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International Journal of Advances in Science and Technology,
Vol. 3, No.1, 2011
Chemical Reaction and Heat source effects on MHD Free Convection
Flow past a Vertical Plate under Oscillatory Suction Velocity
V.Bhagya Lakshmi1, S.V.K.Varma2 and N.Ch.S.Iyengar3
1
Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India
svulakshmi@gmail.com
2
Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India
svijayakumarvarma@yahoo.co.in
3
School of Computing Science and Engineering, VIT University, Vellore, Tamilnadu, India
nchsniyengar48@gmail.com
Abstract
The objective of this paper is to analyze effects of Chemical reaction and Heat source on MHD flow past a
vertical plate under oscillatory suction velocity. It is assumed the permeability of the porous medium fluctuates
with time. The governing equations of the flow field are solved by using perturbation technique. The expressions
for the velocity, temperature and concentration fields are obtained. Skin friction, the rate of heat and mass
transfer in terms of Nusslet number and Sherwood number are also derived. The effects of the flow parameters
such as Grashoff number for heat transfer and mass transfer (Gr,Gc), Heat source parameter (Q), Prandtl
number (Pr), Magnetic parameter (M), Schmidt number (Sc) and Chemical reaction parameter Kr on the
velocity, temperature, concentration, skin-friction, nusslet number and Sherwood number have been analyzed
through the graphs and Tables.
Keywords: Heat and Mass Transfer, Chemical Reaction, Oscillating suction velocity, Magnetic field.
1. Introduction
A number of scholars have developed their extensive research on the study of heat and mass transfer due to
its day-to-day applications in science and technology. The phenomenon of heat and mass transfer are observed in
buoyancy induced motions in the atmosphere, in water bodies, quasi-solid bodies such as earth and so on. In many
transport processes in nature and in industrial applications in which heat and mass transfer are a consequence of
buoyancy effects caused by diffusing of heat and chemical species. The study of such processes is useful for
improving a number of chemical technologies, such as polymer production, chemical oil recovery, underground
energy transform, manufacturing of ceramic and food processing.
Raptis and Kafoussias (1) have studied the influence of a magnetic field upon the steady free convection
flow through a porous medium bounded by an infinite vertical plate with constant suction velocity, and when the
plate temperature is also constant. Raptis (2) has studied mathematically the case of time-varying two- dimensional
natural convective heat transfer of an incompressible, electrically-conducting viscous fluid via a highly porous
medium bounded by an infinite vertical porous plate. Vajravelu and Hadyinicolaou (3) investigated the convective
heat transfer in an electrically conducting fluid at stretching surface with uniform stream velocity.
The present trend in the field of chemical reaction analysis is to give a mathematical model for the system
to predict the reactor performance. Many researches are being carried out across the globe. The study of heat and
mass transfer with chemical reaction is given primary importance in chemical and hydrometallurgical industries.
A study of the first order chemical reaction on the flow past an impulsively started vertical plate with uniform heat
and mass flux by P. Ganesan and R. Muthucumaraswamy (4). The same type of problem with inclusion of constant
wall suction was studied by Makinde.O.D. And P. Sibanda (5), J.R. Fan et.al (6) studied the same problem over a
horizontal moving plate. R. Kandasamy and S.P. Anjalidevi (7) investigated the effect of chemical reaction of the
flow over a wedge. Atul Kumar Singh (8) analyzed the MHD free convection and mass transfer flow with heat
source and thermal diffusion. The paper deals with the study of free convection and mass transfer flow of an
incompressible, viscous and electrically conducting fluid past a continuously moving infinite vertical plate in the
presence of large suction and under the influence of uniform magnetic field considering heat source and thermal
diffusion. Processes involving the mass transfer effect have long been recognized as important principal in chemical
processing equipment. Recently, Mohammad Ferdows, et.al (9) have studied the effect of similarity solution for
MHD flow through vertical porous plate with suction.
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International Journal of Advances in Science and Technology,
Vol. 3, No.1, 2011
In the above stated studies, the oscillatory suction in the presence of time dependent velocity along the
influence of uniform magnetic fields are not studied while such flows are encountered in geophysical problems,
astrophysical problems, soil sciences and so on. Therefore, the aim of the present investigation is to study the
chemical reaction and heat source effects on MHD convective flow past a vertical plate under oscillatory suction
velocity in the presence of a uniform transverse magnetic field. The permeability of the porous medium is
considered to be K t ' K0 1 ein 't ' and the suction velocity is assumed to be t ' 0 1 ein 't '
where 0 0 and 0 is a positive constant.
