SEM 1104 014 Heat Generation Thermal Radiation Soret Effect Unsteady Flow Porous Plate

Canadian Journal on Science and Engineering Mathematics Vol. 2 No. 4, November 2011

210

Heat Generation and Thermal Radiation Effects Combined With Soret

Effect on an Unsteady Flow over a Porous Plate M. A. Samad

1, Sajid Ahmed

2

1Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh.

2Institute of Natural Sciences, United International University, Dhaka-1209, Bangladesh

1Corresponding Author: [email protected]

Abstract

The present investigation comprises of unsteady two dimensional magnetohydrodynamic heat and

mass transfer free convection flow along a porous plate in presence of magnetic field with radiation

and Soret effect. The problem has been analyzed by applying Nachtsheim-Swigert shooting iteration

technique along with sixth order Runge-Kutta integration scheme. The nonlinear partial differential

equations governing the flow field occurring in the problem have been transformed to dimensionless

nonlinear ordinary differential equations by introducing suitably selected similarity variables. The

ensuing equations are simultaneously solved by applying numerical iteration scheme for velocity,

temperature and concentration fields. The results are displayed graphically in the form of velocity,

temperature and concentration profiles. The corresponding skin-friction coefficient and Nusselt

number which are of physical and engineering interest are displayed in tabular form. Several

important parameters such as the Prandtl number (Pr), radiation parameter (N), magnetic field

parameter (M), heat source parameter (Q), suction parameter ( 0v ), time dependency parameter (n)

and Soret number (So) etc. are confronted. The effects of these parameters on the velocity,

temperature and concentration profiles are studied. A comparison of the present results is made with

Samad and Rahman (2006).

Key Words: MHD, Unsteady Flow, Heat Generation, Thermal Radiation.

Introduction

The problems for time dependent flows

are very important in nature. In recent

years a number of works have been done

on unsteady flows and on porous plates.

These types of models have numerous

applications in today’s industrial and

other scientific worlds. Recently, Samad

and Rahman (2006) investigated thermal

radiation interaction with unsteady MHD

flow past a vertical porous plate immersed

in a porous medium. Radiation effects on

free convection flow of a gas past a semi

infinite flat plate was studied by

Soundalgekar and Takhar (1987). Hossain

and Takhar (1996) studied the effect of

radiation using the Rosseland diffusion

approximation on mixed convection along

a vertical plate with uniform free stream

velocity and surface temperature. Ali et

al. (1984) studied radiation effect on

natural convection flow over a vertical

surface in a gray gas. Followed by Ali et

al. Mansour (1990) studied the interaction

of mixed convection with thermal

radiation in laminar boundary flow over a

horizontal, continuous moving sheet with

suction/ injection. Meanwhile the same

problem considering magnetic effect

taking into account the binary chemical

reaction and Soret- Dufour effects was

studied by Alabraba et al. (1992).

The transient free convection flow past a

semi-infinite vertical plate by an integral

method was first studied by Seigal (1958).

Subsequently numerous researchers have

investigated free convection flow past a

semi-infinite vertical plate in different

forms. Raptis and Perdikis (1985) studied

numerically free convection flow through


211

a porous medium bounded by a semi-

infinite vertical porous plate. Sattar

(1992) studied the same problem and

obtained analytical solution by the

perturbation technique adopted by Singh

and Dikshit (1988). Sattar et al. (2000)

studied unsteady free convection flow

along a vertical porous plate embedded in

a porous medium. Anghel et al. (2000)

investigated the Dufour and Soret effects

on free convection boundary layer over a

vertical surface embedded in a porous

medium. Postelnicu (2004) studied

numerically the influence of a magnetic

field on heat and mass transfer by natural

convection from vertical surfaces in

porous media considering Soret and

Dufour effects. Alam and Rahman (2005)

investigated the Dufour and Soret effects

on steady mixed convection flow past a

semi-infinite vertical porous flat plate in a

porous medium with variable suction.

This present work investigated the heat

generation and thermal radiation

interaction combined with Soret effect on

an absorbing emitting fluid permitted by a

transversely applied magnetic field past a

moving vertical porous plate embedded in

a porous medium with time dependent

suction, temperature and concentration.

