plane spiral T-junctionHelical T-junction

Coiled-base channel design is

proposed to enhance heat and

mass transfer.

Coiled-base channel design

has been widely used in

industrial applications due to

compact structure, ease of

manufacture, higher heat and

mass transfer.

The presence of secondary

flow induced by coil curvatureand complex temperature and

concentration profiles caused

by curvature-induced torsionare among significant

phenomena observed in

coiled-base channel.

Length is kept constant for

comparison purpose.


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Physical model

Convective heat and mass transfer

Mixing in the opposing jet at T junction

Surface reactions at the channel wall which include

mass consumptions and generation,

heat release due surface reaction,

multi-step surface reactions including adsorption

reaction, surface reaction, and desorption reaction.

Surface species are calculated from site balance

equations

Surface reactions create sources of bulk phase, which

determines its deposition rate on a surface.

7

Basic mechanisms

Assumptions

The flow is steady-state, laminar, newtonian flow and

species mixture is follows ideal gas law.

There are three types of species: gas, surface (site) and

solid species. The model treats chemical speciesdeposited on surfaces as distinct from the same

chemical species in the gas

Thermo-physical properties of species mixture follows

mixing law of ideal gas with temperature dependent

effect.

Gas phase reaction are closely coupled with surface

reactions.

8

In developing the mathematical model, several assumptions are

taken:


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How to translate this physical phenomena into amathematical model?

What conservation equations do we need to interpret

the physical phenomena?

9

Conservation equations

Mass

Momentum

Species

Energy

0 =u

( )( ) ( )23

p = + +

Tu u u u u I

( ) ( )i i i iD R = +u

( ) ( )p eff tempc T k T S = +u

Inertia/net rate

Pressuregradient

viscous Effect of volumedillatation

convective diffusive reaction

4 2 2 2 2 2i: CH , O , H , H O, CO , HO

Compressible

flow

convective conductive Heat due to

reactions


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Detailed reactions

Theory: consider the rth wall surface reaction written in general forms' ' ' '' '' ''

, , , , , ,

1 1 1 1 1 1

g gb s b sr

N NN N N NK

i r i i r i i r i i r i i r i i r i

i i i i i i

g G b B s G g G b B s G= = = = = =

+ + + + where Gi, Bi, andSi represents the gas phase species, the solid species, and the

surface-adsorbed (or site) species, respectively. g, b, s are the stoichiometric

coefficients for each reactant species; g, b, and s are the stoichiometric coefficients

for each product species; and Kr is the overall reaction rate constant.

The rate of rth reaction is [ ] [ ]' ', ,

, wall wall1

g

i r i r

Ng s

r f r i i

i

k G S=

= The net molar rate of production or consumption of each species i is

given by ( )

( )

( )

rxn

rxn

rxn

'' '

,gas , ,

1

'' '

,bulk , ,1

'' '

,site , ,

1

1,2,3,...,

1, 2,3,...,

1, 2,3,...,

N

i i r i r r g

r

N

i i r i r r br

N

i i r i r r s

r

R g g i N

R b b i N

R s s i N

=

=

=

= =

= =

= =

Reaction rate constant is computed using Arrhenius expresion

/

,r rE RT

f r rk A T e =

Wall surface reaction boundary conditions

It is assumed that, on the reacting surface, the mass flux of each gasspecies is balanced with its rate of production/consumption

[ ]

,wall

wall dep i,wall , i,gas

walli,site

1,2,3,...,

1,2,3,...,

i

i w i g

i

s

D m M R i Nn

SR i N

t

= =

= =

The mass fraction at the wall is related to concentration by

[ ] wall i,wallwall

,

i

w i

GM

=

mdep is the net rate of mass deposition or etching as a result of surfacereaction

dep , ,

1

bN

w i i b ulk

i

m M R=

=

[Si]wall is the site species concentration at the wall, and defined as

[ ] sitewalli iS z=where is the site density and zi is the site coverage of species isite


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Multi-step reaction mechanism

