MHD Boundary Layer Flow of Heat and Mass Transfer in the ... · MHD Boundary Layer Flow of Heat and Mass Transfer in the presence of Heat Generation/Absorption, radiation and chemical

MHD Boundary Layer Flow of Heat and Mass Transfer in the presence of

Heat Generation/Absorption, radiation and chemical reaction of a

temperature dependent Viscous Fluid Past a time dependent permeable

Vertical Plate under Oscillatory Suction Velocity

Adebile E.A1 and Sogbetun L.O

2

Department of Mathematical Sciences

Federal University of Technology, Akure

Abstract

In this research, the researchers studied and made analysis on the MHD boundary layer flow of a

variable viscous fluid over a vertical porous plate in a porous medium of time dependent

permeability in the presence of radiation and chemical reaction under oscillatory suction velocity

taking into account the heat generation/absorption and reaction parameter effects. A time

dependent suction was assumed and the radiative flux was described using the differential

approximation for radiation. The governing system of partial differential equations was

linearised using asymptotic techniques. Computational results and graphical representations

showing the effects of the governing model parameters were made and found to be in good

agreement with those in the literature.

Keywords: heat generation/absorption, reaction parameter, MHD, vertical porous plate,

viscous fluid, suction velocity

International Journal of Engineering Research & Technology (IJERT)

Vol. 2 Issue 1, January- 2013ISSN: 2278-0181

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1.0 Literature review

Interest on MHD flow through a porous plate by researchers has tremendouslyincreased over the

years. This is due to the fact that heat and mas transfer through porous media occur in many

engineering, geophysical and biological applications. For instance, permeable porous plates are

used in the filtration processes and also for heated body to keep its temperature constant and to

make the heat insulation of the surfaces more effective. Many investigators have considered

works on the unsteady oscillatory free convective flow through porous media because of its

importance in chemical engineering; turbo machinery and aerospace technology.

Kumar et al [2] in his work,examined an unsteady oscillatory laminar free convective fluid

through a porous medium along a porous hot vertical plate with time dependent suction in the

presence of heat source/sink. In another development, Soundalgekar et al [3],analysed free

convective effects on the oscillatory flow past an infinite vertical porous plate with constant

suction. Singh et al 43], and Venkateswarlu and Rao [5] in their researches studied the effects of

permeability variation and oscillatory suction velocity on free convection and mass transfer flow

of a viscous fluid past an infinite vertical porous plate in the presence of a uniform transverse

magnetic field. Okedoye et al [6 ], on the other hand, researched on the unsteady

magnetohydrodynamic heat and mass transfer in MHD flow of an incompressible, electrically

conducting, viscous fluid past an infinite vertical porous plate along with porous medium of time

dependent permeability under oscillatory suction velocity normal to the plate.

All these aforementioned references did not considered flows involving effects of heat

generation/absorption and reaction parameter on the oscillatory suction velocity in the presence

of temperature dependent viscosity while such flows are encountered in various fields.Adebile



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and Sogbetun[1] very recently investigated MHD flow of a fluid with temperature dependent

viscosity but considered the steady situationuner the influence of constant suction velocity.In the

present study, we extend the previos work by investiging the effects of heat

generation//absorption and reaction parameter on the unsteady MHD boundary layer flow of a

variable viscous fluid over a vertical porous plate in a porous medium of time dependent

permeability in the presence of radiation and chemical reaction under oscillatory suction

velocity. The permeability of the porous medium is considered to be ''

10

' tineKtK and the

suction velocity is assumed to be ''

10

' tinevtv where 00v and 1 is a positive

constant.

