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					                                                         International Journal of Advances in Science and Technology,
                                                                                                    Vol. 3, No.1, 2011

 Effects of Thermo Diffusion and Chemical Reaction on Transient MHD
      Free Convection Flow over a Vertical plate in the Presence of
                 Temperature Dependent Heat source
                         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
                                                ncsniyengar48@gmail.com


                                                       Abstract
 This paper presents the study of thermo diffusion, magnetic field and chemical reaction effects on an unsteady
convection flow of viscous, incompressible and electrically conducting fluid over a semi infinite vertical porous
plate in the presence of temperature dependent heat source . The governing equations are solved by using
perturbation technique and the expressions for the velocity, temperature and concentration fields are obtained.
The skin friction, the rate of heat transfer and the rate of mass transfer in terms of Nusselt number, Sherwood
number are also derived. The effects of flow parameters like Grashoff number for heat and mass transfer Gr,
Gm, Schmidt number Sc, Prandtl number Pr, Magnetic parameter M, Chemical reaction parameter K , Soret
number So Heat source parameter Q on the velocity, temperature, concentration, Skin friction, Nusselt number
and Sherwood number have been analyzed through the graphs and tables.

Keywords: Magnetic field, Heat and Mass Transfer, Chemical Reaction and Thermo diffusion.

1. Introduction
           In many engineering applications natural convection flows play an important role and hence these have
attracted the attention of many research workers. The phenomenon of mass transfer is very common in the theories
of stellar structure and observable effects are easily detectable at least on the solar surface. On the other hand, the
results of the effects of magnetic field on the flow of an electrically-conducting viscous fluid in the presence of mass
transfer are also useful in stellar atmosphere.
           The effect of the presence of foreign mass on the free convection flow past a semi-infinite vertical plate
was studied by Gebhart and Pera (1). During a chemical reaction between two species, heat is also generated.
In most of these cases of chemical reaction, the reaction rate depends on the concentration of species itself. A
reaction is said to be first order if the rate of reaction is directly proportional to concentration itself. Ganesan and
Loganatha (2) presented numerical solutions of the transient natural convection flow of an incompressible, viscous
fluid past an impulsively started semi-infinite isothermal plate with mass diffusion, taking into account a
homogeneous chemical reaction of first order. Ghaly and Seddeek (3) analyzed the effect of variable viscosity,
chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate. Muhaimin et al (4)
analyzed the effect of chemical reaction, heat and mass transfer on nonlinear MHD boundary layer past a porous
sinking sheet with suction.
           Groot and Mazur (5) showed that if separation due to the thermal diffusion occurs then may even render
an unstable system to stable one. Sharma and Singh have studied the Soret effect due to natural convection between
heated vertical plates in horizontal small magnetic field. Sharif Alam et al (6) numerically studied the Dufour and
Soret effects on combined free forced convection and mass transfer flow past a semi infinite vertical flat plate under
the influence of transverse magnetic field.
           The thermal–diffusion effect, for instance, has been utilized for isotope separation and in mixer between
gases with very light molecular weight and of medium molecular weight the diffusion thermo effect was found to be
order of considerable magnitude such that it can be ignored Eckert and Drake (7). In view of the importance of
above mentioned effects, Kafousia and Williams (8) studied thermal diffusion and diffusion thermo effects on mixed




Special Issue                                         Page 42 of 89                                          ISSN 2229 5216
                                                                    International Journal of Advances in Science and Technology,
                                                                                                               Vol. 3, No.1, 2011

free forced convection and mass transfer boundary layer flow with temperature dependent viscosity. Anghel et al (9)
investigated the Dufour and Soret effects on free convection boundary layer over a vertical surface embedded in
porous medium. Very recently, Postelnicu (10) studied numerically the influence of magnetic field on heat and mass
transfer by natural convection from vertical surface in porous media considering Soret and Dufour effects and
Ahmed (11) has studied the influence of Chemical reaction on transient MHD free convection flow over a vertical
plate in slip-flow regime.
           The purpose of the present investigation is to study the Soret effects on transient hydro magnetic free
convective flow over a vertical plate in slip flow regime with temperature dependent heat source.