Mathematical Formulation

We consider the model of an unsteady

MHD free convection flow of a viscous,

incompressible and electrically

conducting fluid along a vertical porous

flat plate under the influence of uniform

magnetic field with heat generation. The

flow is taken along the x-direction, which

is to be in the upward direction along the

plate and y-axis normal to the plate.

Initially it is assumed that the plate and

the fluid are at a constant temperature ∞T

at all points. At time 0>t the plate is

assumed to be moving in the upward

direction with the velocity )(tU and there

is a suction velocity )(0 tv taken to be a

function of time, the temperature of the

plate raised to )(tT where ∞> TtT )( . The

plate is considered to be of infinite length,

thus all derivatives with respect to x

vanish and so the physical variables are

functions of y and t only. The flow

configuration and the system of

coordinates are shown in Fig. 1.

Fig. 1: Flow configuration and the

coordinates system.

The fluid is considered to be gray;

absorbing- emitting radiation but non-

scattering medium and the Rosseland

approximation is used to describe the

radiative heat flux in the x-direction is

considered negligible in comparison to

the y-direction. Boussinesq and boundary

layer approximations are assumed to hold

in this case.

The following are the governing

equations of the problem using the Darcy-

Forchhemier model:

Continuity equation:

0=∂

∂

y

v (1)

Momentum equation:

( )

22

2

2

uk

bu

ku

B

TTgy

u

y

uv

t

u

−−−

−+∂

∂=

∂

∂+

∂

∂∞

υ

ρ

σ

βυ

(2)

)(0 tv

)(tU

T ∞T

C ∞C

∞U

v

u

y

x


212

Energy equation:

( )y

q

cTT

c

Q

y

u

cy

T

y

Tv

t

T

r

pp

p

∂

∂−−+

∂

∂+

∂

∂=

∂

∂+

∂

∂

∞ρρ

υα

10

2

2

2

(3)

Concentration equation:

2

2

2

2

y

TD

y

CD

y

Cv

t

CTm

∂

∂+

∂

∂=

∂

∂+

∂

∂ (4)

where (u, v) are the components of

velocity along the x and y directions

respectively, t is the time, υ is the

kinematic viscosity, ρ is the density of

the fluid, g is the gravitational

acceleration, β is the coefficient of

volume expansion, B is the magnetic

induction, T and ∞T are the temperature

of the fluid within the boundary layer and

in the free stream respectively, σ is the

electric conductivity, α is the thermal

diffusivity, pc is the specific heat at

constant pressure, k is the permeability of

the porous medium, C and ∞C are the

concentration of the fluid within the

boundary layer and in the free stream

respectively, mD is the chemical

molecular diffusivity, 0Q is the

volumetric rate of heat generation, and

0T

kDD Tm

T = , with Tk is thermal diffusion

ratio, and 0T is the mean temperature.

The boundary conditions corresponding to

the problem are as follows:

0

as,,0

0at)(),(

),(),( 0

>

∞→===

=

==

==

∞∞

t

yCCTTu

ytCCtTT

tvvtUu

(5)

The radiative heat flux rq is simplified by

Rosseland approximation as,

y

Tqr

∂

∂−=

4

1

1

3

4

κ

σ (6)

where 1σ is the Stefan- Boltzmann

constant and 1κ is the mean absorption

coefficient. Here 4T can be expressed as

a linear function of temperature as the

temperature differences within the flow

are sufficiently small. It can be

accomplished by expanding 4T in a

Taylor Series about ∞T and neglecting

higher-orders, thus,

434 34 ∞∞ −≈ TTTT (7)

Using the equation (6) and (7) we get

from (3),

( )2

2

1

3

10

2

2

2

4

y

T

c

TTT

c

Q

y

u

cy

T

y

Tv

t

T

pp

p

∂

∂+−+

∂

∂+

∂

∂=

∂

∂+

∂

∂

∞∞

κρ

σ

ρ

υα

(8)

In light of Sattar and Hossain (1992) let

us introduce a similarity parameter δ as

)(tδδ = (9)

such that δ is a length scale.

With this similarity parameter, a

similarity variable is then introduced as

δη

y= (10)

In terms of this length scale, a convenient

solution of the equation (1) can be taken

as,

0)( vtvvδ

υ−==

where 0v is the suction parameter, which

is positive for suction and negative for

injection.

