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									              International Journal of Scientific Engineering and Technology               (ISSN : 2277-1581)
              Volume No.2, Issue No.2, pg : 56-72                                               1 Feb. 2013

Radiation and Thermo - Diffusion Effects on Mixed Convective Heat and Mass
  Transfer Flow af a Viscous Dissipated Fluid over a Vertical Surface in the
              Presence of Chemical Reaction with Heat Source

                     D Chenna Kesavaiah1, P V Satyanarayana2, S Venkataramana3
 1
   Department of H & BS, Visvesvaraya College of Engineering & Technology, Greater Hyderabad, A.P, India
                                        chennakesavaiah@gmail.com
    2
      Fluid Dynamics Division, School of Advanced Science, VIT University, Vellore - 632 014, T N, India
                 3
                   Department of Mathematics, S V University, Tirupati - 517 502, A.P, India

ABSTRACT                                                   very light molecular weight  H 2 , He  and the medium
The present work analyzes the influence of chemical        molecular weight      N2   air) the diffusion – thermo
reaction on MHD mixed convection heat and mass             effects was found to be of a magnitude just it cannot be
transfer for a viscous fluid past an infinite vertical     neglected.
plate embedded in a porous medium with radiation
and heat generation. The dimensionless governing           The heat and mass transfer simultaneously affecting each
equations for this investigation are solved analytically   other that will cause the cross diffusion effect. The heat
using two - term harmonic and non-harmonic                 transfer caused by concentration gradient is called the
functions. The effects of various parameters on the        diffusion-thermo or Dufour effect. On the other hand,
velocity, temperature and concentration fields as well     mass transfer caused by temperature gradients is called
as the skin-friction coefficient, Nusselt number are       Soret or thermal diffusion effect. Thus Soret effect is
presented graphically and Sherwood number is               referred to species differentiation developing in an initial
presented numerically.                                     homogenous mixture submitted to a thermal gradient
                                                           and the Dufour effect referred to the heat flux produced
Keywords: Radiation, mass transfer, chemical reaction,     by a concentration gradient. The Soret effect, for
heat source and concentration                              instance has been utilized for isotope separation, and in
                                                           mixture between gases with very light molecular weight
                                                            H2 , He   and of medium molecular weight  N2 , air 
   I. INTRODUCTION

The phenomenon of heat and mass transfer has been the      Soret effect [thermal-diffusion] refers to mass flux
object of extensive research due to its applications in    produced by a temperature gradient. These effects are
Science and Technology. Such phenomena are observed        neglected on the basis that they are of a smaller order of
in buoyancy induced motions in the atmosphere, in          magnitude than the effects described by Fourier’s and
bodies of water, quasisolid bodies such as earth and so    Fick’s laws. In view of the importance of this diffusion –
on. This assumption is true when the concentration level   thermo effect. Similarity equations of the momentum
is very low. Therefore, so ever, exceptions the thermal    energy and concentration equations are derived by
diffusion effects for instance, has been utilized for      introducing a time dependent length scale. Malsetty et. al
isotropic separation and in mixtures between gases with    [19] have studied the effect of both the Soret coefficient
                                                           and Dufour coefficient on the double diffusive
IJSET@2013                                                                                                    Page 56
               International Journal of Scientific Engineering and Technology                (ISSN : 2277-1581)
               Volume No.2, Issue No.2, pg : 56-72                                                1 Feb. 2013

convective with compensating horizontal thermal and          spacecraft re-entry aerothermodynamics which operate
solutal gradients. Saritha and Satya Narayana [25]           at higher temperatures, radiation effects can be
thermal diffusion and chemical reaction effects on           significant. Alagoa et al. [3] studied radiative and free
unsteady MHD free convection flow past a semi infinite       convection effects on MHD flow through porous
vertical permeable moving plate. Mohamed [21] Double         medium between infinite parallel plates with time-
- Diffusive convection - radiation Interaction on            dependent suction. Bestman and Adjepong [4] analyzed
Unsteady MHD flow over a vertical moving porous plate        unsteady hydromagnetic free convection flow with
with heat generation and Soret effects. Bhupendra            radiative heat transfer in a rotating fluid. Olanrewaju
Kumar et.al [5] Three-Dimensional mixed convection           et.al [23] further results on the Effects of Variable
flow past an infinite vertical plate with constant surface   Viscosity and Magnetic Field on Flow and Heat Transfer
heat flux. Ahmed and Kalita [2] Soret and magnetic field     to a Continuous Flat Plate in the Presence of Heat
effects on a transient free convection flow through a        Generation and Radiation with a Convective Boundary
porous medium bounded by a uniformly moving infinite         Condition.
vertical porous plate in presence of heat source. Gireesh
Kumar and Satyanarayana [15] Mass transfer effects on        In all these investigations, the viscous dissipation is
MHD unsteady free convective Walter's memory flow            neglected. The viscous dissipation heat in the natural
with constant suction and heat sink.                         convective flow is important, when the flow field is of
                                                             extreme size or at low temperature or in high
Hydromagnetic flows and heat transfer have become            gravitational field. Gebhart [14] shown the importance
more important in recent years because of its varied         of viscous dissipative heat in free convection flow in the
applications in agriculture, engineering and petroleum       case of isothermal and constant heat flux at the plate.
industries. Raptis [24] studied mathematically the case      Israel Cookey et al. [17] investigated the influence of
of time varying two-dimensional natural convective flow      viscous dissipation and radiation on unsteady MHD free
of an incompressible, electrically conducting fluid along    convection flow past an infinite heated vertical plate in a
an infinite vertical porous plate embedded in a porous       porous medium with time dependent suction. Sreekantha
medium. Soundalgekar [28] obtained approximate               Reddy et.al [29] Effects of chemical reaction, radiation
solutions for two-dimensional flow of an incompressible      and thermo-diffusion on convective heat and mass
viscous flow past an infinite porous plate with constant     transfer flow of a viscous dissipated fluid in a vertical
suction velocity, the difference between the temperature     channel with constant heat flux. Md. Abdul Sattar and
of the plate and the free stream is moderately large         Md. Alam [20] Thermal diffusion as well as
causing free convection currents. Takhar and Ram [32]        transportation effect on MHD free convection and Mass
studied the MHD free convection heat transfer of water       Transfer flow past an accelerated vertical porous plate.
at 4 C through a porous medium. Elbashbeshy [12]            Satyanarayana et.al [26] viscous dissipation and thermal
studied heat and mass transfer along a vertical plate        radiation effects on an unsteady MHD convection flow
under the combined buoyancy effects of thermal and           past a semi-infinite vertical permeable moving porous
species diffusion, in the presence of magnetic field.        plate Sudheer Babu et. al [31] Effects of thermal
                                                             radiation and chemical reaction on MHD convective
In all these investigations, the radiation effects are       flow of a polar fluid past a moving vertical plate with
neglected. For some industrial applications such as glass    viscous dissipation.
production and furnace design and in space technology
applications, such as cosmical sight aerodynamics            The effects of radiation on MHD flow and heat transfer
rocket, propulsion systems, plasma physics and               problem have become more important industrially.