1.74e701.88e18H2O(s) + Pt(s) => H(s) + OH(s)24

4.82e704.45e20H2O(s) + O(s) => OH(s) + OH(s)25

1.15e701.56e18OH(s) + Pt(s) => H(s) + O(s)23

1.84e801e17CO(s) + Pt(s) => C(s) + O(s)22

6.28e703.7e20C(s) + O(s) => CO(s) + Pt(s)21

2e703.7e20CH(s) + Pt(s) => C(s) + H(s)20

2e703.7e20CH2(s) + Pt(s) => CH(s) + H(s)19

2e703.7e20CH3(s) + Pt(s) => CH2(s) + H(s)18

00.52.3e16CH4 + 2Pt(s) => CH3(s) + H(s)17

1.05e803.7e20CO(s) + O(s) => CO2(s) + Pt(s)16

2.05e701e13CO2(s) => CO2 + Pt(s)15

1.25e801e13CO(s) => CO + Pt(s)14

00.57.85e15CO + Pt(s) => CO(s)13

4.82e703.7e20OH(s) + OH(s) => H2O(s) + O(s)12

1.74e703.7e20H(s) + OH(s) => H2O(s) + Pt(s)11

1.15e703.7e20H(s) + O(s) => OH(s) + Pt(s)10

1.93e801e13OH(s) => OH + Pt(s)9

00.53.25e8OH + Pt(s) => OH(s)8

4.03e701e13H2O(s) => H2O + Pt(s)7

00.52.37e8H2O + Pt(s) => H2O(s)6

2.13e803.7e202O(s) => O2 + 2Pt(s)5

00.52.01e14O2 + 2PT(s) => 2O(s)4

0-0.51.8e17O2 + 2Pt(s) => 2O(s)3

6.74e703.7e202H(s) => H2 + 2Pt(s)2

00.54.36e7H2 + 2Pt(s) => 2H(s)1

Er (J/kmol)rArReactionNo


Mixture density

Mixture viscosity

Effective thermal conductivity; heat capacity

/pM RT =

( )4 4 2 2 2 2 2 2 2 2 2 2

1

CH CH H H O O H O H O OH OH CO CO CO CO N N/ / / / / / / /M M M M M M M M M

= + + + + + + +

Mean molecular mass

4 2 2 2 2 2

,

with , = CH , H , O , H O, OH, CO, CO , Nx

x

=

2

1 11/2(g) 2 4

, (g)

11 1

8

MM

M M

= + +

eff i ik k = p i p,ii

c c=


74/196

Constitutive relations (Contd)

in out FoMp

=

1,

c

c

c A

V dAA

= u

Figure of Merit is used to evaluate the effectiveness of themixing and reaction rate in the micro-channel T-Junction. It

defined as reactant conversion rate over pumping power

required. Since the mass flow rate is kept constant; hence

Mean velocity

Mixed-mean temperature

Mixed-mean mass fraction

1,

c

mean c

c A

T T dAVA= u

,

1

c

i mean i c

c A

dAVA

= u

Boundary conditions

At the air inletUin = 5 m/s (Re~500)

Tin = 300K

O2 = 0.21

N2 = 1-

O2

At the methane

inletUin = 5 m/s (Re~500)

Tin = 300K

CH4 = 0.9

H2 = 0.1

0i

T = =

At the walls No-slip condition

No species flux

Twall = 1290 K

At the outletPout = 101325


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Numerics

AutoCad for creating geometries Gambit for meshing and labeling boundary conditions:

fine structured mesh near wall to resolve boundary layer;increasingly coarser mesh to the middle of the channel to reducecomputational cost

Mesh independence test were carried out for three differentmesh sizecoarse, medium, finein terms of velocity, pressure,temperature and species.

Fluent for discretization and solving dependent variables Based on finite volume discretization method

Pressure-velocity coupling is solved by well-known SIMPLEmethod

Overall, it requires ~300 MB memory and 2 h solving time on

workstation with Quadcore 2.63 GHz processor for convergencecriteria 10-6 for all dependent variables.

ChemKIN for reaction kinetics To set up details multi-step reaction mechanism and thermo-

physical properties of gas species.

Flow chart for numerical solver


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Results and discussion

Velocity profiles at channel length 50mm

Fully developed

flow exists in

the straight

channel

Secondary flow

is developed in

the coiled base

channel.

Higher velocity

intensity existsin the outer wall

of the coiled

base channel

m/s

Oxygen mass fraction at channel length 50mm

Straight channel has

higher oxygen mass

fraction means that

lesser oxygen is

consumed for

reactions.

Among the coiledbase channel design,

helical coil gives

better conversion

rate.

Secondary flow

enhance mass

transport in the

surface reaction


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Methane mass fraction at channel length 50 mm

At straight channel, the

methane concentration

is higher at the right

side of the wall, it

means that the

methane is not mixed

well with air.

Helical coil yields the

best mixing and

reaction among others

The presence of

secondary flowimprove the mixing rate

of reactant species

Oxygen mass fraction along channel

Helical coil gives the best conversion rate among other designs.

Straight T-junction yields the lowest conversion rate due to poormixing.

