Radiation influence on transient MHD convection over a permeable surface with thermal diffusion

We investigate the impact of radiation on a transient magnetohydrodynamic (MHD) natural convective flow past an upright permeable surface, considering the thermal diffusion. The fundamental equations, a coupled system of nonlinear partial differential equations, defy analytical solutions. Consequently, a numerical solution employing the Galerkin finite-element method was implemented. We explore the flow behavior under varying conditions, encompassing the thermal diffusion, Schmidt number, Grashof number, magnetic field strength, Prandtl number, heat source parameter, and radiative parameter. Results are presented graphically, illustrating the variations in velocity, temperature, and density profiles. Furthermore, the analysis quantifies the effects on the coefficient of skin friction and the Nusselt number. This comprehensive numerical approach provides valuable insights into the complex interplay of these parameters within the specified MHD free convective flow regime.