2. Mathematical Formulation
Consider in an unsteady flow of an incompressible, electrically conducting and viscous fluid past an
infinite vertical porous plate under the oscillatory suction velocity in the presence of chemical reaction and heat
source. In Cartesian coordinate system, let „x‟-axis be along the plate in the direction of the flow and y-axis normal
to it. A uniform magnetic field is applied normal to direction of flow. In the analysis, we assume that the magnetic
Reynolds‟s number is much less than unity so that the induced magnetic field is neglected in comparison to the
applied magnetic field. Further, all the fluid properties are assumed constant except that of the influence of density
variation with temperature. Therefore, the basic flow in the medium is entirely due to buoyancy plate as well as fluid
is assumed to be at the same temperature and the concentration of species is very low so that Soret and Dufer effects
'
are neglected. When t>0, the temperature of the plate is instantaneously raised (or lowered) to Tw and the
'
concentration of species is raised (or lowered) to Cw .
Following the analysis and dimensionless parameters of (10), the governing equations become
1 u u 2u
1 eint
u
2 GrT GmC M 2u
K0 1 e
(1)
4 t y y int
1 T int T 1 2T
1 e Q T (2)
4 t y pr y 2
1 C C 1 2T
1 eint Kr C (3)
4 t y SC y 2
K Q
Where K r 1 , Q 12
2
v0 v0
The corresponding boundary conditions in dimensionless form are
u 0 , T 1 eint , C 1 eint at y 0
u 0 ,T 0 , C 0 as y (4)
3. Method of Solution
In order to solve the System of equations (1), (2) & (3) under the boundary conditions (4) we assume
u y, t u0 y u1 y eint
T y, t T0 y T1 y eint (5)
C y, t C0 y C1 y e int
Substituting (5) in to the equations (1), (2) & (3) and equating the harmonic and non-harmonic terms, we get
u0 u0 a1u0 GrT0 GmC0
'' '
(6)
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Vol. 3, No.1, 2011
u0
u1'' u1' a2u1 GrT1 GmC1 u0
'
(7)
K0
T0'' PT0' PT0 0
r r (8)
T1'' PT1' a3T1 PT0'
r r (9)
C0 ScC0 SC C0 0
'' '
(10)
C ScC a4C1 ScC
''
1
'
1
'
0 (11)
The corresponding boundary conditions are:
u0 u1 0, T0 T1 0, C0 C1 0 at y 0
u0 u1 0, T0 T1 1, C0 C1 1 as y (12)
Solving equations (6)-(11) with the help of boundary conditions (12)
u y, t 9 a7 a8 e
m10 y
a7e m2 y a8e m6 y ]
[a19e m y a14e m y a15e m y a10e m10 y a17e m y a18e m y ]eint
12 4 8 2 6
(13)
T y, t e
m2 y
[(1 a5 )e m4 y a5e m2 y ]eint (14)
C y, t e
m6 y
[(1 a6 )e m8 y a6e m6 y ]eint (15)
To obtain the fluctuating parts of the transient velocity, temperature and concentration are:
u y, t u0 y M r Cosnt M i Sinnt (16)
T y, t T0 y Kr Cosnt Ki Sinnt (17)
C y, t C0 y Lr Cosnt Li Sinnt (18)
Where
M r N15CosB3 y N16 SinB3 y e A3 y N5CosB1 y N6 SinB1 y e A1 y
N7CosB2 y N8 SinB2 y e A2 y N9em y N11em y N13em y 10 2 6
M i N16CosB3 y N15 SinB3 y e A y N6CosB1 y N5 SinB1 y e A y
3 1
N8CosB2 y N7 SinB2 y e A2 y N10em y N12em y N14em y 10 2 6
Kr 1 N1 CosB1 y N2 SinB1 y e A y Ne m y 1 2
Ki 1 N1 SinB1 y N2CosB1 y e A y Ne m y 1 2
Lr 1 N3 CosB2 y N4 SinB2 y e A y N3e m y 1 6
Li 1 N3 SinB2 y N4CosB2 y e A y N4e m y 1 6
The expressions for transient velocity, temperature and concentration fields for nt / 2 are
u ( y, ) u0 y M i (19)
2n
T ( y, ) T0 y Ki (20)
2n
C ( y, ) C0 y Li (21)
2n
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Vol. 3, No.1, 2011
4. Skin Friction, Nusselt Number and Sherwood Number
The Skin friction coefficient at the plate, in terms of amplitude and phase is
u
= 0 X Cos nt (22)
y y 0
The Rate of heat transfer coefficient Nu at the plate in terms of amplitude and phase is
T
Nu = m2 Y Cos nt (23)
y y 0
The Rate of Mass transfer coefficient Sh at the plate in terms of amplitude and phase is
C
Sh = m6 Z Cos nt (24)
y y 0
Where 0 m2 a7 m6 a8 m10 a7 a8
Xi Y Z
X X r X i , Tan , Y Yi Yr , Tan i , Z Zi Z r , Tan i
Xr Yr Zr
X r A3 N15 B3 N16 A1 N5 B1 N6 A2 N7 B2 N8 m10 N9 m2 N11 m6 N13