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 20 40 60 80 100 120

Length / mm

Oxygenmassfraction

helical

straight

in plane spiral

conical


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Mixed mean temperature along channel

Coiled base channel also gives higher heat transfer rate ascompared to straight channel

Coiled base channel is suitable for highly exothermic/endothermicreaction to control the desired environment/temperature.

300

400

500

600

700

800

900

1000

1100

1200

1300

0 20 40 60 80 100 120Length / mm

Temperature/K

conical

in plane spiral

helical

straight

Effect of Reynolds number

Lower mass flow rate performs better conversion rate

This is due to longer residence time of the species

0.03

0.05

0.07

0.09

0.11

0.13

0.15

0.17

0 20 40 60 80 100 120

Length / mm

Oxygen

massfraction

Re 100

Re 500

Re 1000Re increasing


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Effect of coil diameter

Smaller coil diameter produces slightly better conversion rate.

This is due to higher secondary flow produced in smaller coildiameter.

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 20 40 60 80 100 120

Length / mm

Oxygenmassfraction

r 4r 3

r 5

diameter increasing

Pressure drop

Straight channel requires the lowest pressure drop;whereas, the helical coil has the highest pressure drop

Pressure drop increses as the mass flow increasing

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 200 400 600 800 1000

Reynolds

p/pa

straight

conical

in-plane

helical


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Figure of Merit

Straight channel has the highest figure of merit among otherdesigns; however, for industrial application where space is limitedand pumping power is not an issue, such as in pharmaceuticalindustry, coiled base channel design can be a desirable choice

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

3.50E-04

100 500 1000Reynolds

FigureofMerit

straight

conical

in-plane

helical

Concluding remarks

Coiled base channel design can improve heatand mass transfer as compare to straight T-junction channel.

This improvement is due to the presence ofsecondary flow.

However, higher pressure drop is required forcoiled base channel design.

For industrial application where space is limited,conversion rate is the most important, andpumping power is not an issue, coiled basechannel design can be a desirable choice


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Nomenclature3

1

2

3

= density, kgm

= velocity, ms

= pressure, pa

= dynamic viscosity, Pas

= mass fraction of species i

= diffusivity of species i, ms

= reaction rate of species i, kgm

= specific heat

i

i

i

p

p

D

R

c

u

1 1

1

-3

temp

, Jkg K

= temperature, K

= effective thermal conductivity, WmK

= heat release due to reactions, Wm

= gas species, mol= bulk/solid species, mol

= surface-adsorbed/site species,

eff

i

i

i

T

k

S

GB

S

' ''

' ''

' ''

mol

, = stoichiometric coefficient for gas reactant, and product

, = stoichiometric coefficient for bulk reactant, and product

, = stoichiometric coefficient for site reactant, and p

i i

i i

g g

b b

s s roduct

,

= rate of rth reaction

= reaction rate constant using Arrhenius expression

= pre-exponential factor

= temperature exponent

= activation energy for the reaction, Jkgmol

= universal gas co

f r

r

r

r

k

A

E

R

-1 -1 -1

dep

nstant, Jkg mol K

= mean molecular mass

= net rate of mass deposition, kg

= mol fraction

M

m

x

References

[1] O. Deutschmann, L.i. Maier, U. Riedel, A.H. Stroemman, R.W. Dibble,Hydrogen Assisted Catalytic Combustion of Methane on Platinum,

Catalysis Today 59,141--150 (2000).

[2] V. Kumar, M. Paraschivoiu, K.D.P. Nigam, Single phase fluid flow and

mixing in microchannel, Chemical Engineering Science, 2011, in press.

[3] S. Vatisth, V. Kumar, K.D.P. Nigam,A review on the potential application

of curved geometries in process industry, Industrial Engineering Chemistry

Research 47, 3291-3337 (2008).[4] J.C. Kurnia, A.P. Sasmito, A.S. Mujumdar, Evaluation of heat transfer

performance of helical coils of non-circular tubes, J. Zhejiang University

Science: A, 2011, in press.

[5] J.C. Kurnia, A.P. Sasmito, A.S. Mujumdar, Laminar convective heat

transfer in coils of non-circular cross-section tube: a computational fluid

dynamics study, Thermal Science, 2011, accepted.

[6] J.C. Kurnia, A.P. Sasmito, A.S. Mujumdar, Numerical investigation of

laminar heat transfer performance of various cooling channel designs,

Applied Thermal Engineering, 2011, in press.

[7] Fluent user guide documentation, http://www.fluent.com30


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For Self Study

How can one reduce pressure drop in the coiledbase channel design?

What happens if the channel is not in squarecross-section, e.g. circular, triangle, star-shapeetc?

Will reaction and mixing rate improve if we addfins inside the channel?

What if the reactant species are in differentphase, e.g. gas and liquid? Is the modelpresented still valid?