2. Mathematical Analysis
          Consider the two dimensional unsteady flow of viscous incompressible, electrically conducting and heat
generating/absorbing fluid past an infinite vertical porous plate with thermal diffusion in the presence of temperature
dependent heat source. We made the following assumptions:
(i) The fluid properties are assumed to be constant except for influence of density in the body force.
(ii) The transversely applied magnetic field and Reynolds number are very small and hence the induced
      magnetic field is negligible.
(iii) Electric field is neglected.
(iv) Viscous dissipation is neglected.
 Under the above assumptions the basic governing equations are
Continuity equation:
 V '
      0                                                                                                                             (1)
 y '
Momentum equation:
                                                                        2u '  B0 1
u '
                       u '
                            
                                                                                 2
      v0 1   Aei t        g  T '  T   g    C '  C    '2 
                    ' '
                                                                                   u                                                 (2)
t '                    y '                                           y      
Energy equation:
T '
t '          
      v0 1   Aei t
                    ' '

                           
                        T '
                        y '
                             
                                k  2T '
                               C p y '2
                                           Q' T '  T                                                                            (3)

Mass Transform equation:
C '
t '
              
      v0 1   Aei t
                    ' ' C '
                        y '
                                2C '
                              D '2  K '  C '  C   D1 '2
                                y
                                                            2T '
                                                           y
                                                                                                                                     (4)

The corresponding boundary conditions of the problem are
          u ' 
u '  L'  '  T '  T  Tw  T  ei t C '  C   Cw  C  ei t at y  0
                                        ' '                          ' '
                      '       '  '                '      '    '

          y 
u  0, T '  T , C '  C as y  
  '               '         '
                                                                                                                                     (5)
From the equation (1) we get,

                  
 V '  v0 1   Aei t
                               ' '

                                                                                                                                   (6)
Introducing the following non-dimensional quantities
                             4                C p        D1 Tw  T         
                                                                    '   '
     v0 y '
          u'          2
                  t 'v0          '
y   ,u     ,t        ,        ,    , Pr       , S0                , Sc 
         v0       4v          2
                              v0                 k            Cw  C 
                                                                  '      '
                                                                                  D
   T    '
              T 
                 '
                               C  C  G'   '
                                                        g  T '  T 
                                                                       '
                                                                                     g    C '  C 
                                                                                                     '
                                                                                                                  0 L'
                      ,s                                               , Gm                              h
   T                         C  C 
                                                                                                           ,                         (7)
        '
        w      T'                      '
                                         w
                                             '
                                             
                                                 r              3
                                                               v0                             3
                                                                                             v0                    




Special Issue                                                    Page 43 of 89                                            ISSN 2229 5216
                                                          International Journal of Advances in Science and Technology,
                                                                                                     Vol. 3, No.1, 2011

    B02      K '   Q '
M        , K  2 , Q 2                       ,
    02       0     0
Using the above substitutions in equations (2) to (4), following are the equations in non- dimensional form:
1 u                 u  2u
      1   eit          Gr  Gm  Mu                                                                       (8)
4 t                 y y 2
1                   1  2
      1   eit             Q                                                                               (9)
4 t                 y Pr y 2
1                   1  2             2
      1   eit             K  S 0 2                                                                      (10)
4 t                 y Sc y 2           y
     u
u  h ,   1   eit ,   1   eit at y  0
     y
u  0 ,   0 ,   0 as y                                                                                      (11)
To solve the equations (8) to (10) we assume that
 f  y.t   f0  y    eit f1  y   .......                                                                 (12)
Where f stands for u, and  and   1
Substituting (11) into the equations (8) to (10) and equating the coefficient of harmonic and non-harmonic terms,
neglecting the coefficients of  , we obtain
                                     2