X i A3 N16 B3 N15 A1 N6 B1 N5 A2 N8 B2 N7 m10 N10 m2 N12 m6 N14
Yr A1 1 N1 B1 N2 m2 N1 , Yi B1 1 N1 A1 N2 m2 N2
Zr A2 1 N3 B2 N4 m6 N3 , Zi B2 1 N3 A2 N4 m6 N4
5. Results and Discussion
Numerical calculations have been carried out for transient velocity, transient temperature and species
concentration distributions for different values of parameters are displayed in figures (1)-(10). From figures (1)-(4)
we noticed that the maximum velocity attains near the plate in the neighborhood of the point y=2 for y>0 the
velocity decrease and tends to zero as y .
Figs (1) and (2) display the effect of heat source parameter Q on the velocity field for the cases of cooling and
heating of the plates respectively. From (1) it is observed that the transient velocity decreases with an increase in
heat source parameter Q. The reverse effect is observed from the fig (2) in the case of heating of the plate.
Figs (3) & (4) represent the transient velocity profiles due to variations in chemical reaction parameter Kr in
case of cooling and heating of the plate respectively. It is noticed that an increases in Kr the velocity decreases. The
reverse phenomenon is observed from the fig (4) in the case of heating of the plate.
0
Fig (5) shows temperature field due to variations in Prandtl number Pr for air, mercury, water at 4 c at
0.002 and n=5.0. It is seen that an increase in Pr decreases the transient temperature field indicating that
temperature falls more rapidly for water in comparison to air.
Fig (6) shows transient temperature due to variations in heat source parameter Q. It is observed that the
transient temperature decreases with increases in Q values
Fig(7) display the concentration due to variations in Schmidt number Sc for the bases Hydrogen, Helium,
Water - Vapor, Oxygen and Ammonia at 0.002 ,n=5.0 It is observed that concentration field falls slowly and
steadily for hydrogen and helium but falls rapidly to oxygen and ammonia in comparison to water - vapor.
From fig (8) it is observed that the transient concentration decreases with an increase in chemical reaction
parameter Kr.
Figs(9) & (10) shows the in the absence of Chemical reaction and heat source for the cases of cooling and
heating , the results of the present paper are reduced to those obtained by Athul Kumar Singh, Ajay Kumar Singh
and N.P. Singh(13)
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Vol. 3, No.1, 2011
Table-I represents the numerical values of Skin friction coefficient in terms of amplitude X , phase
Tan , Skin friction coefficient m due to steady part of velocity and Skin friction coefficient for variations in
Gr,Gm,Pr,Sc,M,Ko,n,Q and Kr respectively due to cooling of the plate. It is noticed that an increase in Gr or Gm or
Sc or Ko or Q as increase in the value of amplitude X and decreases the amplitude X as increase in Pr or M or
n or Kr. The phase Tan decreases due to increase in Gr or Pr Sc or Q while increases due to increase in Gm or
M or Ko or n or Kr. It is also seen that m , decreases due to increases in Pr or M while an increases in Gr or Gm
or Sc or Ko or N or Q or Kr.
Table-II shows the numerical values of Skin friction coefficient in terms of amplitude X , phase Tan
Skin friction coefficient m due to steady part of velocity and Skin friction coefficient for variations in
Gr,Gm,Pr,Sc,M,Ko,n,Q and Kr respectively due to heating of the plate. It is observed that decrease in Gr or Gm
leads to an increases the value of amplitude X Also it is observed that an increase in Sc or Ko or Q leads to an
increase the value of X while an increase in Pr or M or n or Kr leads to decrease in the value of X . The value of
Tan decreases due to increases in Pr or Sc or n or Q while an increase due to increases in M or Ko or Kr. It is
also we noticed that decrease Tan with decrease in Gr and decreases in Gm in the increases the value of Tan .