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Mass Transport

Considerations in PEM

Fuel Cell Modeling


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1

1

ME6203 Mass TransportMass Transport Considerations

in PEM Fuel Cell Modeling

Prof. Arun S. Mujumdar, ME, NUS

Dr. Poh Hee Joo, IHPC

March 2010

2

Outline - Part 1 (Handout)

Fuel Cell Introduction

Fuel cell Mass Transport

Diffusive transport in electrode

Convective transport in flow structures

Analytical Modeling with MATLAB

Summary


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2

3

Why PEMFC Modeling in MassTransport course?

Fuel cells are becoming important in academicand industrial R&D. Some alreadycommercialized. Much more development isneeded to enhance performance cost-effectively

Excellent industrial illustration of a case wheremath modeling of transport phenomena-including mass transport is critically important

It is an excellent illustration of how very complextransport processes can be modeled and whatare the different levels of math models which arepossible

4

Why PEMFC model?

In ME6203 one objective is to look at advanced masstransport problems of real interest and examine how amodel can be developed based on fundamentals

It is also an example of complex interaction betweenvarious transport phenomena. Illustrates need forsignificant information needed for such a model

Due to time limitation, different levels of modeling e.g.1D, 2D,2.5D, 3D steady/unsteady, single phase/ twophase models etc are not discussed. Model is only asgood as assumptions made- they must be realistic.


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3

5

Mass Transport and PEMFC Whenever there is species movement causing

concentration changes there is mass transport Mechanisms are: diffusion, convection, electro-osmosis

etc PEMFC includes flow in channels, flow in porous media Involves proton and electron transfer, catalytic chemical

reactions, heat transfer etc An excellent-but complex-example for study of transport

phenomena

Here, please focus on the technique of math modelingrather than the complex details which are beyond thescope of this course.

Suitable for Term Paper Projects e.g. 1D analyticalmodeling of different types of fuel cells

6

Preamble

With this preamble , let us proceed to fuel cells..

Numerous resources are available on the web forself-study

Advanced models are being worked on at hundredsof labs around the world-useful for innovation!

Several excellent textbooks available as well No need to go beyond what is in this PPT-except for

those who choose to work on term papers on thissubject.

Poh Hee Joo will be happy to provide relevantresources and ideas to those interested

Caution: Some aspects are complex and areincluded only for completeness of coverage. You donot need to get into those details.


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5

9

Basic Fuel Cell Operation

1. Reactant transport

Efficient delivery of reactants by using flow field plates incombination with porous electrode structures.

2. Electrochemical reaction

Choosing right catalyst and carefully designing reactionzones

3. Ionic (and Electronic) Conduction

Thin electrolyte for ionic conduction, without fuel cross over

4. Product Removal

Flooding by product water can be major issue in PEMFC

10

Transportation

Stationary Power Generation

Residential

Portable Power Generation

Space and Defense

Applications of fuel cells


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6

11

Fuel Cells: Classification

PEM fuel cell Solid oxide fuel cell

Characterized by

Electrolyte materials

Operating temperature

Fuel used

PEM Fuel Cell 2H2 4H+ + 4e

Solid Oxide Fuel Cell H2 + O2-CO2 + H2O + 2e O2 + 2e O

2-

O2 + 4e + 4H+ 2H2O

Polymer membrane Ceramic membrane

800C 600 10000C

At Anode At Cathode

Direct Methanol Fuel Cell CH3OH + H2O CO2 + 6H+ + 6e 3/2O2 + 6H+ + 6e3H2O

12

Fuel Cells: Some Advantages

Replacement for IC Engines intransportation

Higher energy efficiency

Zero or ultra-low emission

Replacement for batteries in portableelectronics

Higher energy density

Nearly zero recharge time

Independent scaling between power(determined by fuel cell size) and capacity(determined by fuel cell reservoir)


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7

13

Fuel Cells: Some Limitations High cost of fuel cell

Low volumetric power density comparing to I.C.engines and batteries

Safety, Availability, Storage and Distribution ofpure hydrogen fuel

Alternative fuels (e.g. methanol, gasoline)

difficult to use directly and require reforming Susceptibility to environmental poisons

Operational temperature compatibility concerns

14

Challenges to Fuel Cell Commercialization

Simple question, but difficult answer

Prototype developed by SERC-PEMFC for2W portable battery charger fuel cell of

NOKIA mobile phone cost about $300


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8

15

Fuel cells: Interdisciplinary field ofscience and engineering:

Thermodynamics

Electrochemistry

Chemistry and Chemical Engineering

Fluid Mechanics

Heat and Mass Transfer

Material Science (metallurgy) and materials engineering

Polymer Science and specifically ionomer chemistry

Design, manufacturing and engineering optimization Solid mechanics and mechanical engineering

Electromagnetism and electrical engineering

Etc etc

16

PEMFC (Interdisciplinary!)

