Effects of Buoyant force, Hall current, and thermal diffusion on an unsteady MHD free convection flow of non Newtonian fluid with semi infinite vertical porous plate

This study investigates the effects of Hall current and thermal diffusion on the unsteady magnetohydrodynamic (MHD) free convective flow of an incompressible, electrically conducting Casson fluid past a vertical porous plate. The analysis incorporates Joule heating and viscous dissipation to understand the coupled thermal and flow dynamics in such systems. The governing non-dimensional equations are solved using the perturbation technique, providing analytical solutions for the velocity, temperature, and concentration profiles within the boundary layer. Graphical representations of these profiles are presented, highlighting the influence of various non-dimensional parameters on the fluid dynamics. The effects of primary parameters, such as Hall current, thermal diffusion, and others, on the velocity and concentration fields are explored. Furthermore, the skin friction factor, Nusselt number, and Sherwood number are computed and tabulated, providing a detailed analysis of the heat and mass transfer characteristics. The results reveal that an increase in the Hall current parameter enhances the primary velocity while reducing the secondary velocity. Additionally, the thermal diffusion parameter increases species concentration, while the Schmidt number reduces it due to lower mass diffusivity. These findings have practical applications in industrial processes involving magnetohydrodynamic systems, such as cooling systems for rotating machinery, and in geophysical fluid dynamics for analyzing flows in porous media under thermal and magnetic influences.