It is noticed that m , decrease due to increases in Pr or Sc or M or n and decreases in Gr or Gm values due to
decreases the values of m , .
Table-III shows the effects of parameters Pr, Q and n on amplitude Y , phase Tan and rate of heat
transfer in terms of Nusselt number N u at 0.002 , nt / 2 . It is observed that the values the amplitude Y ,
Nusselt number N u increases due to increases in Pr while to decreases Y , N u leads to increase in Q or n. The
value ofTan decreases due to increase in Q or n while decreases due to an increase in Pr.
Table-IV represents the effects of parameters Sc, Kr and n on amplitude Z , phase Tan and rate of mass
transfer in terms of Sher-wood number S h at 0.002 , nt / 2 . It is noticed that the Sher-wood number S h
increases as increase in Sc or Kr or n. The phase Tan increases with increase in Sc or Kr or n. It is also observed
that the value amplitude Z increases as increase in Kr or n and it increases with increase in Sc values.
10
Gr=5.0
8 Gm=5.0
Kr=0.07
Pr=0.71
Sc=0.22
Kr=0.08 M=0.5
6
Ko=0.1
Kr=0.09 n=5.0
Q=0.4
U
4 E =0.002
2
0
-2
0 2 4 6 8 10 12 14 16 18 20
Y
Figure1: Velocity profiles variation with Chemical reaction parameter Kr (Gr, Gm>0)
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Vol. 3, No.1, 2011
0.1
0
-0.1
Kr=0.07
-0.2 Kr=0.08
Kr=0.09
-0.3
U
Gr=-5.0
-0.4
Gm=-5.0
Pr=0.71
-0.5 Sc=0.22
M=0.5
-0.6 Ko=10.0
n=5.0
-0.7 Q=0.4
E =0.002
-0.8
0 2 4 6 8 10 12 14 16 18 20
Y
Figure 2: Velocity profiles variation with Chemical reaction parameter Kr (Gr, Gm<0)
0.6
Q=4
Q=6
0.5 Q=6.5
Q=7
0.4
0.3
U
Gr=5.0
0.2 Gm=5.0
Pr=0.71
Sc=0.22
0.1 M=0.5
Ko=5.0
E =0.005
0 Kr=5
n=5.0
-0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Y
Figure 3: Velocity profiles variation with Heat source parameter Q (Gr, Gm>0)
0.1
Gr= -5.0
0 Gm= -5.0
Pr=0.71
Sc=0.22
-0.1 M=0.5
Ko=5.0
E =0.005
-0.2 Kr=5
n=5.0
U
-0.3
Q=7
-0.4
Q=6.5
-0.5 Q=6
Q=5.5
-0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Y
Figure 4: Velocity profiles variation with Heat source parameter Q (Gr, Gm<0)
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Vol. 3, No.1, 2011
1.2
Q=10
1 Q=1
Q=5
0.8 Q=15
0.6
0.4
Q=20
0.2
T
0
-0.2
Pr=0.78
-0.4 E =0.005
n=5.0
-0.6
-0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Y
Figure 5: Temperature profiles variation with Heat source parameter Q
1.4
1.2 Pr=0.25
Pr=0.71
1
0.8
T
Pr11.0
0.6
Pr=7.00
0.4
Q=1.0
E =0.005
0.2 n=5.0
0
0 0.2 0.4 0.6 0.8 1
Y
Figure 6: Temperature profiles variation with Prandtl number Pr
1.2
1
0.8
0.6
Kr=0.2
0.4
C
Kr=10.0
0.2
0
Kr=5.0
Sc=0.6
-0.2 n =5.0
Kr=2.0
E=0.005
-0.4
-0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Y
Figure 7: Concentration profiles variation with Chemical reaction parameter Kr
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1.2
1 Sc=0.66 Sc=0.30
0.8 Sc=0.60 Sc=0.22
Sc=0.78
0.6
C
0.4
Kr=1.0
E=0.005
0.2 n =5.0
0
-0.2
0 0.5 1 1.5 2 2.5
Y
Figure 8: Concentration profiles variation with Schmidt number Sc
0.7
curve Gr Gm M n Ko Pr Sc
0.6 I 2 2 2 5 5 0.7 0.22
II 5 5 2 5 5 0.7 0.22