Membrane ScienceCatalysis

and

Electrochemistry

System Integration

High temperaturecation membrane

Reduce CO poisoningof catalyst)

Membrane for DMFC(prevent methanol crossover)

Anion membrane(use of low cost catalyst)

Alternative catalyst(reduce cost)

High catalyst utilization(reduce catalyst loading)

Improved performance(electro-oxidation/Reduction)

Measurement andCharacterization

(relate performance toelectrochemical processes)

Thermofluidsand

Component Design

Transport phenomena(molecular diffusion,

ion migration,convection)

Multi-phase physics(water management)

Heat transfer(performance stability)

Fluid dynamics(flow channel design)

System design & configuration(reduce cost, improved efficient)

Interconnection(increase power o/p)

Heat and water management(operational stability)

Courtesy of SERC Fuel Cell Project


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9

17

Schematic of a cross sectional view of PEM

Fuel Cell unit

Cathode

Bipolar Plate

Anode

Bipolar Plate

Cathode

Electrode

(GDL)

Anode

Electrode

(GDL)

Membrane

Cathode

Catalyst

Anode

Catalyst

O2 + 2H+ + 2e H2O H2 2H+ + 2e

H2channel

Air

channel

O2 H2H+

Loade-

18

Role of Each Component1. Cathode/Anode Bipolar plate

Electronic Conduction Heat Transport

2. Air/H2 channel Reactant Transport & Product Removal (Mass Transfer) Heat Transport

3. Cathode/Anode GDL

Ionic and Electronic Conduction Reactant Transport & Product Removal (Mass Transfer) Heat Transport

4. Cathode/Anode Catalyst Electrochemical reaction (Mass Transfer reactant consumption and

product generation) Ionic and Electronic Conduction

5. Membrane Ionic conduction Water transport


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19

Water Management in PEMFC

AnodeCathodeElectrolytemembrane

Water produced

within cathode

Water is dragged from

anode to cathode sides by

protons moving through

electrolyte (electro-osmoticdrag)

Water is back diffused from

cathode to anode, if cathode sideholds more water

Water is removed by

O2 depleted air

leaving the fuel cell

Water is removed by

circulating hydrogen

Water is supplied byexternally humidifying

air/O2 supply

Water is supplied byexternally humidifying

hydrogen supply

20

Why Mass Transfer is Important in PEMFCComponent Mass Transport Implication Where mass transport

limitation exists

Air/H2 channel To provide homogenous distributionof reactants across an electrodesurface while minimizing pressuredrop and maximizing water removalcapability

Reactant depletion fordownstream channel

Impurity contamination, e.g.N2

Cathode/Anode GDL Porous electrode support to

reinforce catalyst, allow easy gasaccess to catalyst layer, andenhances electrical conductivity

Liquid water flooding block the

pores for gas diffusion intocatalyst layer

Cathode/Anode Catalyst Electrochemical reaction takesplace at the catalyst layer,consume reactant (H2 and O2) andgenerate product (H2O)

Poor total reaction surfacearea (catalyst loading) foroptimal electrochemicalperformance

Membrane To separate the air and H2 whileallowing liquid water and ionictransport across membrane

Membrane dry-out at hightemperature, and loss of itsproton conducting capability


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21

Fuel Cell : Mass Transport To produce electricity, fuel cell must be continuallysupplied with fuel and ox idant. At the same time,products must be continuously removed so as toavoid strangling the cell. The process ofsupplying reactants and removing products istermed fuel cell mass transport.

Why is it important? Poor mass transport can leadto significant fuel cell performance loss, as thereactant depletion and/or product accumulation

within catalyst layer (not at the fuel cell in let) willadversely affect performance. This is calledconcentration or mass transport loss, and can beminimized by careful optimization of masstransport in the fuel cell electrodes and fuel cellflow structures

22

Transport in Electrode vs. FlowStructure

Difference between mass transport in fuel cell electrode and fuelcell flow structures in one of length scale, and this lead todifference in transport mechanism

For fuel cell flow structures, dimensions are generally on themillimeter or centimeters scale. Flow pattern typically consisted of

well-defined channel arrays. Gas transport in the channel isdominated by fluid flow and convection.

For fuel cell electrodes, it exhibit structure and porosity on themicrometer and nanometer length scale. The tortuous geometryof electrodes insulated gas molecules from convective forcespresent in flow channel. Gas transport within electrodes isdominated by diffusion.