1.1 Nomenclature

:u Velocity along x coordinate :'T Non dimensional fluid temperature

:v Velocity along y coordinate :'C Non dimensional species concentration

:g Acceleration due to gravity :T Fluid temperature

:'U Non dimensional fluid velocity : Reaction parameter

:wT Ambient temperature :* Stefan- Boltzmann constant

:C Species concentration :B Coefficient of mass expansion

:wC Ambient species concentration :B Coefficient of thermal expansion

:0B Transverse magnetic field :w Ambient density

: Skin-friction coefficient : Electrical conductivity

: Heat generation/absorption coefficient : Density of the fluid

:k Thermal conductivity :Sc Schmidt number



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:pc Specific heat at constant pressure :D Molar diffusivity

:A Pre-exponential factor :rcG Mass grashof number

:0v Normal velocity at the plate :rG Thermal grashof number

:*k Mean absorption coefficient : Delta, 10 o

:M Hartmann number : Epsilon, 10 o

:Nu Nuselt number :Sh Sherwood number

: Angular velocity :t Time

:Pr Prandtl number : Fluid viscosity

2.0 Mathematical Formulation

A magnetohydrodynamic flow of viscous, incompressible, electrically conducting fluid past an

infinite vertical plate in a porous medium under suction velocity is considered. The x- axis is

taken along the plate in the direction of the flow and y- axis normal to it. A uniform magnetic

field is applied normal to the direction of the flow. It is assumed that the magnetic Reynold

number is less than unity so that the induced magnetic field is neglected in comparison to the

applied magnetic field. We further assumed that all the fluid properties are constant except that

of the influence of density variation with temperature. Thus, the basic flow in the medium is

entirely due to buoyancy force caused by temperature difference between the wall and the

medium. Initially at 0t , the plate as well as fluid is assumed to be at the same temperature and

the concentration of species is very low so that the Soret and Dofour effect are neglected [6].

When 0t , the temperature of the plate is instantaneously raised (or lowered) to '

wT and the



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concentration of species is raised (or lowered) to '

wC . Under the above assumptions and taking

the usual Boussinesq’s approximation into account, the governing equations for momentum,

energy and concentration are presented below:

0'

'

dy

dv

(2.1)

CCAy

CD

y

Cv

t

C '

2'

'2

'

''

'

'

(2.2)

TTy

T

c

k

y

Tv

t

T

p

t ''

2'

'2

'

''

'

'

(2.3)

'2

0

'

'''*

'

'

''

''

'

'

1

1 UB

ek

UCCgTTg

y

U

yy

Uv

t

Uiwt

(2.4)

The boundary conditions are:

0'U TTTeT w

iwt1'

ww

iwt CCCeC 1'at 0'y

0'U , TT ' CC '

as 'y (2.5)

The suction velocity from equation (2.1) is assumed to be )1(0

' iwtevv where

00v and

1 is positive constant.

Introducing the following non dimensional quantities:

'

0 yvy

f

tvt

'2

0 0

'

v

UU

2

0

'4

v

nw

TT

TT

w

'



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CC

CCC

w

'

2

2

0

'vkk

2

0v

A

3

0

*

v

TTgG w

rD

Sc

t

P

k

cPr

0

0

v

BM

2

0

'

v and

3

0v

CCgG w

rc

Below are the non-dimensional governing equations for momentum, energy and concentration of

the unsteady state and their boundary conditions:

Cy

C

Scy

Ce

t

C iwt

2

211

4

1

(2.6)

2

2

Pr

11

4

1

yye

t

iwt (2.7)

UMeky

U

yCGG

y

Ue

t

Uiwtrcr

iwt 2

1

11

4

1

(2.8)

The relevant boundary conditions in dimensionless form are:

,0U ,1 iwte iwteC 1 on 0y

,0U ,0 0C as y (2.9)

The fluid viscosity was assumed to obey the Reynolds model [7]

e (2.10)

Where , is a parameter depending on the nature of the fluid. Using equation (2.10) in equation

(2.8), we obtain



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UMeky

Ue

yCGG

y

Ue

t

Uiwtrcr

iwt 2

1

11

4

1

(2.11)