)(tU , )(tT and )(tC are now considered to

have the following form [Sattar and

Hossain (1992)]:

−+=

−+=

=

∞∞

∞∞

+

n

n

n

CCCtC

TTTtT

UtU

2*0

2*0

22*0

)()(

)()(

)(

δ

δ

δ

(11)


213

We take n as a non-negative integer

and 0U , 0T and 0C are respectively the

free stream velocity, mean temperature

and mean concentration.

Here0

*δ

δδ = , with 0δ is the value of δ

at 0tt = .

With the intention to make the equations

(2), (8) and (4) dimensionless, the

following transformations are introduced:

−+=

−+=

==

∞∞

∞∞

+

)()(

)()(

)()()(

2*0

2*0

22*0

ηφδ

ηθδ

ηδη

n

n

n

CCCC

TTTT

fUftUu

(12)

Using these transformations we obtain the

following system of nonlinear ordinary

differential equations [following Sattar et

al. (2000), Sattar and Maleque (2000)]:

0)1

44()2(

21

0

=−++

++−′++′′

fDa

FsGrf

Da

Mnfvf

θ

η

(13)

043

Pr3)4(

43

Pr3

43

Pr3)2(

2

0

=′+

+−

+−′

+++′′

fEcN

NQn

N

N

N

Nv

θ

θηθ

(14)

04)2( 0 =′′+−′++′′ θφφηφ SoScnScScv

(15)

where 0

200 )(

U

TTgGr

υ

δβ ∞−= is the local

Grashof number, ρυ

δσ 22B

M = is the local

magnetic parameter, α

υ=Pr is the Prandtl

number, 2δ

kDa = is the local Darcy

number, υ

δ0Re

U= is the local Reynolds

number, δ

bFs = is the Forchhemier

number and Re

22

01

+

=

nb

Fsδ

δ

δ is the

modified Forchhemier number,

31

1

4 ∞

=T

kN

σ

κ is the radiation parameter,

0

0

1Uc

QQ

pρ

δ= is the heat source

parameter, Re1QQ = is the modified heat

source parameter, mD

Scυ

= is the Schmidt

number and )(

)(

0

0

∞

∞

−

−=

CC

TTDSo T

υ is the Soret

number.

The boundary conditions corresponding to

the above equations for 0>t are:

∞→===

====

ηφθ

ηφθ

as0,0,0

0at1,1,1

f

f (16)

Numerical Computation

We have applied Nachtsheim-Swigert

(1965) shooting iteration technique along

with the sixth order Runge-Kutta

integration scheme to obtain the

numerical solutions of the nonlinear

ordinary differential equations (13)-(15)

under the boundary conditions (16). A

step size of 01.0=∆η has been chosen to

satisfy the convergence criterion of 610− in

all cases. The maximum value of η was

selected in accordance with the values of

each group of parameters

10 ,,,,Pr,,,, QScSoNGrnMv to satisfy the

accuracy requirement.


214

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01

0.005

0.001f

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 0.5, Sc = 0.22, Ec = 1.0

Gr= +10

Fig. 2: Velocity profiles for various step

sizes.

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

η

θ0.010.0050.001

Vo = 1.0, Pr = 0.71, M = 2.0N = 0.5, Sc = 0.22, Ec = 1.0

Gr = +10

Fig. 3: Temperature profiles for various step

sizes.

The code has been verified by taking

three different step sizes as 01.0=∆η ,

005.0=∆η , and 001.0=∆η , which were

found to be in excellent agreement among

them (Fig. 2 and Fig. 3).

Results and Discussion

To discuss the results of this model, the

numerical solutions are illustrated in the

form of non-dimensional velocity,

temperature and concentration profiles.

Large values (+ve and -ve) of Grashof

number (Gr) have been considered due to

natural convection.

Effect of suction parameter ( 0v ) on the

velocity, temperature and concentration

profiles are shown in Fig. 4, Fig. 5, and

Fig. 6 respectively. We observe that with

the increase of suction parameter the

velocity profile decreases. This is because

due to increasing suction the matters are

removed from the flow field in large

amount and thus reducing the velocity of

the flow field (Samad and Rahman,

2006). This also stabilizes the flow from

getting turbulent. A similar event happens

for the temperature and concentration

profiles in Fig. 5 and Fig. 6. In the Fig. 7,

Fig. 8 and Fig. 9 the effects of Prandtl

number is shown. We see that with the

increase of the Prandtl number the

velocity profiles decrease for 10+=Gr and

increase for 10−=Gr . The temperature

profiles decrease with the increase of the

Prandtl number. The concentration

profiles increase with the increase of the

Prandtl number.