IJSET@2013                                                                                                     Page 57
               International Journal of Scientific Engineering and Technology                (ISSN : 2277-1581)
               Volume No.2, Issue No.2, pg : 56-72                                                1 Feb. 2013

Many processes in engineering areas occur at high            investigated the effect of the first order homogeneous
temperature, and knowledge of radiation heat transfer        chemical reaction on the process of an unsteady flow
becomes very important for the design of the pertinent       past a vertical plate with a constant heat and mass
equipment. Nuclear power plants, Gas turbines and            transfer. Chamkha [7] studied the MHD flow of a
various propulsion devices, for aircraft, missiles,          numerical of uniformly stretched vertical permeable
satellites and space vehicles are examples of such           surface in the presence of heat generation/ absorption
engineering areas. Shercliff [27] and Ferraro and            and a chemical reaction. Muthucumaraswamy [22]
Plumpton [13]. Hossian and Rees [16] examined the            presented heat and mass transfer effects on a
effects of combined buoyancy forces from thermal and         continuously moving isothermal vertical surface with
mass diffusion by natural convection flow from a             uniform suction by taking into account the homogeneous
vertical wavy surface. Combined heat and mass transfer       chemical reaction of first order.
in MHD free convection from a vertical surface has been      Kesavaiah Ch et.al [18] Effects of the chemical reaction
studied by Chein-Hsin-Chen [8]. Further, the effect of       and radiation absorption on an unsteady MHD
Hall current on the fluid flow with variable                 convective heat and mass transfer flow past a semi-
concentration has many applications in MHD power             infinite vertical permeable moving plate embedded in a
generation, in several astrophysical and meteorological      porous medium with heat source and suction
studies as well as in plasma flow through MHD power          Keeping the above application in view we made attempt
generators. From the point of application, model studies     in this paper to study the present work analyzes the
on the Hall Effect on free and forced convection flows       influence of a first - order homogeneous chemical
have been made by several investigators. Datta and Jana      reaction on MHD mixed convection heat and mass
[10], Acharya et al.[1] and Biswal and Sahoo [6] have        transfer for a viscous fluid past an infinite vertical plate
studied the Hall effect on the MHD free and forced           embedded in a porous medium with radiation and heat
convection heat and mass transfer over a vertical surface.   generation. The dimensionless governing equations for
Stanford Shateyi et.al [30] The effects of thermal           this investigation are solved analytically using two -
radiation, hall currents, Soret and Dufour on MHD flow       term harmonic and non-harmonic functions
by mixed convection over a vertical surface in porous
media.                                                       II. FORMULATION OF THE PROBLEM

The growing need for chemical reactions in chemical          We consider the mixed convection flow of an
and hydrometallurgical industries requires the study of      incompressible, viscous, electrically conducting viscous
heat and mass transfer with chemical reaction. There are     fluid embedded in a uniform porous medium in the
many transport processes that are governed by the            presence of thermal diffusion, chemical reaction,
combined action of buoyancy forces due to both thermal       radiation, thermal and concentration buoyancy effects
and mass diffusion in the presence of the chemical           such that x  -axis is taken along the plate in upwards
reaction effect. These processes are observed in nuclear     direction and y  -axis is normal to it. A transverse
reactor safety and combustion systems, solar collectors,     constant magnetic field is applied i.e. in the direction of
as well as metallurgical and chemical engineering. Their
                                                              y  - axis. Since the motion is two dimensional and
other applications include solidification of binary alloys
                                                             length of the plate is large therefore all the physical
and crystal growth dispersion of dissolved materials or
particulate water in flows, drying and dehydration           variables are independent of x  . Let u  and v  be the
operations in chemical and food processing plants, and       components of velocity in x  and y  directions,
combustion of atomized liquid fuels. Dekha et al. [11]       respectively, taken along and perpendicular to the plate.

IJSET@2013                                                                                                      Page 58
                       International Journal of Scientific Engineering and Technology                             (ISSN : 2277-1581)
                       Volume No.2, Issue No.2, pg : 56-72                                                             1 Feb. 2013

The governing equations of continuity, momentum and                    qr 
energy for a flow of an electrically conducting fluid                         4(T   T ) I                               (7)
                                                                       y 
along a hot, non-conducting porous vertical plate in the                               
                                                                                                      eb
presence of concentration and radiation is given by                    where I   K w
                                                                                       0
                                                                                                     T 
                                                                                                           d  , K w  is the absorption
v                                                                    coefficient at the wall and eb is Planck’s function, I 
     0                                               (1)
y 
                                                                       is absorption coefficient
v  v0 (Constant)                                   (2)              The boundary conditions are
p 
   
      0  p  is independent of y                    (3)             u   0,      T   Tw , C  C ; y   0
y                                                                                                                           (8)
                                                                       u*  0, T   T , C   C ; y   
            u       2u 
  v               2   g  T   T                          Introducing the following non-dimensional quantities
            y      y
                                                      (4)                   u              v0 y                T   T
                                                                      u      ,     y               ,     T
  g  *  C   C    B02u           
                                                u                          v0                                  Tw  T
                                        K
                                                                            C   C         g Tw  T 
              T  
                           T  2                                     C            , Gr 
 C p  v               k 2  Q0 T  T                               C w  C
                                                                                                  3
                                                                                                  v0
              y         y
                                                     (5)                             v0
                                                                                       2
                                                                                                                  4 I 
                                            2                          Ec                       ,          R
                                  u                                        Tw  T 
                                