3.0 Method of Solution

To solve equations (2.6), (2.7) and (2.11), we seek an asymptotic expansion about for our

dependent variables of the form

.....0, 2

10

iwteUyUtyU (3.1a)

.....0, 2

10

iwteyty (3.1b)

.....0, 2

10

iwteCyCtyC (3.1c)

Corresponding to the species equation we have

00

'

0

''

0 CScScCC (3.2)

,100C 00 yC as y

'

01

'

1

''

14

1ScCCiwScScCC

(3.3)

,101C

01 yC as y

Corresponding to the energy equation we have

0PrPr 0

'

0

''

0 (3.4)

100 00 as y



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'

01

'

1

''

1 Pr4

1PrPr iw (3.5)

101 01 as y

Corresponding to the momentum equation we have

000

2

0

'

0

'

0

1CGGUM

kUUe

yrcr (3.6)

,000U ,00U

'

0111

2

0

1

'

1

'

1

1

4

1UCGGUM

kiwUUUe

yrcr (3.7)

,001U 01U

Solving equations (3.2)-(3.5) and substitute the results into (3.1b) and (3.1c), we have

iwtnyxyny eeaeaeyC 108 (3.8)

iwtmyymy eeaeaety 53, (3.9)

Where

44

2

1 2 iwSSSx ccc ccc SSSn 4

2

1 2

4

2

10iw

SnSn

nSa

cc

c



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108 1 aarrr PPPm 4

2

1 2

44

2

1 2 iwPPP rrr

4

2

5iw

PmPm

mPa

rr

r

53 1 aa

To solve equations (3.6)-(3.7), we make use of the following transformation:

Let o where 1 . Thus we assumed the following:

tohUUU ......01000 (3.10)

tohUUU ......11101

(3.11)

Substitute equations (3.12)-(3.14) into equations (3.6)-(3.7) and compile the order of .

We have

0000

2

0

00

2

00

21

CGGUMkdy

dU

dy

Udrcr

(3.12)

0)0(00U 0)(00U

01

01

2

0

01

2

01

2

00 UMkdy

dU

dy

Ud

dy

dU

dy

d (3.13)

0)0(01U 0)(01U

dy

dUCGGUM

kiw

dy

dU

dy

Udrcr

00

1110

2

0

10

2

10

21

4

1

(3.14)

,0010U 010U



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dy

dUUM

kiw

dy

dU

dy

Ud

dy

dUe

dy

d

dy

dU

dy

d iwt 01

11

2

0

11

2

11

2

10

1

10

0

1

4

1

,0011U 011U (3.15)

Based on the solutions obtained in equations (3.12) and (3.15), we calculate equation (3.1a) to be

iwt

yyynyxyy

ymymnymxmyymymy

ynyxymyyy

ynymyymnmyymynymyy

e

eaeaeaeaeaea

eaeaeaeaeaeaea

eaeaeaeaeaea

eaeaeaeaeaeaeaeaeaeatyU

43424140

2

3938

373635

2

34333230

292827262523

22212019

2

181715141311,

(3.16)