0''  Pr0'  Pr0  0                                                                                           (13)
                   i 
1''  Pr1'   Q   Pr1   APr0'                                                                            (14)
                4
0  Sc0  KSc0  Sc S00''
 ''     '
                                                                                                                  (15)
                 i     
1''  Sc1'        K  Sc1   ASc0' Sc S01''                                                             (16)
                 4      
              i      
u1''  u1'    M  u1  Gr1  Gm1  Au0     '
                                                                                                                  (17)
              4       
u0  u0  Mu0  Gr0  Gm0
    ''     '
                                                                                                                  (18)
Where the primes denote differentiation with respect to y and corresponding boundary conditions are
        u         u 
u0  h  0  u1  h  1  0  1 1  1 0  1 1  1 at y  0
        y         y 
                                                                                                                  (19)
u 0  0 , u1  0 , 0  0 , 1  0 , 0  0 , 1  0 as              y 
The solutions of the equations (13) to (18) under the boundary conditions (19) are
 u  y, t   u0  y    eit  Ar  iAi                                                                       (20)
  y, t   e m y   eit  Br  iBi 
                   2
                                                                                                                  (21)
  y, t   0  y    eit  Cr  iCi                                                                        (22)
Where
Ar   B21CosA6 y  B22 SinA6 y  e A5 y  B11e m2 y   B13CosA2 y  B14 SinA2 y  e A1 y  B15e m6 y 
          B17CosA4 y  B18 SinA4 y  e A3 y  B19em  10 y




Special Issue                                        Page 44 of 89                                      ISSN 2229 5216
                                                               International Journal of Advances in Science and Technology,
                                                                                                          Vol. 3, No.1, 2011

Ai   B22CosA6 y  B21SinA6 y  e A5 y  B16e m6 y   B14CosA2 y  B13SinA2 y  e A1 y  B12e m2 y 
     B18CosA4 y  B17 SinA4 y  e A3 y  B20em y       10



Br   1  B1  CosA2 y  B2 SinA2 y  e A y  B1e m y
                                              1                2



Bi    1  B1  SinA2 y  B2CosA2 y  e A y  B2e m y
                                                  1                2



Cr   B9CosA4 y  B10 SinA4 y  e A3 y  B3e m y   B5CosA2 y  B6 SinA2 y  e  A y  B7e  m y
                                                      6                                        1         2



Ci   B10CosA4 y  B9 SinA4 y  e A3 y  B4e m y   B6CosA2 y  B5SinA2 y  e  A y  B8e m y
                                                      6                                       1         2



The expressions for transient velocity, temperature and concentration fields for                             t   / 2   are:
u( y, t )  u0  y    Ai                                                                                               (23)
 ( y, t )  0  y    Bi                                                                                              (24)

 ( y, t )  0  y    Ci                                                                                              (25)

3. Skin Friction, Nusselt Number and Sherwood number
 The Skin-friction coefficient   at the plate, in terms of amplitude and phase is:
      u 
      m   P Cos t                                                                                            (26)
     y  y 0
The rate of heat transfer coefficient  Nu  at the plate in terms of amplitude and phase is:

        
 Nu        m2   Q Cos t                                                                                       (27)
       y  y 0
The rate of mass transfer coefficient  Sh  at the plate in terms of amplitude and phase is:

       
Sh        m   R Cos t                                                                                         (28)
      y  y 0
Where,
 m  m6b8  m2b7  m10b9 , m  m6 1  b2   m2b2                  , P  P  iP , Q  Qr  iQi , R  Rr  iRi
                                                                              r    i

          Pi         Q          R
 Tan       , Tan  i , Tan  i
          Pr         Qr         Rr
4. Results and Discussions
           The effects of Heat source parameter Q, Chemical reaction parameter K, Soret number So, Grashof number
for heat and mass transfer Gr and Gm Prandtl number Pr, Magnetic parameter M, Schmidt number Sc,
Rare fraction parameter h, Suction parameter A, Frequency parameter  on the velocity, temperature, concentration
fields are shown in figures (1)-(10). From figs (1)-(4) it is observed that in the neighborhood of the plate the velocity
increases as y increases , attains the maximum value at y  0.5 and then decreases rapidly as the fluid moves far
away from the plate y  0.5 .
          Fig (1) shows the velocity profile for various values of Soret number So. It is seen that the velocity
increases with an increase in the value of Soret number So.
          From fig (2) it is noticed that the velocity increases with an increase in Soret number So and it decreases as
an increase in Chemical reaction parameter.
          From fig (3) it is observed that the velocity increases with an increase in the heat source parameter Q and it
decrease with an increase in the magnetic parameter M.
         The effects of heat source parameter Q on the temperature field are studied through the fig (4). It is observed
that the temperature increases as the heat source parameter Q increase.