III 2 2 2 5 5 7.0 0.22
0.5 IV 2 2 2 5 5 0.7 0.66
V 2 2 2 5 5 0.7 0.22
VI 2 2 2 10 10 0.7 0.22
0.4
VI
0.3
U
I
III
0.2
V
IV
0.1 II
0
-0.1
0 5 10 15
Y
Figure 9: Velocity profiles variation with different parameters when Kr=0, Q=0(Gr, Gm>0)
0.1
0
VI
-0.1 V
III
-0.2
IV
I
-0.3
U
II
-0.4 curve Gr Gm M n Ko Pr Sc
I -2 -2 2 5 5 0.7 0.22
II -5 -5 2 5 5 0.7 0.22
-0.5 III -2 -2 2 5 5 7.0 0.22
IV -2 -2 2 5 5 0.7 0.66
-0.6 V -2 -2 2 5 5 0.7 0.22
VI -2 -2 2 10 10 0.7 0.22
-0.7
0 5 10 15
Y
Figure 10: Velocity profiles variation with different parameters when Kr=0, Q=0(Gr, Gm<0)
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Vol. 3, No.1, 2011
TABLE-I
Values of Amplitude X , phase Tan and Skin-friction coefficients due to cooling of the plate
Pr Sc X Tan
2.5396
2.0 2.0 7.0 0.66 0.5 5.0 5.0 1.0 0.08 2.2049 0.0814 2.5400
2.0 5.0 7.0 0.66 0.5 5.0 5.0 1.0 0.08 2.6220 -0.6362 3.0295 3.0323
5.0 2.0 7.0 0.66 0.5 5.0 5.0 1.0 0.08 5.8446 0.3712 5.8603 5.8563
2.0 2.0 11.4 0.66 0.5 5.0 5.0 1.0 0.08 2.1861 -0.0060 2.4017 2.4018
2.0 2.0 7.0 0.78 0.5 5.0 5.0 1.0 0.08 2.3740 0.0144 2.2754 2.2753
2.0 2.0 7.0 0.66 1.0 5.0 5.0 1.0 0.08 1.4322 0.1695 1.8815 1.8810
2.0 2.0 7.0 0.66 0.5 10.0 5.0 1.0 0.08 2.3745 0.1506 2.7066 2.7059
2.0 2.0 7.0 0.66 0.5 5.0 10.0 1.0 0.08 1.6578 -0.1375 2.5400 2.5404
2.0 2.0 7.0 0.66 0.5 5.0 5.0 1.5 0.08 2.2619 0.0197 2.6012 2.6011
2.0 2.0 7.0 0.66 0.5 5.0 5.0 5.0 0.09 2.1978 0.0925 2.5757 2.5753
TABLE-II
Values of Amplitude X , phase Tan and Skin-friction coefficients m , due to heating of the plate
Gr Gm Pr Sc M Kop n Q Kr X Tan m
-2.0 -2.0 7.0 0.66 0.5 5.0 5.0 1.0 0.08 2.2047 0.0814 -2.5400 -2.5396
-2.0 -5.0 7.0 0.66 0.5 5.0 5.0 1.0 0.08 2.6220 -0.6362 -3.0295 -3.3267
-5.0 -2.0 7.0 0.66 0.5 5.0 5.0 1.0 0.08 5.8446 0.3712 -5.8603 -5.8644
-2.0 -2.0 11.4 0.66 0.5 5.0 5.0 1.0 0.08 2.1861 -0.0060 -2.4017 -2.4017
-2.0 -2.0 7.0 0.78 0.5 5.0 5.0 1.0 0.08 2.3740 0.0144 -2.2754 -2.2755
-2.0 -2.0 7.0 0.66 1.0 5.0 5.0 1.0 0.08 1.4322 0.1695 -1.8815 -1.8819
-2.0 -2.0 7.0 0.66 0.5 10.0 5.0 1.0 0.08 2.3745 0.1506 -2.7066 -2.7073
-2.0 -2.0 7.0 0.66 0.5 5.0 10.0 1.0 0.08 1.6578 -0.1375 -2.5400 -2.5395
-2.0 -2.0 7.0 0.66 0.5 5.0 5.0 1.5 0.08 2.2619 0.0197 -2.6012 -2.6013
-2.0 -2.0 7.0 0.66 0.5 5.0 5.0 5.0 0.09 2.1978 0.0925 -2.5757 -2.5761
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TABLE-III
Amplitude of Y , phase Tan and rate heat transfer N u
S.No pr n Q Y Tan Nu
1 07.0 5.0 1.0 23.8247 -0.9794 5.8246
2 11.4 5.0 1.0 145.6866 -3.5348 10.5728
3 07.0 5.0 1.5 18.7427 -0.6948 4.8443
4 07.0 10.0 1.0 21.4710 0.6608 5.8150
TABLE-IV
Amplitude of Z , Phase Tan and rate of mass transfer S h
S.No Sc n Kr Z Tan Sh
1 0.22 5.0 0.04 0.5398 0.8174 0.1403
2 0.66 5.0 0.04 1.1000 0.6728 0.5933
3 0.22 5.0 0.04 0.5371 0.8342 0.1157
4 0.22 10.0 0.05 0.7485 0.8946 0.1388
6. References
[1] A. A. Raptis and N. Kafousias, “Heat transfer in flow through a porous medium bounded by an infinite
vertical plate under action of a magnetic field”, Int. J. Energy res. Vol.6, pp.241-245, 1982.