Where

2

0

1411

2

1M

k

2

0

1411

2

1M

kccc SSSn 4

2

1 2

rrr PPPm 42

1 2

44

2

1 2 iwPPP rrr

2

0

1

4411

2

1M

k

iw

2

0

1

4411

2

1M

k

iw

44

2

1 2 iwSSSx ccc

2

0

2

13

1M

kmm

Ga r

2

0

2

14

1M

knn

Ga rc

141311 aaa

2

0

2

1155

17

1M

kmm

aeameama

iwtiwt

2

0

2

2

135

18

124

21

Mk

mm

maeaa

iwt



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2

0

2

1455

19

1M

kmnmn

namneameana

iwtiwt

2

0

2

113

20

1M

k

eaaa

iwt

2

0

2

313

21

1M

kmm

meaama

iwt

2

0

2

314

22

1M

knn

enaana

iwt

22212019181715 aaaaaaa

2

0

2

3

25

1

4M

k

iw

aGa rt

2

0

2

135

26

1

4M

k

iwmm

maaGa rt

2

0

2

8

27

1

4M

k

iwxx

aGa rc

2

0

2

1410

28

1

4M

k

iwnn

naaGa rc

2

0

2

11

29

1

4M

k

iw

aa

292827262523 aaaaaa

2

0

2

235

32

1

4

1

Mk

iwmm

ameaa

iwt

2

0

2

2125326525

33

1

4M

k

iwmm

aamemaameaama

iwtiwt

2

0

2

18

2

265

34

1

424

21

Mk

iwmm

amaeaa

iwt

2

0

2

275

35

1

4

1

Mk

iwmxmx

xaxmeaa

iwt



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2

0

2

1952828

36

1

4M

k

iwmnmn

aenaamnnamna

iwt

2

0

2

1729529

37

1

4M

k

iwmm

aameaama

iwt

2

0

2

323

38

1

4M

k

iw

eaaa

iwt

2

0

2

3

2

25

39

1

424

2

Mk

iw

eaaa

iwt

2

0

2

327

40

1

4M

k

iwxx

exaaxa

iwt

2

0

2

22328

41

1

4M

k

iwnn

aenaana

iwt

2

0

2

20329

42

1

4M

k

iw

aeaaa

iwt

2

0

2

15

43

1

4M

k

iw

aa

43424140393837363534333230 aaaaaaaaaaaaa

Skin-friction coefficient at the plate is

iwt

y

e

aanaxaaa

mamnamxamamamaa

anaxamaaa

namaamnamamaanamaay

U

434241403938

37363534333230

292827262523

22212019181715141311

0

2

2

2

(3.17)

Heat transfer coefficient uN at the plate is

ti

y

u emaamy

N 53

0 (3.18)



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Mass transfer coefficient hS at the plate is

ti

y

h enaxany

CS 108

0

(3.19)

4.0 Discussion of Results

In order to investigate the effect of various varying parameters on the flow behaviour and the

temperature distribution within the boundary layer, computational results were obtained for

various values of ,,,,,,,, 0kSGGM crcr and t with fixed values for rP and cS . These

parameters were assigned the following values ,2.0,2.0,0.1,2.1,5.0 0kGGM rcr

2.0,2.0,5.0 and 2t except where stated otherwise while the values of rP and

cS were taken to be 0.71 and 0.6 respectively for plasma. It should be noted that 0,0 and

0 represent destructive, no and generative chemical reactions respectively. Also,

0,0 and 0 indicates heat absorption, no heat generation/absorption and heat

generation respectively. The figures are presented in 3-dimensional figures.

From equation (2.10), we could see that increase in viscosity parameter leads to decrease in

viscosity.

Numerical values of skin friction are showed in Table 4.1. We observed that an increase in

viscosity parameter, mass Grashof number or the thermal Grashof number increases skin friction

whereas increase in magnetic parameter or reaction parameter leads to a decrease in skin friction

coefficient.



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Table 4.2 displayed the effects of viscosity parameter on the dimensionless velocity. It is

discovered thatincrease in viscosity parameter bring about increase in the fluid velocity near the

plate only while reverse is the case as we move away from the plate. The fluid velocity increased

and reached its maximum value at very short distance from the plate and then decreased to zero.

Figures 4.1 - 4.10, show the effect of the varying parameters on the velocity field. It is observed

that maximum velocity occurs in the body of the fluid close to the surface. Figures 4.1-4.2

highlight the effects of delta and epsilon on the fluid velocity. It could be seen that increase

in delta or epsilon increases velocity. We observed in figure 4.3 that increase in destructive

chemical reaction 0 parameter reduces the velocity field while increase in the generative

chemical reaction 0 parameter increases the velocity. We displayed the effect of on

velocity in figure 4.4; it is shown that increases in brings about increase in velocity field.