                         q                                                                                       C p v02
                         r     
                         y       y                                                               C p
                                                                             Q0           Kr 
                                                                       Q            , Kr  2 , Pr 
     C        2C                                                         C p v0
                       Kr   C   C 
                                                                                   2
                                                                                            v0        k
v         DM
     y       y 2                                                                                        DT Tw  T 
                                                     (6)                       B0 2 2
                  T                                                  M               ,            S0                       (9)
                                                                                                              Cw  C 
                        2
               DT 2                                                           v0 2
                  y
                                                                                   * g  Cw  C                    
Here, g is the acceleration due to gravity, T                
                                                                 the   Gm                   3
                                                                                                             ,   Sc 
                                                                                            v0                          D
temperature of the fluid near the plate, T the free stream                 III. SOLUTION OF THE PROBLEM
temperature, C          
                            concentration,  the coefficient of
                                                                       In the equations (4), (5), (6) and (8), we get
thermal expansion, k the thermal conductivity, P the
pressure, C p the specific heat of constant pressure, B0
                                                                        2u u      1
the magnetic field coefficient,  viscosity of the fluid,                      M   u   GrT  Gm C (10)
                                                                       y 2
                                                                             y     K
q  the radiative heat flux,  the density,  the magnetic              2T      T
permeability of fluid V0 constant suction velocity,  the
                                                                             Pr      F  Q  Pr T
                                                                       y 2
                                                                                 y
kinematic viscosity and D molecular diffusitivity.                                                           2
                                                                                                                               (11)
                                                                                               u 
                                                                                      Pr Ec  
                          
The radiative heat flux qr is given by equation (5) in                                         y 
the sprit of Cogly et.al [9]                                            2C      C                  2T
                                                                             Sc     ScKrC   ScS0 2                        (12)
                                                                       y 2      y                 y
IJSET@2013                                                                                                                            Page 59
                International Journal of Scientific Engineering and Technology                                            (ISSN : 2277-1581)
                Volume No.2, Issue No.2, pg : 56-72                                                                            1 Feb. 2013

where Gr is Grashof number, Gm is the mass Groshof            u0  0,  u1  0, T0  1 
number, Pr is Prandtl number, M is magnetic                                            y0
                                                              T1  0, C0  1, C1  0 
parameter, R is Radiation parameter, Sc is Schmidt                                                                                              (21)
                                                              u0  0, u1  0, T0  0 
number, Q is heat source parameter, Ec is the Eckert                                  y
                                                              T1  0, C0  1, C1  0 
number, M is magnetic parameter Kr is Chemical
                                                              Solving equations (15) to (20) with the help of (21), we
reaction parameter and S 0 is Soret number.
                                                              get
The corresponding boundary condition in dimensionless
                                                              u  y   A1e m 2 y  A2e m 4 y  A3e                               A4e m6 y
                                                                                                                          m2y
form are reduced to
u  0,    T  1, C  1              y0
                                                   (13)
                                                                               
                                                                     Ec A5e m 8 y  A6 e 2 m 6 y  A7 e 2 m 2 y
u  0, T  0, C  0               y
                                                                                             A9 e 2 m2 y  A10 e
                                                                                                                                   m2  m6  y
                                                                     A8e
                                                                                   2m 4 y

The physical variables u, T and C can expand in the
                                                                     A11e
                                                                                     m2  m4  y
                                                                                                                           A12 e
                                                                                                                                    m2  m4  y
                                                                                                            
power of Eckert number  Ec  (E). This can be possible
                                                                    A13e
                                                                               m2  m6  y
                                                                                               A14 e
                                                                                                                m4  m6  y
                                                                                                                               A15e 2 m 2 y
physically as Ec for the flow of an incompressible fluid
is always less than unity. It can be interpreted physically         A16 e m 8 y  A17 e m 8 y  A18e 2 m 6 y
as the due to the Joules dissipation is super imposed on            A19 e 2 m 2 y  A20 e 2 m 4 y  A21e 2 m 2 y
the main flow.
                                                                    A22 e
                                                                                   m 2 m 6  y
                                                                                                                       A23e m 2  m 4  y
                                       
u  y   u0  y   Ec u1  y   O  E   2

                                                                                         A25e
                                                                                                      m 2m 6  y
                                                                                                                         A26e
                                                                                                                                    m 4m 6  y
                                                               A24 e
                                                                         m 2m 4  y

T  y   T  y   Ec T  y   O  E  (14)
                                           2
           0             1
                                                                    A27 e 2 m 2 y  A28e m 10 y  A29e m 12 y 
u  y   C  y   Ec C  y   O  E 
           0                 1
                                               2


Using equation (14) in equations (10)–(12) and equating
the coefficient of like powers of E, we have                    y   em y  2
                                                                                                   Ec       B e    1
                                                                                                                        2 m6 y
                                                                                                                                  B2e 2 m2 y
                                                                     B3e 2 m4 y  B4 e 2 m2 y  B5e
                                                                                                                                         m2  m6  y
   
               1
u0  u0   M   u0   Gr T0  Gm C0 (15)
              K                                                    B6 e
                                                                                    m2  m4  y
                                                                                                    B7 e
                                                                                                                m2  m4  y
                                                                                                                               B8e
                                                                                                                                         m2  m6  y


T0  Pr T0   F  Q  Pr T0  0                (16)              B9e
                                                                                      m4  m6  y
                                                                                                       B10e 2 m2 y  B11e m8 y                   
C0  ScC0  KrScC0  ScS0T0
                                                (17)
                                                              C  y   D1e
                                                                                    m2y
                                                                                              D2e
                                                                                                            m4y
                                                                                                                                  
                                                                                                                         Ec D3e m8 y
   
               1
u1  u1   M   u1   Gr T1  Gm C1 (18)
              K                                                     D4 e 2 m6 y  D5e 2 m2 y  D6e 2 m4 y
                                                                      D7 e 2 m2 y  D8e
                                                                                                        m2  m6  y
                                                                                                                          D9e
                                                                                                                                      m2  m4  y
T1  Pr T1   F  Q  Pr T1   Pr u02        (19)
                                                                                                                          D11e
                                                                                                                                   m2  m6  y
                                                                      D10 e
                                                                                       m2  m4  y
C1 ScC1  KrScC1  ScS0T1                   (20)                                                         
The corresponding boundary conditions are                            D12 e
                                                                                     m4  m6  y
                                                                                                     D13e 2 m2 y  D14 e m10 y             
                                                              Skin – friction:

                                                              The skin-friction coefficient at the plate is given by
IJSET@2013                                                                                                                                             Page 60
                 International Journal of Scientific Engineering and Technology                (ISSN : 2277-1581)
                 Volume No.2, Issue No.2, pg : 56-72                                                1 Feb. 2013

     u                                                     Final results are computed for the main physical
     A1m2  A2 m4  A3m2  A4 m6                         parameters which are presented by means of graphs. The
     y  y 0
                                                              influence of the thermal Grashof number Gr  , solutal
              Ec  A5 m8  2 A6 m6  2 A7 m2
                                                              Grashof number  Gm  , the magnetic field parameter
          2 A8 m4  2 A9 m2   m2  m6  A10
               m2  m4  A11   m2  m4  A12              M  ,   heat source parameter    Q ,   thermal radiation

           m2  m6  A13         m4  m6  A14            parameter   F  , Prandtl number  Pr  , Porosity
              2 A15 m2  A16 m8  A17 m8            Heat     parameter  K  chemical reaction parameter  Kr  ,
              2 A18 m6  2 A19 m2  2 A20 m4                 Soret number  S0  and Schmidt number  Sc  on the
              2 A21m2        m2  m6  A22                 velocity, temperature and concentration profiles can be
          A23  m2  m4    m2  m4  A24                  analyzed from Figures (1) - (26). The values of
                                                              Gr & Gm are taken to be both positive as this value
           m2  m6  A25   m4  m6  A26                  represent respectively cooling and the Eckert number
          2 A27 m2  2 A28 m10  A29 m22                     Ec  is taken to be 0.001 .
Transfer:
                                                              Velocity Profiles
The rate of heat transfer in terms of Nusselt number at
the plate is given by
                                                              The velocity profiles for different values of the Grashof
      T                                                    number Gr  and the modified Grashof numbers Gc 
Nu        m2  Ec 2 B1m6  2m2 B2
      y  y 0                                              are defined in Figures (1) and (2) respectively. It can be
                                                              observed that an increase in Gr or Gc leads to the rise
              2m4 B3  2m2 B4   m2  m6  B5
                                                              in the values of velocity, Here, the positive values of Gr
                 m2  m4  B6   m2  m4  B7              correspond to a cooling of the surface by natural
               m2  m6  B8   m4  m6  B9                convection. In addition, the curves show that the peak
                                                              value of the velocity increases rapidly near the wall of
              2m2 B10                   m8 B11
                                                              the porous plate as Gr or Gc increases, and then
Sherwood number                                               decays to the free stream velocity. The effect of thermal
                                                              radiation parameter on the velocity field has been
      C                                                    illustrated in Figure (3). It is seen that as the thermal
Sh        m 2 D1  m 4 D2  Ec m8 D3                     radiation parameter increases the velocity field
      y  y 0                                              decreases. For various values of the permeability
                  2m6 D4  2m2 D5  2m4 D6                   parameter  K  , the profiles of the velocity across the
                  2m2 D7          m2  m6  D8             boundary layer are shown in Figure (4). The velocity
                m2  m4  D9   m2  m4  D10              increases for increasing values of the permeability
                 m2  m6  D11   m4  m6  D12
                                                              parameter K . Figure (5) illustrate the variation in
                                                              velocity distributions across the boundary layer for
                2m2 D13               m10 D14              various values of the chemical reaction parameter  Kr  .

   IV. RESULTS AND DISCUSSION                                 It can be seen that the velocity decreases in the

IJSET@2013                                                                                                       Page 61
                  International Journal of Scientific Engineering and Technology                  (ISSN : 2277-1581)
                  Volume No.2, Issue No.2, pg : 56-72                                                  1 Feb. 2013

destructive reaction  Kr  0 . The MHD and the                 profiles for different values of the Prandtl number  Pr 
concentration boundary layer become thin as the reaction         is shown in Figure (12). The results show that an
parameters. For different values of the magnetic field           increase of the Prandtl number results in a decrease in
parameter  M  , the velocity profile is plotted in Figure      the thermal boundary layer thickness and a more
                                                                 uniform temperature distribution across the boundary
(6). It is obvious that the effect of increasing values of
                                                                 layer. The reason is that the smaller values of Pr are
the parameter M results in a decreasing velocity
                                                                 equivalent to increasing the thermal conductivities, and
distribution across the boundary layer. Figure (7) present
                                                                 therefore heat is able to diffuse away from the heated
the velocity profiles for different values of the Prandtl
                                                                 surface more rapidly than for the larger values of Pr .
number  Pr  . The results show that the effect of              Hence, the thicker the boundary layer is the shower the
increasing values of Pr results in a decrease of the             rate of heat transfer. At high Prandtl fluid has low
velocity that physically is true because the increase in         velocity, which in turn also implies that at lower fluid
the Prandtl number is due to the increase in the                 velocity the specie diffusion is comparatively lower and
viscosities of the fluid which makes the fluid thick and         hence higher specie concentration is observed at high
hence causes a decrease in the velocity of fluid. The            Prandtl number. Figures (13) present the decreasing
effects of internal heat generation parameter  Q  on the       result of temperature when heat source parameter is
                                                                 increasing. Figures (14) - (16) shows the temperature
velocity are displayed in Figure (8). It is clear that as the
                                                                 profiles for different values of Gm, Gr and Sc . It is
parameter  Q  increases, the velocity profiles lead to a
                                                                 observed that an increasing values of Gm, Gr and
fall. Figure (9) depicts the effect of Soret number  Sr        Sc the results decreases the thermal boundary layer
on the fluid velocity and we observed an increase in the         thickness across the plate.
fluid velocity as Soret number      Sr    increases. This is
                                                                 Concentration Profiles
because an increase in the volumetric rate of generation
connotes increase in buoyancy force thereby increasing
fluid velocity. For different values of the Schmidt              The radiation  F  effects shows in figure (17). It is
number  Sc  , the velocity profiles are plotted in Figure      observed that and increasing values of F the
                                                                 concentration profiles increases. Figures (18) and (19)
(10). It is obvious that the effect of increasing values of
                                                                 depict the effect of various values of the mass and
Sc results in a decreasing velocity distribution.
                                                                 thermal    Grashof     numbers     Gm, Gr      on    the
Temperature profiles                                             concentration boundary layer thickness. It is interesting
                                                                 to note that increase in this parameters bring a small
Figure (11) show the effect of radiation parameter on the        increase across the plate. The effect of permeability
temperature profile. A rise in F causes a significant fall       parameter K on the concentration profile is illustrated
in the temperature values from the highest value at the          in Figure (20). These results show that the with
wall    y  0    across the boundary layer to the free         increasing permeability parameter concentration profiles
                                                                 decreases. Figure (21) show the effect of the chemical
stream. Thus, greater value of F corresponds to smaller
                                                                 reaction    parameter      on     concentration    profiles
radiation flux and the minimum temperature is observed.
                                                                 respectively. It is noticed that species concentration and
Thermal radiation thereby reduces the rate of energy
                                                                 thermal boundary layer are decreasing, as the values of
transport to the fluid. The variation of the temperature
                                                                 chemical reaction are increasing. Figure (22) shows the

