Steady MHD Natural Convection Heat and Mass Transfer Flow above a Vertical Porous Surface with Thermal Diffusion and Inclined Magnetic Field

Abstract

In this study the effect thermal diffusion and inclined magnetic field on the steady laminar natural convection heat and mass transfer flow of viscous incompressible MHD electrically conducting fluid past a vertical porous surface is considered under the influence of induced magnetic field. The governing non-dimensional 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 have been solved by using the perturbation technique. On introducing the non-dimensional concept and applying usual Boussinesq’s approximation, the solutions for velocity fields, temperature distribution, induced magnetic fields and mass concentration are obtained up to the second order approximations for different selected values of the established dimensionless parameters and numbers. The influences of these various establish parameters and numbers on the velocity and temperature fields, induced magnetic field and mass concentration are exhibited under certain assumptions and are studied graphically. Further, the effects of these dimensionless parameters on the coefficients of skin friction and rate of heat and mass transfers are also studied in tabular form in the present analysis. The effect of different angle of inclinations of the externally applied uniform magnetic field on the field variables have been investigated for the present problem. It is observed that with other useful associated parameters, the thermal diffusion and the angle of inclination of the applied magnetic field have a retarding influence on the fluid velocity, induced magnetic field and mass concentration as well. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number, magnetic parameter and suction parameter have their own dependency on the concerned independent field variables like the velocity, temperature, concentration and induced magnetic fields as well as on other physical parameters of interests like local skin-friction coefficient (Cf), Nusselt number (Nu) and Sherwood number (Sh).