Furthermore, we investigate the effect of Hartmann number M on the fluid velocity in figure 4.5.

We discovered that increase in Hartmann number M reduces the velocity field as a result of an

opposing force (Lorentz force). Also, figure 4.6 shows that increase in permeability increases the

velocity. The effectsof mass and thermal Grashof numbers on the velocity field are shown in

fugures 4.7 and 4.8 respectively. We discovered that velocity increases as either mass or thermal

Grashofnumber increases. Figure 4.9 and 4.10 show that increase in and t increase the

velocity.

Figure 4.11 show the effect of chemical reaction parameters on concentration field. It is observed

that for a generative chemical reaction, there exist oscillations in the field away from the surface.

This brings about the presence of minimum and maximum concentration in the field which

however less than the surface concentration. For destructive chemical reaction, the boundary



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layer reduces as the reaction parameters increases. Also there is reduction in concentration field

as reaction parameter increases positively.

In figure 4.13, we display the concentration field as a function of ty, , it could be seen that

concentration decreases as the flow progresses and decreases faster as we move away from the

boundary. While concentration is displayed as a function of t, in figure 4.12. Oscillation is

observed along axiswith a steep decrease in the field as y increases.

We displayed in figure 4.14- 4.16, the temperature profile for various values of parameters under

consideration.

It could be seen from figure 4.14 that heat absorption 0 resulted in decreases in the fluid

body temperature, while heat 0 increases the fluid body temperature which leads to

presence of extremes temperature in the body of the fluid greater than the surface temperature.

In figure 4.16 and 4.15, we show the temperature profile as a function of ty, and t,

respectively. It is observed that the temperature decreases as y increases, and oscillatory field along t and

axis which is more pronounced at the initial stage continuous as y increases.



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02

46

810

-0.2

-0.1

0

0.1

0.2

-0.1

0

0.1

0.2

0.3

ydelta

02

46

810

-0.2

-0.1

0

0.1

0.2

-0.1

0

0.1

0.2

0.3

yepsilon

02

46

810

-2

-1

0

1

2

-0.1

0

0.1

0.2

0.3

yphi

02

46

810

-2

-1

0

1

2

-0.1

0

0.1

0.2

0.3

yreaction parameter

Table 3.10: Skin-friction coefficient when 0 Table 3.11: Velocity yU distribution for various values of

