INTRODUCTION:
Convective flow with simultaneous heat and mass transfer under the influence of a magnetic field and chemical reaction have attracted a considerable attention of researchers because such process exist in many branches of science and technology. Possible applications of this type of flow can be found in many industries viz. in the chemical industry, cooling nuclear reactors and magnetohydrodynamic (MHD) power generators. Free convection flow occurs frequently in nature. It occurs not only due to temperature difference, but also due to concentration difference or combination of these two. Many transport processes exit in industrial applications in which the simultaneous heat and mass transfer occur as a result of combined buoyancy effects of diffusion of chemical species. Free convection flows in a porous media with chemical reaction have wide applications in geothermal and oil reservoir engineering as well as in chemical reactors of porous structure.
Moreover, considerable interest has been evinced in radiation interaction with convection and chemical reaction for heat and mass transfer in fluids. This is due to the significant role of thermal radiation in the surface heat transfer when convection heat transfer is small, particularly, in free convection problems involving absorbing-emitting fluids.
Nandeep et al. [1] analyzed MHD boundary layer flow past an exponentially permeable shrinking sheet of a Casson fluid. Hayat et al. [2] considered two-dimensional boundary layer flow of carreau fluid past a permeable stretching sheet. Raju, Sandeep [3] studied the effects of nonlinear thermal radiation and non-uniform heat source/sink in unsteady three-dimensional flow of Carreau and Casson fluids past a stretching surface in the presence of homogeneous heterogeneous reactions and the governing equations are solved by R-K based shooting method. Chakravarthula SK. Raju et al. [4] discussed the influence of thermal radiation and chemical reaction on the boundary layer flow of a MHD Jeffery Nano fluid over a permeable cone in the presence of thermophoresis Brownian motion effects. Casson fluid flow in the stagnation point region of a sphere with cross diffusion effects has been considered by Pushpalatha et al. [5]. Hakiem and Amin [6] have examined the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. Najeeb Alam Khan and Faqiha Sultan [7] have considered the double diffusive Darcian convection flow of Eyring-Powell fluid from a cone embedded in a homogeneous porous medium with the effects of Soret and Dufour and the governing equations are numerically solved by non-perturbation scheme. Louis Gosselin, Alaxander K. da Silva [8] has been investigated to maximize the heat transfer rate removed from a warm plate by the Nano fluid. Chamkha and Aly [9] have obtained the numerical solution of steady natural convection boundary-layer flow of a nanofluid consisting of a pure fluid with nanoparticles along a permeable vertical plate in the presence of magnetic field, heat generation or absorption and suction or injection effects. The induced magnetic field effect on the stagnation point flow of a non-Newtonian fluid over a stretching sheet with homogeneous-heterogeneous reactions and non-uniform heat source or sink and the ordinary differential equations are numerically solved by R-K and Newton’s method has been considered by Raju et al. [10]. The Magneto hydrodynamic three-dimensional boundary layer flow of an incompressible casson fluid in a porous medium has been obtained by Shehzad et al. [11]. Hayat et al. [12] have been investigated the mixed convection flow of non-Newtonian Nano fluid over a stretching surface in presence of thermal radiation, heat source/sink and first order chemical reaction. Raju et al. [13] have been analyzed the flow, heat and mass transfer behavior of casson fluid past an exponentially permeable stretching surface in presence of thermal radiation, magnetic field, viscous dissipation, heat source and chemical reaction. Nadeep et al. [14] have been studied magneto hydrodynamics Casson fluid flow in two lateral directions past a porous linear stretching sheet. Jasmine Benazir et al. [15] have been analyzed the effects of double dispersion, non-uniform heat source/sink and higher order chemical reaction on unsteady, free convective, MHD Casson fluid flow over a vertical cone and flat plate saturated with porous medium. Jagdish