Special Issue                                              Page 45 of 89                                      ISSN 2229 5216
                                                          International Journal of Advances in Science and Technology,
                                                                                                     Vol. 3, No.1, 2011

         The variation of temperature for different values of Prandtl number Pr is shown in fig (6). From this it is
noticed that the temperature decreases as the Pr increases.
         Fig (6) shows the effects of Soret number So on the concentration  . It is observed that the concentration
increases with an increase in So values. It is also noticed that the concentration of species is more near the plate and
decreases slowly as it moves far away from the plate.
        Fig (7) displays the effects of chemical reaction parameter K on the concentration  . It is seen that the
concentration decreases with an increase in chemical reaction parameter K the species concentration decreases
slowly as it moves far away from the plate
        Fig (8) shows that in the absence of Heat source parameter Q and Soret number So, the results of the present
paper in good agreement with that of Ahmed Sahin (11).
       Fig (9) displays the in the absence of rare fraction parameter h , the results of the present paper are reduced to
obtained by Ahmed Sahin (11).
      From Fig (10) we observed that, in the absence of Heat source parameter Q and Soret number So the results of
the present paper is good agreement with that of Ahmed Sahin (11).
      Table-I represents the effects of parameters Gr, Gm, Pr, Sc, Q, K, So and M on the Skin-friction  in terms of
amplitude P ,phase Tan , Skin friction coefficient          m     due to steady part of the velocity and Skin friction
coefficient  at     0.002 ,  t   / 2 , A  0.2 and h  0.5 .It is observed that an increase in the values of Gr
or Gm or Pr or So leads to an increase in the value of amplitude P while an increase in the value of Sc or Q or K or
M leads to decrease in the value of amplitude P .The value of Tan decreases with an increase in Pr or Gr or So
values it increases with an increase in Gr or Q or Sc or K or M. It is also we seen that the Skin friction
coefficients  ,  m decreases due to increases in Gr or Sc or K or So while decreases due to increase in Gm or Pr or
Q or M.
      Table-II shows the effects of the parameters Pr , Sc , Q , K and S0 on the rate of mass transfer in terms of Sher-
wood number S h , amplitude R and phase Tan at             0.002 ,  t   / 2     and A  0.2 . It is observed that the
value of S h decreases with an increase in Pr or K or So and it increases with an increase in Sc or Q values. The
value of amplitude R increases with an increase in Pr or Q or K or So and it decreases with an increase in Sc
values. It is also noticed that the value of Tan decreases with an increase in Pr or Sc Q or K and it increases with
an increase in So values.
      Table-III represents the effects of parameters Pr and Q on the rate of heat transfer in terms of Nusselt
number N u , amplitude Q and phase Tan at           0.002 ,  t   / 2      and A  0.2 .It is noticed that the values
of Nusselt number and amplitude Q increases with an increase in Pr or Q values. The value of Tan increases
with an increase Pr values and it decreases with an increase in values of Q.

                       4.5
                                                   So=8.0
                        4                          So=6.0                           Pr=0.71
                                                                                    Gc=5.0
                                                    So=4.0                          Q=4.0
                       3.5
                                                                                    Sc=0.22
                                                    So=2.0
                                                                                    K=5.0
                        3
                                                                                    Gr=5.0
                                                                                    M=3.0
                       2.5                                                          h=0.5
                   U




                                                                                    A=0.2
                        2                                                           omega=10.0
                                                                                    epsilon=0.002
                       1.5

                        1

                       0.5

                        0
                             0   0.5   1     1.5      2       2.5       3     3.5      4     4.5      5
                                                               y