[2] A. A. Raptis “Flow through a porous medium in the presence of Magnetic field”, Int J.Energy. Res vol.10,
pp.97-101,1986.
[3] Vajravelu, K.K. and Hadyinicolaou. A. „Convective heat transfer in an electrical conducting fluid
at stretching surface with uniform stream velocity. Int. J. Engg. Sci., Vol.35, Pp.1273-1284, 1997.
[4] P.Ganesan and R. muthucumaraswamy. “First order Chemical Reaction on flow past an
impulsively started vertical plate with uniform heat and mass flux”. Acta Mechanica 147, pp 45-
57, 2001.
[5] Mankinde.O.D. and P.sibanda, “MHD mixed-convective flow heat and mass transfer past a vertical
plate in a porous medium with constant wall suction‟. Journal of Heat Transfer, 130, 112602/1-
8, 2008.
[6] J.R. Fan, J.M. Shi and X.A. Xu, “Similarity solution of mixed convection with diffusion and
chemical reaction over a horizontal moving plate”. Acta Machanica 126,Pp 59-69,1998.
[7] R. Kandasamy and S.P. Anjali devi, “Effects of chemical reaction, heat and mass transfer on non-
linear laminar boundary later flow over a wedge with suction or injection. J. of Comp and Appl.
Mechanics, 5 pp 21-31, 2004.
[8] Atul Kumar Singh, “Free convection and mass transfer flow with heat source and thermal
diffusion”. Journal of Energy Heat and Mass Transfer, 23 Pp 167-178, 2001.
[9] Mohammad Ferdows, Masatiro Ota, Abdus Sattar and Mohamud Alan, “Similarity solution for
MHD flow through vertical porous plate with suction”. Journal of Applied Mechanics, 6(1), Pp 15-25,
2005.
[10] Athul Kumar Singh, Ajay Kumar Singh and N.P. Singh. “Heat and mass transfer in MHD flow of
a viscous fluid past a vertical plate under oscillatory suction velocity”. Indian J. Pure appl, Math, 34(3),
429-442, March 2003.
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Vol. 3, No.1, 2011
Authors Profile
V.Bhagya Lakshmi, (M.Sc., M.phil), is a research scholar, Department of
Mathematics, S. V. University, Tirupati, A.P. India.
Dr. S. Vijaya Kumar Varma(M.Sc. Ph.D) is currently working as professor in
Department of Mathematics in S.V. University, Tirupati, he has 24 years of
experience with various levels and 30 years of research experience. Fluid
dynamics, Heat and mass transfer in fluid flows and magneto hydro dynamics are
the areas of research of his interest. He published 60 papers in national and
international journals. Under his guidance 8students awarded PhDs and 20
students awarded M.Phil. He has attended several national and international
conferences and workshops.
Dr.N.Ch.S.N. Iyengar (M.Sc, M.E, Ph.D) is a Senior Professor at the School of
Computing Science and Engineering at VIT University, Vellore, Tamil Nadu,
India. His research interests include Agent based Distributed Computing, Data
Mining, Privacy, hiding, Security, Cryptography, Intelligent computational
methods and Bio informatics. He has authored several textbooks and had nearly
110 research Publications in International Journals. He chaired many international
conferences and d delivered invited/ technical lectures/ keynote addresses besides
being International programmer committee member.
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