*Velocity scale could also affect t ransport

mechanism


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23

Transport in Electrodes: Diffusive

Transport

An electrochemicalreaction on catalyst layerside of an electrode andconvective mixingon theother flow channel side ofthe electrode set upconcentration gradients,leading to diffusivetransport across theelectrode.

o

Rc

o

Pc

*

Pc

*

Rc

Flow

Structure

Flow

channel

Anode

Electrode

Catalyst

Layer

Electrolyte

Reactants (R) In

Products (P) Out

JR

JP

jrxn

Concen

tration

Reaction in catalyst

layer consumes R,

generates P

Schematic of mass transport situation withintypical fuel cell electrode

24

Faradays Law

From Faradays Law : current ievolved by anelectrochemical reaction is a direct measure ofthe rate of electrochemical reaction

n is the number of electrons transferred,

Fis Faradays constant, 96,485 C/mol,

is the rate of electrochemical reaction, mol/s.

*The current density

Jis the molar flux, mol/cm2s.

dt

dNnF

dt

dQi ==

dt

dN

nFJdt

dN

AnF

A

ij =

==1


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Transport in Electrode: Diffusive Transport

At steady state, the diffusion flux of reactants andproducts down the concentration gradient across theelectrode (diffusion layer) will exactly match theconsumption/production rate of reactants and productsat the catalyst layer.

Diffusion flux(kmol/m2s) of reactants to the catalystlayer may be described by

From Faradays Law

Using the flux balance equation, one can solve forreactant concentration in the catalyst layer

effRRnFD

jcc = 0*

dx

dcDJdiff =

o

RReff

diff

ccDJ

=*

o

RReff cc

nFDj

=

*

26

Transport in Electrode: DiffusiveTransport

Limiting Current Density,jL Limiting current density of fuel cell will be encountered

when reactant concentration in the catalyst layer drops

all the way to zero. Fuel cell mass transport design strategies focus onincreasing the limiting current density by:

1. Ensuring a high reactant concentration at flow channel bydesigning good flow structures that even distribute reactants

2. Ensuring that effective diffusivity is large and diffusion layerthickness is small by carefully optimizing fuel cell operatingconditions, electrode structure, and diffusion layer thickness.

Theoretical typicaljL are on the order of 1-10A/cm2

0

Reff

L

cnFDj =


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27

Question 11. Discuss the factors that determinejL,

limiting current density. List three ways toincreasejL.

28

Answer for Question 1

AnswerThe limiting current density is given byFactors determining thejL are reactant concentration at flowchannel, effective diffusivity and diffusion layer thickness. Wecould increasejL by

Ensuring a high reactant concentration at flowchannel by designing good flow structures thateven distr ibute reactants

Ensuring effective diffusivity is large;Ensuring diffusion layer thickness is small

by carefully optimizing fuel cell operatingconditions, electrode structure, and diffusionlayer thickness

0

Reff

L

cnFDj =


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29

Typical process of reactanttransport to reactant sites

If considering the convection mass transfer across electrode surface,how is the limiting current density being derived?

sRc

Flow channel

x

x = 0

x =H

HE

Gas Diffusion

Layer (porous)

Catalyst Layer

(porous)

Reactant molar

flux, JR

Convection, hm DiffusionDiffusion and

reactiono

Rc

*Rc

30

Process of reactant transport to reactant sites

Convection mass transfer at the electrode surface

Diffusion mass transport through the Gas Diffusion Layer

Combining Equation 1 & 2

( )sRoRm cchJ =

=

E

R

s

Reff

H

ccDJ

*

=m

R

o

R

R

ccJ

*

eff

E

m

mD

H

hR +=

1

(1)

(2)

From Faradays Law, current density is proportional to the rate ofelectrochemical reaction

(3)

nFJdt

dN

AnF

A

ij =

==1 ( )*1 RoReff

E

m

CCD

H

hnFj

+=

Limiting current density oReff

E

m

L CD

H

hnFj

1

1

+=

(4)

(5)


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31

Transport in Electrode: DiffusiveTransport

Concentration affects fuel cell performance through reactionkinetics.

This is because reaction kinetics also depend on the reactant andproduct concentration at the reaction sites.

Reactant depletion/product accumulation in the catalyst layerslead to fuel cell performance loss.

This is called fuel cell concentration (or mass transport) loss.

conc - Voltage loss due to reactant depletion in the catalyst layer IncreasingjL can greatly extend a fuel cells potential operating

range; therefore mass transport design is an active area ofcurrent fuel cell research.

jj

j

nF

RT

L

Lconc

+=

1

1

32

Question 22. Using the limiting current density equation, calculate

the limiting current density for a fuel cell cathoderunning on air at 1 Atm and 25C. Assume only O2 andN2 and ignore the presence of water vapor. Massfraction of O2 in air is 0.23. Assume the diffusion layeris 500m and has a porosity of 40%.