Special Issue                                         Page 46 of 89                                       ISSN 2229 5216
                                                                            International Journal of Advances in Science and Technology,
                                                                                                                       Vol. 3, No.1, 2011

                                                Figure 1. The velocity profiles with variation in S 0

                           4

                                                                        K=5.0,So=10.0                   Gc=5.0
                          3.5
                                                                                                        Gr=5.0
                                                                                                        Sc=0.22
                           3                                                K=5.0,So=6.0                Q=2.0
                                                                                                        Pr=0.71
                                                                            So=4.0,K=5.0                M=3.0
                          2.5
                                                                                                        h=0.5
                                                                                                        A=0.2
                           2                                                 So=4.0,K=10.0              omega=10.0
                 U



                                                                                                        epsilon=0.002
                          1.5                                                So=4.0,K=15.0


                           1


                          0.5


                           0
                                0         0.5         1     1.5         2          2.5       3    3.5       4    4.5    5
                                                                                   y

                                                 Figure 2.Velocity profiles with variation in Sc , K


                  4

                                                                Q=4.0                                   Pr=0.71
                3.5
                                                                                                        Gc=5.0
                                                                                                        So=4.0
                  3                                                                                     Sc=0.22
                                                                                                        K=5.0
                                                                  Q=3.0
                2.5                                                                                     Gr=5.0
                                                                                                        M=3.0
                                                                  Q=2.0                                 h=0.5
                  2
            U




                                                                                                        A=0.2
                                                                   Q=1.0                                omega=10.0
                1.5                                                                                     epsilon=0.002


                  1


                0.5


                  0
                      0             0.5          1        1.5      2          2.5        3       3.5       4     4.5    5
                                                                               y

                                           Figure 3. Velocity profiles with variation in M , Q


                1.4

                                                                                                            Pr=0.71
                1.2                                                                                         A=0.2
                                                                                                            omega=10

                 1
                                                                        Q=5.0

                0.8                                                         Q=7.0
           T




                                                                             Q=10.0
                0.6
                                                                               Q=15.0


                0.4


                0.2


                 0
                      0             0.2         0.4       0.6     0.8          1         1.2     1.4      1.6    1.8    2
                                                                               y

                                           Figure 4. Temperature profiles with variation in Q




Special Issue                                                          Page 47 of 89                                        ISSN 2229 5216
                                                                              International Journal of Advances in Science and Technology,
                                                                                                                         Vol. 3, No.1, 2011


                1.4

                                                                                                                  Q=4.0
                1.2                                                                                               A=0.2
                                                                                                                  omega=10

                    1                                                   Pr=0.25
                                                                              Pr=0.71
                0.8                                                                  Pr=7.1
          T



                                                                                            Pr=11.4
                0.6


                0.4


                0.2


                    0
                        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 for different values of Pr

                        1
                                                                             So=5.0                        Pr=0.71
                    0.9                                                                                    Sc=0.22
                                                                               So=4.0
                                                                                                           Q=2.0
                    0.8                                                                                    K=5.0
                                                                                    So=3.0
                                                                                                           A=0.5
                    0.7                                                                                    omega=10
                                                                                          So=2.0
                                                                                                           epsilon=0.005
                    0.6

                    0.5
                C




                    0.4

                    0.3

                    0.2

                    0.1

                        0
                            0        0.5           1       1.5      2          2.5          3       3.5       4       4.5     5
                                                                               Y



                                                Figure 6. Concentration profiles with variation in S0

                            1
                                                                               K=5.0                         Pr=0.71
                        0.9                                                                                  Sc=0.22
                                                                                K=7.0                        Q=2.0
                        0.8                                                                                  So=5
                                                                                     K=9.0
                                                                                                             A=0.5
                        0.7                                                                                  omega=10
                                                                                          K=12.0             epsilon=0.005
                        0.6

                        0.5
                 C




                        0.4

                        0.3

                        0.2

                        0.1

                            0
                                0         0.5          1     1.5         2          2.5         3     3.5         4     4.5       5
                                                                                    y