Fig 3.1: Velocity field as function of ,y


y 2.0U 1.0U 0.0U 1.0U 2.0U

0 0 0 0 0 0

2 0.0945 0.0943 0.0941 0.0939 0.0937

4 -0.0085 -0.0086 -0.0086 -0.0086 -0.0087

6 -0.0261 -0.0261 -0.0261 -0.0261 -0.0261

8 -0.0134 -0.0134 -0.0134 -0.0134 -0.0134

10 -0.0008 -0.0008 -0.0008 -0.0008 -0.0008

rG rcG 1.0 0k 1.0 0.0 2.0

-2.0 1.0 0.5 -0.5 0.2 -0.2 -0.2664 -0.2900 -0.3373

-1.0 1.0 0.5 -0.5 0.2 -0.2 0.0740 0.0779 0.0857

0.0 1.0 0.5 -0.5 0.2 -0.2 0.4143 0.4458 0.5087

1.2 1.0 0.5 -0.5 0.2 -0.2 0.8228 0.8873 1.0164

1.2 -1.0 0.5 -0.5 0.2 -0.2 -0.0059 -0.0043 -0.0011

1.2 0.0 0.5 -0.5 0.2 -0.2 0.4084 0.4415 0.5076

1.2 1.0 0.0 -0.5 0.2 -0.2 0.8405 0.9067 1.0392

1.2 1.0 1.0 -0.5 0.2 -0.2 0.7759 0.8359 0.9560

1.2 1.0 0.5 -1.0 0.2 -0.2 0.7981 0.8612 0.9872

1.2 1.0 0.5 1.0 0.2 -0.2 0.7169 0.7776 0.8988



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02

46

810

-2

0

2

4

-0.2

0

0.2

0.4

0.6

yGrc

02

46

810

-2

0

2

4

-0.2

0

0.2

0.4

0.6

yGrt

02

46

810

1214

-4

-2

0

2

4

-2

-1

0

1

yk0

02

46

810

0

1

2

3

4

-0.1

0

0.1

0.2

0.3

yM

02

46

810

-10

-5

0

5

10

-0.1

0

0.1

0.2

0.3

yw

02

46

810

0

1

2

3

4

-0.1

0

0.1

0.2

0.3

yt

Fig 3.3: Velocity field as function of ,y Fig 3.4: Velocity field as function of ,y

Fig 3.5: Velocity field as function of My,

Fig 3.6: Velocity field as function of 0,ky

Fig 3.7: Velocity field as function of rcGy, Fig 3.8: Velocity field as function of rtGy,



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02

46

810

-10

-5

0

5

10

-0.5

0

0.5

1

1.5

yw

02

46

810

-2

-1

0

1

2

-0.5

0

0.5

1

yu

02

46

810

0

1

2

3

4

-0.5

0

0.5

1

1.5

yt

02

46

810

-10

-5

0

5

10

0

0.5

1

1.5

yw

02

46

810

-2

-1

0

1

2

-0.5

0

0.5

1

yphi

02

46

810

0

1

2

3

4

0

0.5

1

1.5

yt


Fig 3.10: Velocity field as function of ty,

Fig 3.11: Concentration field as function of ,y Fig 3.12: Concentration field as function of ty,

Fig 3.13: Concentration field as function of ,y Fig 3.14: Temperature field as function of ,y



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Fig 3.15: Temperature field as function of ,y Fig 3.16: Temperature field as function of ty,

Numerical Method

Applying Crank-Nicolson formula to equations (2.6), (2.7) and (2.11), we have

jijijiji DCRCQCP ,31,131,31,13 (5.1)

jijijiji DRQP ,21,121,21,12 (5.2)

jijijiji DURUQUP ,11,111,11,11 (5.3)

With corresponding conditions (2.9) becoming

0,0 jU jiwt

j e1,0 jiwt

j eC 1,0

0, jU 0, j 0, jC (5.4)

Where

f

t

fSc

rS 13

y

t

f

f

fSc

rP

42

23

fSc

rQ 13

fSc

r

y

t

f

fR

24

23

jijijiji CRCSCPD ,13,3,13,3

yf

tf

f

rRP

4Pr2

1 2

'

2Pr

11

'

2f

rRQ

Pr2

1

4

'

22

f

rR

y

t

f

fR

f

t

f

rRS

Pr

11

'

2

jijijiji CRCSCPD ,12,2,12,2

y

f

f

t

f

rdP

42

2

'

11

f

rdQ

'

11 1

y

f

f

t

f

rdR

42

2

'

11

2

'

11 1 d

f

t

f

rdS



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43,11,1,11,1 ddf

tURUSUPD jijijiji

Thus, y and t are constant mesh sizes along y and t directions respectively. We need a

scheme to find single values at next level time in terms of known values at an earlier time level.

A forward difference approximation for the first order partial derivatives of ,C and U with

respect to t and y and a central difference approximation for the second order partial derivative

of ,C and U with respect to t and y are used. We used the following transformations

4

1f jiwt

ef 12 ed1

2

0

2

1M

kd rtGd3 CGd rt4 1

2

'

y

tr

We have converted partial differential equations (2.6), (2.7) and (2.11) that hold everywhere in

some domain into a system of simultaneous linear equations (5.1)-(5.3) to get approximate

solutions. The corresponding code (programme) is written in Mathlab for calculating numerical

solutions for concentration, temperature and velocity.