Hint* : Using Chapman-Enskog theory (Chp 5, Cussler)to find the binary diffusion coefficient, andBruggemann correction to account for the effectivediffusivity in porous structure. Molar concentration forO2 can be obtained by mole fraction of O2 multiply bythe total molar concentration for the air mixture. n isthe number of electrons consumed per mole of thereactant consumed. Molecular weight for N2 and O2are 28 and 32, respectively


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33

Answer for Question 2 In the H2-O2 fuel cell, the electrochemical reaction at

the cathode is given by O2 + 4H+ + 4e H2O. Hence

n = 4. F is the Faraday constant, 96,485 C/mol. Thebinary diffusion coefficient is given by Chapman-Enskog theory.O2= 3.467. N2= 3.798. O2-N2=3.6325. From the necessary calculation, = 0.9186.Therefore, Dij= 2x10-5 m

2/s. From Bruggemanncorrection Dij,eff= 5.06 x 10-6 m

2/s. From the ideal gasequation, total molar concentration for the mixture is =

40.9 mol/m3. Molecular weight for the mixture O2-N2 is= 28.92. Mole faction of O2 = = 0.20786. Therefore,molar concentration of O2 = 8.5015 mol/m3. Limitingcurrent density = 33,204 A/m2 = 3.32A/cm2

34

Transport in Flow Structure:Convective Transport

Fuel cell flow structures are designed to distributereactants across fuel cell

One could possibly use single-chamber structure, andencapsulate the entire fuel cell collector in a singlecompartment. Unfortunately, this would make reactantstend to stagnant inside the chamber, leading to poorreactant distribution and high mass transport losses;hence poor fuel cell performance

Conversely, employing intricate flow structure containingmany small flow channels keeps the reactants constantlyflowing across fuel cell, encouraging uniform convection,mixing and homogenous reactant distribution.


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35

Convective Transport Contd Analyzing convective gas transport in the

complex real world flow structures is only reallypossible with numerical methods. A commontechnique is to use CFD modeling

However, basic analysis of simple flow scenariosis still possible with the principle of fluid

mechanics, which can still yield great insight intofuel cell mass transport and flow structuredesign

36


Pressure difference between inlet and outlet drives the fluid flow. Although gas flowing in stream-wise direction along flow channel,

convective mass transport can also occur in transverse direction fromflow channel into (or out of) electrode. This happens whenconcentration of species iis different at the electrode surface versusthe flow channel bulk.

Inlet Outlet

u

JC

JD

Convection transfer at surface

Diffusion Electrode

Membrane

x

y

Dh


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37


Mass flux (kg/m2s) due to convective mass transfermay be estimated by

Mass transfer convection coefficient, hm, is dependenton the channel geometry, the physical properties ofspecies iandj, and the wall conditions. It can be foundfrom the nondimensional Sherwood number

( )isimiC hJ = ,,

h

ij

mD

DShh =

38


Gas is depleted along flow channel

As hydrogen or air is consumed continuously alonga flow channel, the reactants tend to becomedepleted, especially near the outlet. Depletion poses

adverse effect on fuel cell performance, sinceconcentration losses increase as reactantconcentrations decrease.

A simple 2D mass transport model for fuel cellcathode is developed. This is to determine how theoxygen concentration decreases along flow channelusing macro-scale mass flux balance.

*Refer to Note 1 for O2 mass concentration profilealong cathode catalyst layer.

* important


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39

Transport in Flow Structure: Convective

Transporty

x

Electrolyte

Cathode catalyst layer

Gas diffusion layer

Cathode flow channel

HC

HE

E

C

CONV

EyOJ =2inu

2O

2O

DIFF

EyOJ =2

RXN

CyOJ =2

Schematic of a 2D fuel cell transport model including diffusion and convection

Gas is depleted along flow channel

To find oxygen concentration profile along the catalystlayer

40

Convective Transport in Flow Structure :Assumptions

1. Steady state and isothermal operation

2. Flow channel has a square cross section.

3. The catalyst layer is infinitely thin.

4. Water exists only in vapor form.5. Diffusive mass transport dominates in

the diffusion layer. Furthermore, only y-direction diffusion is considered.