IJSET@2013                                                                                                         Page 62
                International Journal of Scientific Engineering and Technology                      (ISSN : 2277-1581)
                Volume No.2, Issue No.2, pg : 56-72                                                      1 Feb. 2013

effects of the magnetic parameter M . It is observed that        chemical reaction and radiation. In the light of present
the concentration decreases with increasing values of            investigation, it is found that the concentration of the
 M . The influence of Prandtl number and heat source             fluid increased during a generative chemical reaction and
parameter are on the concentration field is seen in Figure       decreased during a destructive chemical reaction.
(23) and (24). It is noticed that the increase in the Prandtl    Further, the momentum boundary layer thickness
       Sherwood number  Sh                number        and    decreases while thermal boundary layer thickness and
                                            heat       source    concentration profiles decreases with increasing
  Sc        Sh         F           Sh              parameter     permeability parameter.        Increasing Soret number
 0.22        -         0.5     -0.8783                though     reduce the thermal boundary layer thickness, while
          0.4078                            increases      the   reverse trend is seen in concentration profiles.
 0.30        -         1.0     -0.8533      concentration of
          0.4985                            the fluid. The       Table: (1)
 0.38        -         1.5     -0.8302      influence of S 0
          0.5842
                                            on             the
 0.46        -         2.0     -0.8085
                                            concentration of
          0.6664
                                            the          fluid
medium is seen in Figure (25). In general it is noted that
increase in Soret number contributes to increase in
concentration of the medium. Further the effect is found
to be diminishing as we move away from the plate.
Figure (26) reflects that with increase in Schmidt
number  Sc  the fluid concentration decreases. Figure
                                                                 REFERENCES
(27) and (28) shows the effects of Prandtl number and
magnetic field on skin friction and Nusselt number
versus thermal Grashof number. It is observed that               [1] Acharya M, Dash G C and Singh L P (2001): Indian J.of
increasing values of       Pr, M    the results in both the        Physics B, 75 B (1), p. 168
                                                                 [2] Ahmed N and Kalita H (2012): Soret and magnetic field
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                                                                     porous medium bounded by a uniformly moving infinite
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                                                                 [3] Alagoa K D, Tay G and Abbey T M (1999): Radiative and
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                                                                     free convection effects of a MHD flow through porous
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                                                                     pp.455-468.
    V. CONCLUSIONS                                               [4] Bestman A R and Adjepong S K (1998): Unsteady
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                                                                 [5] Bhupendra Kumar Sharma, Tara Chand and Chaudhary R
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                                                                     C (2011): Three-Dimensional Mixed Convection Flow past
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                                                                     an Infinite Vertical Plate with Constant Surface Heat Flux,

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    American Journal of Computational and Applied                 [20]Md. Abdul Sattar, Md. Alam (1995): Thermal diffusion as
    Mathematics, 1(1): pp. 27-32                                       well as transportation effect on MHD free convection
[6] Biswal S and Sahoo P K(1994): Proc. Nat. Acad. Sci.,               and Mass Transfer flow past an accelerated vertical
    69A, p. 46.                                                        porous plate, Ind. J. of Pure and App. Maths., 24, p. 679.
                                                                  [21] Mohamed R A (2009): Double-Diffusive Convection-
[7]Chamkha A J (2003): MHD flow of a numerical of                      Radiation Interaction on Unsteady MHD Flow over a
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    presence heat generation\absorption and a chemical                 Soret Effects, Applied Mathematical Sciences, Vol. 3, no.
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    422.                                                          [22]Muthucumaraswamy R (2002): Effects of a chemical
[8] Chein-Hsin-Chen, Int.J.Eng.Science, 42,699-713, 2004.            reaction on a moving isothermal surface with suction, Acta
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    6, p. 551.                                                    [23]Olanrewaju P O, Anake T, Arulogun O T and Ajadi D A
 [10]Datta N and Jana R N (1976): J. Phys. Soc. Japan, 40,           (2012): Further Results on the Effects of Variable
    pp. 1469-1475                                                    Viscosity and Magnetic Field on Flow and Heat Transfer
[11] Dekha R, Das U N and Soundalgekar V M (1994):                   to a Continuous Flat Plate in the Presence of Heat
    Effects on mass transfer on flow past an impulsively             Generation and Radiation with a Convective Boundary
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[12] Elbashbeshy E M A (1997): Int. Eng. Sc, 34, pp. 515-522.        presence of magnetic field, Int. J. Energy Res., Vol.10, pp.
[13]Ferraro V C A and Plumption C (1996): An Introduction            97-101.
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[14]Gebhart B (1962): Effects of viscous dissipation in natural      diffusion and chemical reaction effects on unsteady MHD
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[15]Gireesh Kumar J and Satyanarayana P V (2011): Mass               moving plate, Asian Journal of Current Engineering and
    transfer effects on MHD unsteady free convective Walter's        Maths, 1: 3, pp. 131 – 138.
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[16]Hossain M A and Rees D A S (1999): Acta Mech., 136,              on an unsteady MHD convection flow past a semi-infinite
    pp. 133-141.                                                     vertical permeable moving porous plate International
[17]Israel-Cookey C, Ogulu A and Omubo-Pepple V B                    Journal of Mathematical Archive, 2(4), pp. 476 - 487.
    (2003): Influence of viscous dissipation on unsteady MHD      [27]Shercliff    J    A     (1965):    A     text     book    of
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    in porous medium with time-dependent suction, Int. J.         [28]Soundalgekar V M, Gupta S K and Birajdar N S (1979):
    Heat Mass Transfer, Vol. 46, pp. 2305-2311.                      Effects of mass transfer and free convection effects on
[18]Kesavaiah D Ch, Satyanarayana P V and Venkataramana              MHD Stokes problem for a vertical plate, Nucl., Eng.
    S (2011): Effects of the chemical reaction and radiation         Design, Vol. 53, pp. 309-346.
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[30] Stanford Shateyi, Sandile Sydney Motsa, and Precious
     Sibanda (2010): The effects of thermal radiation, hall
     currents, Soret, and Dufour on MHD flow by mixed
     convection over a vertical Surface in porous media,
     Mathematical Problems in Engineering.
[31] Sudheer Babu M, Satyanarayana P V, Sankar Reddy T
     and Umamaheswara Reddy D (2011): Effects of thermal
     radiation and chemical reaction on MHD convective
     flow of a polar fluid past a moving vertical plate with
     viscous dissipation, Elixir Appl. Math. 40: pp. 5168-
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[32] Takhar H S and Ram P C (1994): Magneto hydrodynamic
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               International Journal of Scientific Engineering and Technology                     (ISSN : 2277-1581)
               Volume No.2, Issue No.2, pg : 56-72                                                     1 Feb. 2013

                                                                                 2
                                                                          4ScS0 m4 B3
   APPENDIX                                                 D6  
                                                                      4m2  2Scm2  KrSc
                                                                        2

                                                                                  2
                                                                          4ScS0 m2 B4
           Pr  Pr 2  4 Pr  F  Q                      D7  
   m2                                                             4m2  2Scm2  KrSc
                                                                        2