                                                Figure 7. Concentration profiles with variation in K




Special Issue                                                            Page 48 of 89                                                ISSN 2229 5216
                                                                   International Journal of Advances in Science and Technology,
                                                                                                              Vol. 3, No.1, 2011


                      3

                                                           Curve Gr Gm Pr    Sc  K Q h                            M So
                                             I              I   10  10 0.71 0.22 5 0 0.5                          5  0
                    2.5                                     II    5  5 0.71 0.22 5 0 0.5                          5  0
                                                            III   5  5 0.25 0.66 5 0 0.5                          5  0
                                                            IV    5  5 0.71 0.22 15 0 0.5                         5  0
                      2                                     V     5  5 0.71 0.22 5 0 0.5                           3 0
                                                           V

                    1.5
                U


                                                                      II

                      1                                                IV
                                                                     III

                    0.5



                      0
                           0   0.5       1       1.5           2       2.5      3          3.5       4        4.5        5
                                                                       y

                Figure 8. Velocity profiles with variation in different parameters when Q=0, So=0
                      8
                                                                Q=4,M=3
                                                                                                 Gc=5.0
                      7
                                                                                                 Gr=5.0
                                                                                                 Sc=0.22
                      6                                                                          So=4.0
                                                                                                 K=5.0
                                                                                                 Pr=0.71
                      5
                                                                                                 M=3.0
                                                               Q=3,M=3                           h=0.5
                      4                                                                          A=0.2
                 U




                                                                                                 omega=10.0
                                                                                                 epsilon=0.002
                      3                                        Q=2,M=3


                      2
                                                                           Q=2,M=5
                                                                                     Q=2,M=7
                      1


                      0
                           0   0.5       1       1.5           2       2.5      3          3.5      4         4.5        5
                                                                       y

                      Figure 9: Velocity profiles with varion in different parameters when h=0

                      1

                                                                   Curve     Pr       Sc    K  So            Q
                                                                      I      0.71     0.22 6    0            0
                    0.8
                                                                     II      0.71     0.22 10   0            0
                                                                    III       0.71     0.66  6   0            0
                                                       I
                    0.6
                C




                                                   II
                                                               III
                    0.4



                    0.2



                      0



                    -0.2
                           0         1                 2                3              4                 5               6
                                                                       y

                    Figure 10: The concentration profiles for different parameters when Q=0,So=0




Special Issue                                                  Page 49 of 89                                                 ISSN 2229 5216
                                                         International Journal of Advances in Science and Technology,
                                                                                                    Vol. 3, No.1, 2011

                                                        TABLE-I

                  Values of amplitude and P phase Tan and Skin friction coefficients  ,  m

    Gr      Gm      Pr     Sc        Q           K     So      M             P    Tan          m              

    5.0     5.0    0.25    0.22      3.0         5.0   4.0     5.0      1.8215   -0.2843       2.3870      2.3880

    6.0     5.0    0.25    0.22      3.0         5.0   4.0     5.0      2.0237   -0.2934       2.2304      2.2315

    5.0     6.0    0.25    0.22      3.0         5.0   4.0     5.0      1.9836   -0.2751       3.0211      3.0221

    5.0     5.0    0.71    0.22      3.0         5.0   4.0     5.0      2.5278    -5919        3.4078      3.4104

    5.0     5.0    0.25    0.66      3.0         5.0   4.0     5.0      1.6107   -0.2553       2.2698      2.2706

    5.0     5.0    0.25    0.22      5.0         5.0   4.0     5.0      1.7955   -0.2626       2.5223      2.5242

    5.0     5.0    0.25    0.22      3.0       10.0    4.0     5.0      1.7479   -0.2277       2.2416      2.2423

    5.0     5.0    0.25    0.22      3.0         5.0   6.0     5.0      1.8396   -0.2893       2.4509      2.4519

    5.0     5.0    0.25    0.22      3.0         5.0   4.0     6.0      1.6179   -0.2492       2.0640      2.0648

                                                        TABLE-II

                                  The values of R and Tan for Sherwood number



      Pr          Sc         Q             K           So                R           Tan                  Sh