6. Convection mass transport dominates inthe flow channel


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41


From Faradays Law, if fuel cell is producing a current density at locationX,then the O2mass flux (kg/cm2s) that is consuming is given by

( )F

XjMJ O

rxn

CyXx

O422 ,

^

===

The O2 flux consumed by the electrochemical reaction must be provided bydiffusion in the gas diffusion layer, described by Ficks law

E

EyXxO

CyXxO

eff

O

diff

EyXx

OH

DJ ====

==

= ,,

,

^22

22

O2mass flux due to mass transport through the gas diffusion layer is providedby convective mass transport between the flow channel and gas diffusion layer

=

======

channelyXxO

EyXxOm

conv

EyXx

O hJ,,

,

^

222

(1)

(2)

(3)

42

Mass flux balance between convective transport in flowstructure and diffusion transport in GDL

1. O2mass flux consumed by theelectrochemical reaction at the catalystlayer

2. O2mass flux due to diffusion masstransport through the gas diffusion layer

3. O2mass flux provided by convectivemass transport between the flow channeland gas diffusion layer surface.

Mass f lux 1 Mass flux 2 Mass flux 3= =


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43


To maintain the flux balance, O2mass flux in equations 1, 2 & 3 must be same

conv

EyXx

O

diff

EyXx

O

rxn

CyXx

O JJJ======

==,

^

,

^

,

^

222

( )F

XjMJ O

diff

EyXx

O422 ,

^

===

( )eff

O

EOEyXxOCyXxO D

HF

XjM

2

222 4,,=

====

( )

m

OchannelyXx

OEyXx

OhF

XjM

1

4222 ,,=

====

The following relations can be derived

(4)

(5)

(6)

(7)

44


Couple ydirection O2mass transport in the diffusion layer to thexdirection O2mass transport in the flow channel by considering the overall flux balance inthe control volume (dotted box)

O2leaving out of the top of the control volume can be related to the currentdensity produced by fuel cell.

(8)

(9)

(10)

dxJHuHuX

conv

Ey

OchannelyXx

OCinchannelyx

OCin =

==== =

0

^

,,0 222

( ) =

=

X

O

Xconv

Ey

O dxF

xjMdxJ

00

^

422

Combining equations 6, 7, 8 & 9

( ) ( ) ( )

++= ====

X

Cin

eff

O

E

m

O

channelyXxO

CyXxO dx

Hu

xj

D

XjH

h

Xj

F

M

0,,

2

2

22 4


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45


Assume current density is constant along thexdirection

hm can be determined based on constant-flux Sherwood number

(11)

(12)

(13)

Final expression for oxygen concentration profile along the catalyst layer

++=

====Cin

eff

O

E

m

OchannelyXx

OCyXx

OHu

X

D

H

hF

jM

2

222

1

4,,

C

OF

mH

DShh 2=

++=

====Cin

eff

O

E

OF

C

OchannelyXx

OCyXx

OHu

X

D

H

DSh

H

F

jM

22

222 4,,

Linear profile

46


Three terms that affect O2concentration profile at thereaction site for fuel cell are1.Inlet flow velocity, uin

Supplying more O2 improves mass transport, thus

increasing O2concentration at the catalyst layer2.Diffusion layer thickness, HE

Decreasing diffusion layer thickness also increases theO2concentration at the catalyst layer.

3.Channel size, HC A little tricky as HCappears in both numerator of the

first term and denominator of third term in theparentheses. However, with constant volume flow rate,uinHC is constant. Therefore, decreasing channel sizewill increase the O2concentration.


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47


Flow Structure Pattern

Flow plate typically contain dozen or evenhundreds of fine channels (or groves) tohomogenously distribute gas flow over the fuelcell surface. The shape, size and pattern offlow channels can significantly affect fuel cellperformance.

In PEMFCs, flow field design effort often focuson the water removal capability of cathodeside.

48


Three basic flow structure patterns are1. Parallel flow

Low overall pressure drop between gas inlet andoutlet

However, when the width of the flow field is relativelylarge, flow distribution in each channel may not beuniform

2. Serpentine flow Excellent water removal capability, as only one flow

path exists in the pattern and liquid water is forced toexit the channel

However, in large area cell, serpentine design leadsto large pressure drop

3. Interdigitated flow Promotes forced convection of the reactant gases

through the gas diffusion layer. Far better water management, leading to improved

mass transport Significant pressure drop, but possible to be

overcome by employing extremely small rib spacing.

Inlet

Outlet

Inlet

Outlet

Inlet

Outlet


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49

Analytical Modelling with MATLAB Motivation

Shorter turnaround time

Accessibility

Working with basics: enhancing understanding

Issues:

Oversimplification

Disregard for physical factors

Incapable of complex reality simulations

Way out:

Compare results with numer

selected topics in heat and mass transfer

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