5.1 Tables and Graphical Presentations: Numerical Solution

To ensure the validity of our analytical solutions, we have compared our numerical solutions

with the exact solutions for concentration, temperature and velocity for some variation

parameters affecting fluid profile. These parameters are assigned the values

3.0,0.1,5.0,1.0,1.0,5.0,1.0,0.1,0.5,0.1 AtnRGGM rcr in case 5.

The corresponding code (programme) is written in Mathlab for calculating both the exact and

numerical solution. In table 5.1 - 5.3, the comparison between analytical values and numerical

values for concentration, temperature and velocity are presented. The error differences are

reasonable and passable. The closeness of curves corresponding to both exact and numerical



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0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

numerical

analytical

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

numerical

analytical

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

numerical

analytical

solutions in all the cases considered in figure 5.1-5.3 further confirm the accuracy of our method

of solution.

Table 5.1: Comparison between exact and Table 5.2: Comparison between exact and

numerical values for concentration numerical values for temperature

Table 5.3: Comparison between exact and

numerical values for velocity

Figure 5.1: Concentration profiles

Figure 5.2: Temperature profiles Figure 5.3: Velocity profile

y Analytical Numerical Error

0 1 1 0

2 0.2529 0.2524 0.0005

4 0.064 0.0637 0.0003

6 0.0162 0.0161 0.0004

8 0.0041 0.0041 0

10 0.001 0.001 0


0 1 1 0

2 0.1746 0.1739 0.0007

4 0.0305 0.0303 0.0002

6 0.0053 0.0053 0

8 0.0009 0.0009 0

10 0.0002 0.0002 0


0 0 0 0

2 0.0837 0.1015 0.0178

4 0.0185 0.0222 0.0037

6 0.0042 0.005 0.0008

8 0.0010 0.0011 0.0001

10 0.0002 0.0003 0.0001



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REFERENCE

[1] Adebile ,E .A.and Sogbetun MHD Flow of A Non-Newtonian Fluid With Temperature

Dependent Viscosity Past A Vertical Plate In The Presence Of Radiative Heat Flux And

Chemical Reaction. International Journal of Engineering Research & Technology (IJERT) Vol.

1 Issue 10,

[2] A. Kumar, B. Chand and Kaushik, On Unsteady Oscillatory Laminar Free Convection

Flow of an Electrically Conducting Fluid through Porous Medium along a Porous Hot

Vertical Plate with Time Dependent Suction in the Presence of Heat Source/ Sink, J. of

Acad Math, vol. 24, 339 – 354, 2002.

[3] V. M. Soundalgekar, Free Convection Effects on the Oscillatory Flow Past an Infinite

Vertical Porous Plate with Constant Suction 1, Proc. Royal Soc. London A 333, 25-36,

1973.

[4] A.K. Singh, A.K. Singh and N.P. Singh, Heat and Mass Transfer in MHD Flow of a

Viscous Fluid Past a Vertical Plate under Oscillatory Suction Velocity, Ind. J. of Pure

Appl. Math, vol. 34, 429-442, 2003.

[5] K. Venkateswarlu and J. A. Rao, Numerical Solution of Heat and Mass Transfer in MHD

Flow of a Viscous Fluid Past a Vertical Plate under Oscillatory Suction Velocity, IE(I)

Journal-MC, 206 -212, 2005.

[6] Okedoye, A. M. and Bello, O. A., MHD Flow of a Uniformly Stretched Vertical

Permeable Surface under Oscillatory Suction Velocity, J. of the Nigerian Association of

Mathematical Physics vol. 13, 211-220, 20008.



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[9]. Massoudi, M. and Phuoc, T. X., Flow of a Generalized Second Grade Non-Nowtonian

Fluid with Variable Viscosity, Continum Mech. Thermodyn. 16, 529-538, 2004.



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MHD Boundary Layer Flow of Heat and Mass Transfer in the ... · MHD Boundary Layer Flow of Heat and Mass Transfer in the presence of Heat Generation/Absorption, radiation and chemical