The effect of the radiation parameter N is

demonstrated in the Fig. 10, Fig. 11, and

Fig. 12. The velocity profiles decrease

with the increase of the radiation

parameter N for 10+=Gr and increase

for 10−=Gr . The temperature profiles

decrease with the increase of N. For the

large values of N (for example N = 5.0),

the thermal boundary layer reduces

immensely. So, if we allow radiation in

the flow field then controlling the

temperature as well as the fluid flow

becomes a lot easier. This has large

application in industries where a high

temperature is a byproduct. The

concentration profiles increase with the

increase of N. The effects of magnetic

field parameter M on velocity,

temperature and concentration profiles are

shown in Fig. 13, Fig. 14, Fig. 15

respectively. The velocity curves in Fig.

13 show that the rate of fluid flow is

significantly reduced with the increase of

magnetic field parameter M. The oblique

magnetic field opposes the transport

phenomena. The Lorenz force variation

happens with the variation of the

magnetic field parameter M and the


215

increase of the Lorenz force produces

more resistance to the transport

phenomena (Ishak et al. 2008).

The effects of the values of n are shown

in the Fig. 16, Fig. 17, and Fig. 18. The

values of n indicate the time dependency

of the flow. When n = 0, it means the

flow is steady. With the increase of the

values of n the velocity profiles, the

temperature profiles and the concentration

profiles decrease. This indicates that time

dependency is a very important feature of

this flow. The effect of the values of heat

generation parameter Q is illustrated in

the Fig. 19, Fig. 20, and Fig. 21. When

heat is generated in the flow field, the

flow activities increase. We see that with

the increase of the heat generation

parameter Q the velocity and the

temperature profiles increase in the Fig.

19 and Fig. 20. This is because of the fact

that soaring heat contributes to the

increase of the velocity and thermal

boundary layer thickness. But the

concentration profiles decrease with the

increase of the heat generation parameter

as shown in Fig. 21.

In the Fig. 22, Fig. 23 and Fig. 24 the

effects of the Soret number So are

demonstrated. The velocity and the

temperature profiles do not show any

difference due to the variation of the

values of Soret number. On the other hand

as the Soret number is related to the mass

transfer of the flow, the concentration

profiles show a large amount of variation.

In the Fig. 24 we see that with the

increase of the Soret number So, the

concentration profiles increase. Thus in

order to affect the concentration without

changing the velocity or the temperature

varying the Soret number So would be

fine.

0 0.25 0.5 0.75 1 1.25 1.5

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Pr = 7.0, M = 1.0, Q = 1.0,N = 1.0, Sc = 1.0, Ec = 5.0

Gr = +10Vo = 0.0, 0.5, 1.0, 1.5, 2.0

Gr= -10Vo = 0.0, 0.5, 1.0, 1.5, 2.0

Fig. 4: Velocity profiles for various values of 0v .

0 0.25 0.5 0.75 1 1.25 1.50

0.2

0.4

0.6

0.8

1

θ

η

Pr = 7.0, M = 1.0, Q = 1.0,N = 1.0, Sc = 1.0, Ec = 1.0

Gr = +10Vo = 0.0, 0.5, 1.0, 1.5, 2.0

Fig. 5: Temperature profiles for various values of

0v .

0 0.25 0.5 0.75 1 1.25 1.50

0.2

0.4

0.6

0.8

1

φ

η

Pr = 7.0, M = 1.0, Q = 1.0,N = 1.0, Sc = 1.0, Ec = 1.0

Gr = +10Vo = 0.0, 0.5, 1.0, 1.5, 2.0

Fig. 6: Concentration profiles for various values

of 0v .


216

0 0.5 1 1.5 2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Vo = 1.0, M = 1.0, Q = 1.0,N = 1.0, Sc = 1.0, Ec = 1.0

Gr= -10Pr = 0.10, 0.71, 1.0, 7.0, 10

Gr= +10Pr = 0.10, 0.71, 1.0, 7.0, 10

Fig. 7: Velocity profiles for various values of Pr .