                       2                                                   ScS0  m2  m6  B5
                                      
                                                            D8  
           Sc  Sc 2  4 KrSc                                       m2  m6          Sc  m2  m6   KrSc
                                                                                   2

   m4                         
          
                    2           
                                                                              ScS0  m2  m4  B6
                                                            D9  
                                                                      m2  m4          Sc  m2  m4   KrSc
                                                                                   2
           1 1 4N 
   m6   
                        
                         
                2                                                            ScS0  m2  m4  B7
                                                            D10  
                                                                       m2  m4         Sc  m2  m4   KrSc
                                                                                    2
           Pr  Pr 2  4 N 
   m8                     1
                                                                              ScS0  m2  m6  B8
                   2                                      D11  
                              
                                                                       m2  m6         Sc  m2  m6   KrSc
                                                                                    2

                                1
   N1  Pr  F  Q  , N   M                                               ScS0  m4  m6  B7
                                K                         D12  
                                                                       m4  m6         Sc  m4  m6   KrSc
                                                                                    2
            Sc  Sc 2  4 KrSc 
   m10                        
                                
                                                                              2
                       2                                               4ScS0 m2 B10
                                                          D13   2
                                                                   4m2  2Scm2  KrSc
            2  2  4N     
   m12   
                           
                                                           D14    D3  D4  D5  D6  D7  D8
                2          
                    2
                                                                   D9  D10  D11  D12  D13 
              ScS0 m2
   D1   2                                                           Gr                   GmD2
         m2  Scm2  KrSc                                   A1              , A2   2
                                                                  m  m2  N
                                                                       2
                                                                       2                m4  m4  N
                           1
   D2  1  D1 , N   M                                  A3   2
                                                                     GmD1
                                                                              , A4    A1  A2  A3 
                           K                                    m2  m2  N
                          2
                   ScS0 m8 B11
      D3   2                                              A5  
                                                                     GrB11
                                                                              , A6  
                                                                                           GrB1
               m8  Scm8  KrSc                                    m  m8  N
                                                                       2
                                                                                       4m6  2m6  N
                                                                                         2
                                                                       8
                  2
            ScS0 m8 B11                                                GrB2
D3                                                        A7  
         m8  Scm8  KrSc
          2
                                                                   4m2  2m2  N
                                                                     2

                    2
             4ScS0 m6 B1
D4  
         4m6  2Scm6  KrSc
           2
                                                                        GrB3
                                                            A8  
                    2
            4ScS0 m B2                                               4m  2m4  N
                                                                           2

D5                2                                                      4

         4m  2Scm2  KrSc
           2
                                                                         GrB4
           2                                                A9  
                                                                   4m  2m2  N
                                                                           2
                                                                           2

                                                                                 GrB5
                                                            A10  
                                                                     m2  m6   Pr  m2  m6   N
                                                                               2




IJSET@2013                                                                                                        Page 66
                     International Journal of Scientific Engineering and Technology                     (ISSN : 2277-1581)
                     Volume No.2, Issue No.2, pg : 56-72                                                     1 Feb. 2013

                             GrB6                                 A29    A5  A6  A7  A8  A9  A10
A11  
           m2  m4         Pr  m2  m4   N
                        2
                                                                       A11  A12  A13  A14  A15  A16

A12  
                             GrB7                                     A17   A18  A19  A20  A21  A22
           m2  m4         Pr  m2  m4   N                      A23  A24  A25  A26  A27  A28 
                        2


                             GrB8                                                2 2                      2
                                                                                                     Pr m2 A12
A13                                                             B1   2
                                                                            Pr m6 A4
                                                                                           B2   2
           m2  m6         Pr  m2  m6   N
                        2
                                                                        4m6  2 Pr m6  N1       4m2  2 Pr m2  N1
                             GrB9                                                2 2
                                                                            Pr m4 A2
A14                                                             B3   2
           m4  m6         Pr  m4  m6   N
                        2
                                                                        4m4  2 Pr m4  N1
             GrB11                                                                   2
                                                                               Pr m2 A32
A16                                                             B4  
          m8  m8  N
             2
                                                                           4m2  2 Pr m2  N1
                                                                             2


              GrB10               GmD3                                             2 Pr m6 m4 A1 A4
A15                   A17   2                                 B5  
          4m2  2m2  N        m8  m8  N                                  m2  m6         Pr  m2  m6   N1
                 2                                                                       2


           GmD4                   GmD5
A18                  A19  
        4m6  m6  N
           2
                               4m2  m2  N
                                  2
                                                                  B6  
                                                                                    2 Pr m2 m6 A1 A2
                                                                            m2  m4         Pr  m2  m4   N1
                                                                                         2
            GmD6
A20  
        4m4 2  m4  N                                                              2 Pr m2 m4 A3 A2
                                                                  B7  
                                                                            m2  m4         Pr  m2  m4   N1
                                                                                         2
            GmD7
A21  
        4m2 2  m2  N                                                              2 Pr m2 m6 A3 A4
                                                                  B8  
                    GmD8                                                    m2  m6         Pr  m2  m6   N1
                                                                                         2
A22  
         m2  m6    m2  m6   N
                   2
                                                                                    2 Pr m4 m6 A2 A4
                                                                  B9  
                            GmD9                                            m4  m6         Pr  m4  m6   N1
                                                                                         2
A23  
           m2  m4    m2  m4   N
                        2
                                                                                     2
                                                                              2 Pr m2 A1 A3
                         GmD10                                    B10  
A24                                                                       4m2  2 Pr m2  N1
                                                                              2

           m2  m4    m2  m4   N
                        2

                                                                  B11    B1  B2  B3  B4  B5
                         GmD11
A25                                                                   B6  B7  B8  B9  B10 
           m2  m6    m2  m6   N
                        2


                         GmD12
A26  
           m4  m6    m4  m6   N
                        2


             GmD13               GmD14
A27                  A28   2
          4m  2m2  N
             2
             2                m10  m10  N




IJSET@2013                                                                                                            Page 67
                        International Journal of Scientific Engineering and Technology                                          (ISSN : 2277-1581)
                        Volume No.2, Issue No.2, pg : 56-72                                                                          1 Feb. 2013


       2                                                                         1.2

                    sc=0.65, S 0=1.0,Ec=0.001,Pr=0.025,Gr=5.0                      1
     1.5                                                                                              Sc=0.65,S0=1.0,Ec=0.001,Pr=0.75,Gr=5.0
                    Gm=1.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0
                                                                                 0.8                  Gm=5.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0
       1
                             Gm=1.0,2.0,3.0,4.0
                                                                                 0.6
 u




                                                                             u
     0.5                                                                         0.4