Prakash et al. [16] have been studied flow, heat and mass transfer characteristics of unsteady mixed convective magneto hydrodynamic flow of a heat absorbing fluid in an accelerated vertical wavy plate, subject to varying temperature and mass diffusion, with the influence of buoyancy, thermal radiation and Duffer effect. Shehzed et al. [17] have been investigated the convective heat and mass conditions in three-dimensional flow of an oldroyd-B Nano fluid and the governing problem solved numerically by convergent approximate solutions. The mixed convection boundary layer flow of a magneto hydrodynamic second grade fluid over an unsteady permeable stretching sheet discussed by Hayat and Qusim [18]. Parha et al. [19] have been analyzed the mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent fluid. Sajid and Hayat [20] have been studied the effect of radiation on the boundary layer flow and heat transfer of a viscous fluid over an exponentially stretching sheet. Anur Ishak [21] has been studied the effect of radiation on magneto hydrodynamic boundary layer flow of a viscous fluid over an exponentially stretching sheet. Mustafa et al. [22] have been discussed the unsteady flow and heat transfer of a Casson fluid over a moving flat plate with a parallel free stream. Mohammad Mehdi Rashidi et al. [23] have been examined heat and mass transfer in a steady two-dimensional magneto hydrodynamic viscoelastic fluid flow over a stretching vertical surface by considering Soret and Dufour effects. The boundary layer flow and heat transfer characteristic of second order fluid and second grade fluid with variable thermal conductivity and variation over an exponentially stretching sheet in porous medium have been studied by Singh et al.[24]. Iskandar Waini et al. [25] studied the effect of aligned magnetic field towards the flow and heat transfer of the upper-convected Maxwell (UCM) fluid over a Stretching/Shrinking sheet. Ali and Sandeep [26] investigated the heat transfer behavior of electrically conducting MHD flow of a Casson nanofluid over a Cone, wedge and a plate and a Cattaneo-Christov heat flex model with variable source/sink and nonlinear radiation effects. Anantha Kumar et al. [27] analyzed the thermo diffusion and diffusion thermo effects on MHD Casson fluid over a linear/nonlinear Stretching sheet and the governing equation are solved numerically using Range-Kutta based Shooting technique. The influence of aligned magnetic field on an unsteady flow of a Casson fluid past a vertical permeable oscillating plate in presence of radiation, chemical reaction and heat generation/absorption analyzed by Ramana Reddy et al.[28]. Ananth et al. [29] analyzed the Stagnation-point flow of a Casson fluid toward a stretching sheet with nonlinear thermal radiation and induced magnetic field effects. The induced magnetic field and non-uniform heat Source or Sink effects on the stagnation-point flow of a non-Newtonian fluid towards a stretching sheet in the presence of homogeneous-heterogeneous reaction investigated by Raju et al. [30]. Naveed Ahmed et al. [31] discussed squeezing flow of an electrically conducting Casson fluid has been taken into accound and the governing equations are solved analytically by using the variation of parameters method.
Thus the present’s investigation is concerned with the study of variable magnetic field effect and radiative Casson fluid in two dimensional MHD flow, heat and mass transfer of viscous incompressible fluid pass a permeable vertical plate in a porous medium. The effects of various physical parameters on the velocity, temperature and concentration profiles as well as on local skin friction co-efficient and local Nusselt number are shown graphically.
FORMULATION OF THE PROBLEM:
Consider two dimensional laminar boundary layer flow
of a viscous incompressible electrically conducting and heat absorbing fluid
fast a semi-infinite vertical permeable plate embedded in a uniform
porous medium which is subject to thermal and concentration buoyancy effects.
As shown in Fig.1, 
-
axis is along the plate and 
-
is perpendicular to the plate. The wall maintained at a constant temperature 
and
concentration 
higher
than the ambient temperature 
and
concentration 
respectively.
Also, it is assumed that there exists a homogeneous chemical reaction of first
order with rate constant R between the diffusing species and the fluid.