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

θ

η

Vo = 1.0, M = 1.0, Q = 1.0,N = 1.0, Sc = 1.0, Ec = 1.0

Gr= +10Pr = 0.10, 0.71, 1.0, 7.0, 10

Fig. 8: Temperature profiles for various values of

Pr .

0 0.25 0.5 0.750

0.2

0.4

0.6

0.8

1

φ

η

Vo = 1.0, M = 1.0, Q = 1.0,N = 1.0, Sc = 1.0, Ec = 1.0

Gr= +10Pr = 0.10, 0.71, 1.0, 7.0, 10


of Pr .

0 0.5 1 1.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Vo = 1.0, M = 1.0, Q = 1.0,Pr = 7.0, Sc = 1.0, Ec = 1.0

Gr = +10N = 0.01, 0.10, 0.50, 1.0, 5.0

Gr = -10N = 0.01, 0.10, 0.50, 1.0, 5.0

Fig. 10: Velocity profiles for various values of N .

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

θ

η

Vo = 1.0, M = 1.0, Q = 1.0,Pr = 7.0, Sc = 1.0, Ec = 1.0

Gr = +10N = 0.01, 0.10, 0.50, 1.0, 5.0

Fig. 11: Temperature profiles for various values

of N .

0 0.25 0.5

0.2

0.4

0.6

0.8

1

φ

η

Vo = 1.0, M = 1.0, Q = 1.0,Pr = 7.0, Sc = 1.0, Ec = 1.0

Gr = +10N = 0.01, 0.10, 0.50, 1.0, 5.0


of N .


217

0 0.5 1 1.5 2

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Vo = 1.0, Pr = 0.71, Q = 1.0,N = 0.5, Sc = 1.0, Ec = 1.0

Gr= +10M = 0.0, 1.5, 3.0, 4.0, 6.0

Gr= -10M = 0.0, 1.5, 3.0, 4.0, 6.0

Fig. 13: Velocity profiles for various values of M .

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

θ

η

Vo = 1.0, Pr = 0.71, Q = 1.0,N = 0.5, Sc = 1.0, Ec = 1.0

Gr= -10M = 0.0, 1.5, 3.0, 4.0, 6.0


of M .

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

φ

η

Vo = 1.0, Pr = 0.71, Q = 1.0,N = 0.5, Sc = 1.0, Ec = 1.0

Gr= -10M = 0.0, 1.5, 3.0, 4.0, 6.0


of M .

0 0.5 1 1.5 2 2.5 3 3.5 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Vo = 1.0, Pr = 0.71, Q = 1.0,N = 0.5, Sc = 1.0, Ec = 1.0

Gr= +10n = 0.0, 0.5, 1.0, 1.5, 2.0

Gr= -10n = 0.0, 0.5, 1.0, 1.5, 2.0

Fig. 16: Velocity profiles for various values of n .

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

θ

η

Vo = 1.0, Pr = 0.71, Q = 1.0,N = 0.5, Sc = 1.0, Ec = 1.0

Gr= +10n = 0.0, 0.5, 1.0, 1.5, 2.0


of n .

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

φ

η

Vo = 1.0, Pr = 0.71, Q = 1.0,N = 0.5, Sc = 1.0, Ec = 1.0

Gr= +10n = 0.0, 0.5, 1.0, 1.5, 2.0


of n .


218

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 2.0, Sc = 0.22, Ec = 1.0

Gr= +10Q= 0.0, 2.0, 4.0, 5.0, 6.0

Gr= -10Q= 0.0, 2.0, 4.0, 5.0, 6.0

Fig. 19: Velocity profiles for various values of Q .

0 0.25 0.5 0.75 1 1.25 1.5 1.75 20

0.2

0.4

0.6

0.8

1

θ

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 2.0, Sc = 0.22, Ec = 1.0

Gr= +10Q= 0.0, 2.0, 4.0, 5.0, 6.0


of Q .

0 0.25 0.5 0.75 1 1.25 1.5 1.75 20

0.2

0.4

0.6

0.8

1

φ

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 2.0, Sc = 0.22, Ec = 1.0

Gr= +10Q= 0.0, 2.0, 4.0, 5.0, 6.0


of Q .

0 0.5 1 1.5 2 2.5 3

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 0.05, Sc = 0.22, Q = 5.0

Gr= +10So = 0.08, 0.4, 2.0, 3.0, 4.0

Gr= -10So = 0.08, 0.4, 2.0, 3.0, 4.0

Fig. 22: Velocity profiles for various values of So .