     0.71         0.22      2.0            5.0         5.0             2.4520        0.0524              -8.318

     07.0         0.22      2.0            5.0         5.0             9.5566        0.0296              -2.384

     0.71         0.66      2.0            5.0         5.0             0.6855        0.0464              15.503

     0.71         0.22      5.0            5.0         5.0           21.6395          -4.373             -6.600

     0.71         0.22      2.0            8.0         5.0             2.7650         -0.655             -20.211

     0.71         0.22      2.0            5.0         10.0            5.6744         0.160              -15.243




Special Issue                                          Page 50 of 89                                    ISSN 2229 5216
                                                      International Journal of Advances in Science and Technology,
                                                                                                 Vol. 3, No.1, 2011

                                                    TABLE-III
                               The values of Q and Tan for Nusselt number N u


        S.No            Pr             Q                  Q                  Tan                    Nu

          1            0.25           6.0              0.5268                0.0932                1.7110

          2            0.71           6.0              1.2487                0.1396                2.4287

          3            07.0           6.0              13.4562               0.1161               10.8624

          4            0.71           10.0             15.6160               0.0815               12.5666


References
[1]      Gebhart, B. and Pera, L. “The nature of vertical natural convection flows resulting from the combine
         buoyancy effects of thermal and mass diffusion”, Int. J. Heat and Mass Transfer, 14(12), 2025-2050,
         1971.
[2]      Ganesan, P. and Loganathan, P. „„Heat and Mass flux effects on a moving vertical plate with chemically
          reactive species diffusion”, J. Engineering Phys. And Thermophys, 75(4), 899-909, 2002.
[3]      Ghaly, A. Y. and Seddeek, M. A. Chebyshev. “Finite difference method for the effects of chemical
          reaction, heat and mass transfer on laminar flow along a semi-infinite horizontal plate with temperature
         dependent viscosity”, Chaos Solutions & Fractals, 19(1), 61-70, 2004.
[4]      Muhaimin, Ramasamy, Kandasamy, I. Hashim Azme and B. Khamis. “On the effect of Chemical reaction,
         Heat and Mass Transfer on non-linear MHD boundary layer past a Porous sinking sheet with suction”,
        Theoret.Appl. Mech., 36(2), 101-117, 2009.
[5]     De Groot, S. R. and Mazur, P. Non-equilibrium Thermodynamics, Dover, New York‟s 1984.
[6]     A.Sharif Alam, Md. and Thammas, At. “Dufour and Soret effects on steady MHD combined free- forced
         convective and mass transfer flow past a semi infinite vertical plate”, Int. J. Tech. Vol.2, 2006.
[7]      E.R.G.Eckert and R.M.Drake. “Analysis dissipation effects on unsteady free convective flow past an
         Infinite vertical porous plate with variable suction”, I.J. Heat Mass transfer, Vol.17, pp.85-92, 1972.
[8]     N.G.Kafoussias and E.M. Williams. “Thermal-diffusion and diffusion-thermo effects on mixed free-forced
        convective and mass transfer boundary layer flow with temperature dependent viscosity”, Int. J. Engg. Sci.,
        vol.33, pp.1369-1384, 1995.
[9]     M.Anghel, H.S. Takhar and I.Pop. “Dofour and Soret effects on free convection boundary layer over a
        vertical surface embedded in a porous medium”, Studia Univesitatis Babes-Bolyai. Mathematica, XLV (4),
        pp.11-21, 2000.
[10]    Postelnicu. “Influence of magnetic field on heat and mass transfer by natural convection from vertical
        surfaces in porous media considering Soret and Dufour effects”, Int. J. heat mass transfer, vol.47, pp.1467-
        1472, 1984.
[11]    Ahmed Sahin. “Influence of chemical reaction on transient MHD free convection flow over a vertical plate
        in slip-flow regime”, Emirates Journal for Engineering Research, 15 (1), 25-34, 2010.




Special Issue                                      Page 51 of 89                                    ISSN 2229 5216
                                       International Journal of Advances in Science and Technology,
                                                                                  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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