Steady MHD Free Convection Heat and Mass Transfer Flow about a Vertical Porous Surface with Thermal Diffusion and Induced Magnetic Field

Abstract

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing nondimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution, mass concentration and induced magnetic field to the second order approximations are obtained for different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields, mass concentration and the induced magnetic fields are exhibited under certain assumptions and are studied graphically. The effects of these dimensionless parameters on the coefficients of skin friction and heat transfer are also studied in tabular form in the present analysis. It is observed that the effects of thermal-diffusion and suction have great importance on the velocity, temperature, induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables. Further, for more accuracy of the analytical approximate results, a numerical solution have been obtained by using standard initial value solver numerical procedure based on the sixth order Runge-Kutta integration scheme along with Nachtsheim-Swigert iteration technique. Finally, a comparison has been made between the numerical results and analytical approximate results and a very good agreement is found between the results.