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

θ

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 0.05, Sc = 0.22, Q = 5.0

Gr= +10So = 0.08, 0.4, 2.0, 3.0, 4.0


of So .

2 3 40

0.02

0.04

0.06

0.08

0.1

0.12

0.14

φ

η

Vo = 1.0, Pr = 0.71, M = 2.0,N = 0.05, Sc = 0.22, Q = 5.0

Gr= +10So = 0.08, 0.4, 2.0, 3.0, 4.0


of So .


219

Table 1: Skin-friction coefficients fC for

different values of 0v for Pr = 0.71, Ec =

0.2, N = 0.5, M = 0.5, n = 1.0, So = 1.0.

0v Gr with Q =

0.0 with Q =

2.0 Samad et

al. 2006

0.0 10 -2.02397 -1.93645 -2.0239

0.5 10 -2.20140 -2.10787 -2.20139

1.0 10 -2.39637 -2.29712 -2.39638

2.0 10 -2.84176 -2.73247 -2.84188

0.0 -10 -6.16329 -6.28518 -6.16298

0.5 -10 -6.51235 -6.64218 -6.51201

1.0 -10 -6.87308 -7.00983 -6.87269

2.0 -10 -7.62299 -7.76993 -7.62243

Table 2: Skin-friction coefficients fC for

different values of 0v = 0.5, Gr = 10, Pr =

0.71, Ec = 0.2, n = 1.0, So = 1.0.

M N with Q =

0.0 with Q =

2.0 Samad et

al. 2006

0.0 0.5 -2.11352 -2.01778 -2.11351

1.5 0.5 -2.37177 -2.28238 -2.37175

3.0 0.5 -2.61503 -2.53124 -2.61501

5.0 0.5 -2.91939 -2.84212 -2.91936

0.5 0.01 -1.77483 -1.76620 -1.71445

0.5 0.10 -1.93142 -1.87832 -1.92589

0.5 0.50 -2.20140 -2.10787 -2.20139

0.5 1.0 -2.32428 -2.22053 -2.32422

Table 3: Rate of heat transfer uN for

different values of M and N for Pr = 0.71,

Ec = 0.2, N = 0.5, M = 0.5, n = 1.0, So =

1.0.

0v Gr with Q =

0.0 with Q =

2.0 Samad et

al. 2006

0.0 10 0.96751 0.75644 0.96755

0.5 10 1.01869 0.81023 1.01875

1.0 10 1.07175 0.86629 1.07183

2.0 10 1.18321 0.98468 1.18337

0.0 -10 0.84112 0.61457 0.84126

0.5 -10 0.88633 0.66218 0.88650

1.0 -10 0.93369 0.71244 0.93390

2.0 -10 1.03479 0.82057 1.03513

Table 4: Rate of heat transfer uN for

different values of M and N for 0v = 0.5,

Gr = 10, Pr = 0.71, Ec = 0.2, n = 1.0, So

= 1.0.

M N with Q =

0.0 with Q =

2.0 Samad et

al. 2006

0.0 0.5 1.01988 0.81143 1.01995

1.5 0.5 1.01630 0.80782 1.01636

3.0 0.5 1.01273 0.80421 1.01279

5.0 0.5 1.00805 0.79945 1.011811

0.5 0.01 0.25708 0.24223 0.17387

0.5 0.10 0.51828 0.42120 0.51118

0.5 0.50 1.01869 0.81023 1.01875

0.5 1.0 1.28084 1.02057 1.28088

Conclusion

In this work we have investigated the heat

generation and thermal radiation

interaction effects with unsteady MHD

flow past a moving porous plate

immersed in a porous medium. From the

studies above we can derive the following

conclusions:

1. The suction can be used to control the

boundary layer very effectively.

2. Prandtl number has significant effect

on the flow field.

3. Allowing the radiation parameter to

vary gives flexibility to control the

flow temperature.

4. Heat generation has significant effect

on the velocity and temperature of the

flow.

5. The time dependency parameter n

influences the flow patterns.

6. Soret number has strong effects on the

concentration of the flow field.


220

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Documents

SEM 1104 014 Heat Generation Thermal Radiation Soret Effect Unsteady Flow Porous Plate