       0
                                                                                 0.2

                                                                                   0           Kr=0.5,1.0,1.5,2.0
     -0.5
         0          2                4            6          8          10
                                         y                                       -0.2
                                                                                     0        1           2          3           4          5        6
             Figure (1): Velocity profiles for different values of Gm                                               y
                                                                                         Figure (5): Velocity profiles for different values of Kr
       1
                 Sc=0.65,S =1.0,Ec=0.001,Pr=0.025,Gr=5.0                           2
                             0
     0.8         Gm=1.0,F=3.0,Q=1.0, Kr=0.5,K=1.0, M=2.0                                            Sc=0.65,S 0 =1.0,Ec=0.001,Pr=0.025,Gr=5.0
                                                                                 1.5                Gm=1.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0
     0.6
                                                                                   1




                                                                             u
     0.4                    Gr=1.0,2.0,3.0,4.0
 u




                                                                                 0.5

     0.2
                                                                                   0
                                                                                             M=0.5,1.0,1.5,2.0
       0
                                                                                 -0.5
                                                                                     0                    5                     10                   15
     -0.2                                                                                                           y
         0                       5       y          10                  15               Figure (6): Velocity profiles for different values of M
             Figure (2): Velcoity profiles for different values of Gr
                                                                                 1.2
     1.4
                                                                                   1              Sc=0.65,S0=1.0,Ec=0.001,Pr=0.025,Gr=5.0
     1.2                 Sc=0.65, S 0=1.0;Ec=0.001,Pr=0.025,Gr=5.0                                Gm=1.0,F=3.0,Q=1.0, Kr=0.5, K=1.0,M=2.0
                         Gm=2.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0                   0.8
       1
                                                                                 0.6
     0.8
                                                                             u




     0.6                                                                         0.4
 u




     0.4                                                                         0.2

     0.2                                                                           0
               F=1.0,2.0,3.0,4.0                                                           Pr=0.025,0.50,0.075,0.1
       0                                                                         -0.2
                                                                                     0                    5                      10                  15
     -0.2                                                                                                            y
         0                   5                      10                  15                Figure (7): Velocity profiels for different values of Pr
                                         y
              Figure (3): Velocity profiles for different values of F
                                                                                 1.2
       2
                                                                                   1              Sc=0.65,S0=1.0,Ec=0.001,Pr=0.025,Gr=5.0
                        Sc=0.65,S0=1.0,Ec=0.001,Pr=0.025,Gr=5.0
                                                                                                  Gm=2.0,F=3.0,Q=1.0,Kr=0.5, K=1.0, M=2.0
     1.5                Gm=2.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0                    0.8

                                                                                 0.6
       1
                                                                             u




                         K=1.0,2.0,3.0,4.0
                                                                                 0.4
 u




     0.5
                                                                                 0.2


       0                                                                           0       Q=2.0,4.0,6.0,8.0

                                                                                 -0.2
                                                                                     0                    5                      10                  15
     -0.5                                                                                                            y
         0                       5                    10                15
                                         y                                                Figure (8): Velocity profiles for different values of Q
              Figure (4): Velocity profiles for different values of K



IJSET@2013                                                                                                                                                Page 68
                      International Journal of Scientific Engineering and Technology                                                (ISSN : 2277-1581)
                      Volume No.2, Issue No.2, pg : 56-72                                                                                1 Feb. 2013

     0.7                                                                            1

     0.6           Sc=0.65, S 0=1.0,Ec=0.001,Pr=0.75,Gr=5.0                                     Ec=0.001,Pr=0.025,Q=1.0Gr=5.0,Gm=2.0
                   Gm=1.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0                          0.8
     0.5

                                                                                  0.6
     0.4
 u




                                                                              
     0.3                                                                                               F=1.0,2.0,3.0,4.0
                           S0=1.0,2.0,3.0,4.0                                     0.4

     0.2
                                                                                  0.2
     0.1

       0                                                                            0
        0      1       2         3      4         5       6        7     8           0                  5             10                15                 20
                                        y                                                                             y
             Figure (9): Velocity profiles for different values of S 0                     Figure (11): Temperature profiles for different values of F

                                                                                    1

     1.2                                                                                         Ec=0.001,F=2.0,Q=1.0,Gr=5.0,Gm=2.0
                                                                                  0.8
       1               Sc=0.65,S0=1.0,Ec=0.001,Pr=0.025,Gr=5.0
                       Gm=1.0, F=3.0, Q=1.0,Kr=0.5,K=1.0,M=2.0
                                                                                  0.6
     0.8




                                                                              
                                                                                                    Pr=0.025,0.050,0.075,0.10
     0.6
                                                                                  0.4
 u




     0.4
                                                                                  0.2
     0.2
              Sc=0.22,0.30,0.60,0.78
       0                                                                            0
                                                                                     0         2      4      6      8      10       12      14      16     18
                                                                                                                       y
     -0.2                                                                                   Figure (12): Temperature profiles for different values of Pr
         0                   5                      10                   15
                                         y
             Figure (10): Velocity profiles for different values of Sc              1

                                                                                               Ec=0.001,Pr=0.025,F=2.0,Gr=5.0,Gm=2.0
                                                                                  0.8


                                                                                  0.6
                                                                              




                                                                                                      Q=1.0,2.0,3.0,4.0
                                                                                  0.4


                                                                                  0.2


                                                                                    0
                                                                                     0        2       4     6      8       10      12      14      16      18
                                                                                                                       y
                                                                                            Figure (13): Temperature profiles for different values of Q


                                                                                  1.2

                                                                                    1
                                                                                                   Ec=0.001,Pr=0.71,F=2.0,Q=5.0,Gr=5.0
                                                                                  0.8

                                                                                  0.6
                                                                              




                                                                                                   Gm=1.0,2.0,3.0,4.0
                                                                                  0.4

                                                                                  0.2

                                                                                    0

                                                                                  -0.2
                                                                                      0                0.5             1                1.5             2
                                                                                                                       y
                                                                                          Figure (14): Temperature profeiles for different values of Gm



IJSET@2013                                                                                                                                                      Page 69
                        International Journal of Scientific Engineering and Technology                                             (ISSN : 2277-1581)
                        Volume No.2, Issue No.2, pg : 56-72                                                                             1 Feb. 2013

      1                                                                             1

                                                                                            Sc=0.65,       S 0=0.5,    Ec=0.001,   Pr=0.75
     0.8           Ec=0.001,Pr=0.71,F=3.0,Q=1.0,Gm=10.0
                                                                                   0.8      F=2.0,Q=5.0,Kr=0.5,K=0.5,M=2.0,Gm=50.0


     0.6                                                                           0.6
 




                                                                               C
                                                                                                       Gr=5.0,10.0,15.0,20.0
     0.4              Gr=5.0:5.0:20.0                                              0.4


     0.2                                                                           0.2


      0                                                                             0
       0          0.5        1         1.5          2          2.5         3
                                                                                     0             1           2              3             4           5
                                        y
                                                                                                                      y
            Figure (15): Temperature profiles for different values of Gr
                                                                                         Figure (19): Concentration profiles for different values of Gr

     1.4                                                                            1

     1.2        Ec=0.001,Pr=0.75,F=1.0,Q=4.0,Gr=4.0                                           Sc=0.65,S0=1.0,Ec=0.001,Pr=0.025,Gr=50.0
                Gm=10.0, M=1.0,K=0.5, Kr=0.5,S 0=3.0                               0.8
                                                                                              F=2.0, Q=50.0, Kr=0.5, M=2.0, Gm=100.0
      1

     0.8                                                                           0.6
 




                                                                               C
                                                                                                   K=0.5,1.0,1.5,2.0
     0.6          Sc=0.22,0.08,0.38,0.46
                                                                                   0.4
     0.4
                                                                                   0.2
     0.2

      0                                                                             0
       0                0.5             1                1.5               2         0       1        2      3        4        5        6       7      8
                                       y                                                                              y
            Figure (16): Temperature profiles for different values of Sc                 Figure (20): Concentration profiles for different values of K

      1                                                                             1
                  Sc=0.65,S0=2.0, Ec=0.001, Pr=0.025
                                                                                                  Sc=0.65,S0=2.0,Ec=0.001,Pr=0.025,Gr=5.0
     0.8          Q=1.0,Kr=0.5,K=0.5,M=2.0,Gm=2.0
                                                                                   0.8            F=1.0,Q=1.0, Kr=0.5,K=0.5,M=2.0,Gm=2.0

     0.6
                                                                                   0.6
 C




                                                                               C




     0.4             F=1.0,2.0,3.0,4.0                                                        Kr=0.5,1.0,1.5,2.0
                                                                                   0.4

     0.2
                                                                                   0.2

      0
       0            2            4             6             8           10         0
                                       y                                             0                         5                  10                    15
           Figure (17): Concentration profiles for different values of F                                              y
                                                                                         Figure (21): Concentration profiles for different values of Kr
      1
                                                                                    1
             Sc=0.65,    S 0=0.5,   Ec=0.001,    Pr=0.75
     0.8     Gr=50.0,F=2.0,Q=5.0,Kr=0.5,K=0.5,M=2.0                                            Sc=0.65,S =0.5,Ec=0.001,Pr=0.75,K=0.5
                                                                                                           0
                                                                                   0.8         Gr=60.0, F=2.0, Q=5.0, Kr=0.5, Gm=20.0

     0.6
                    Gm=5.0,10.0,15.0,20.0
                                                                                   0.6
 C




     0.4
                                                                               C




                                                                                   0.4
     0.2

                                                                                   0.2
      0
       0              1           2             3             4           5                      M=0.5,1.0,1.5,2.0
                                        y
                                                                                    0
           Figure (18): Concentration profiles for different values of Gm            0             1               2          3             4          5
                                                                                                                      y
                                                                                         Figure (22): Concentration profiles for different values of M



IJSET@2013                                                                                                                                                   Page 70
                          International Journal of Scientific Engineering and Technology                                             (ISSN : 2277-1581)
                          Volume No.2, Issue No.2, pg : 56-72                                                                             1 Feb. 2013

       1
                      Sc=0.65,        S 0=0.5,    Ec=0.001,    Gr=5.0
                      F=2.0,Q=1.0,Kr=0.5,K=0.5,M=2.0,Gm=10.0
     0.8


     0.6                                                                               2.2

                                                                                                Sc=0.65,S 0=1.0,Ec=0.001,Pr=0.71,Gr=5.0
 C




                          Pr=0.025,0.050,.075,0.10                                      2
     0.4                                                                                        Gm=1.0,F=3.0,Q=1.0,Kr=0.5,K=1.0,M=2.0
                                                                                       1.8

     0.2                                                                               1.6




                                                                                  
                                                                                       1.4
       0
        0             1                2             3               4       5
                                         y                                             1.2
            Figure (23): Concentration profiles for different values of Pr
                                                                                        1
                                                                                                                     Pr=0.5,1.0,1.5,2.0
      1
                                                                                       0.8
                                                                                          1        1.5       2       2.5      3    3.5       4       4.5      5
                           Sc=0.65,       S 0=2.0, Ec=0.001,   Pr=0.025                                                      Gr
     0.8
                           F=1.0,Q=1.0,Kr=0.5,K=0.5,M=2.0,Gm=2.0                             Figure (27): Effect of Prandtl number on skin friction versus Gr

                                                                                        1
     0.6
 C




                    Q=1.0,2.0,3.0,4.0                                                  0.9
     0.4
                                                                                       0.8

     0.2
                                                                                  Nu   0.7
                                                                                                      M=0.5,0.6,0.7,0.8
      0                                                                                0.6
       0              2               4             6            8          10
                                         y
            Figure (24): Concentration profiles for different values of Q                      Ec=0.001,Pr=0.75,F=1.0,Q=4.0,Gr=4.0,M=2.0
                                                                                       0.5
                                                                                               Gm=10.0, K=0.5, Sc=0.65, Kr=0.5, S 0=2.0
       1
                                                                                       0.4
                                                                                          1        1.5      2       2.5     3       3.5      4      4.5      5
                 Sc=0.65, S 0=2.0, Ec=0.001,             Pr=0.025                                                          Gr
     0.8         F=1.0,Q=1.0,Kr=0.5,K=0.5,M=2.0,Gm=2.0                                           Figure (28): Effect of Magnetic field on Nusselt number



     0.6
 C




                   S0=1.0,2.0,3.0,4.0
     0.4


     0.2


       0
        0                     5                     10                      15
                                         y
            Figure (25): Concentration profiles for different values of S 0

       1

                   S0=2.0,Ec=0.001,Pr=0.025,Gm=2.0
     0.8           F=1.0,Q=1.0,Kr=0.5,K=0.5,M=2.0


     0.6
 C




                      Sc=0.22,0.30,0.60,0.68
     0.4


     0.2


       0
        0                        5                        10                 15
                                         y
            Figure (26): Concemtration profiles for different values of Sc



IJSET@2013                                                                                                                                                        Page 71
             International Journal of Scientific Engineering and Technology   (ISSN : 2277-1581)
             Volume No.2, Issue No.2, pg : 56-72                                   1 Feb. 2013




IJSET@2013                                                                                  Page 72

								
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