Hall current and thermal diffusion effects on an unsteady MHD free convection flow of non-Newtonian fluid

We investigate the effects of Joule combustion, Hall current, and thermal dispersion on an unstable MHD free convection heat and mass transfer revolving flow of a dense, indestructible, and electrically conducting second-grade fluid that is passing through an exponential plate embedded in a porous medium. This flow was realized in the context of a heat source and viscous dissipation. By the perturbation approach, it is possible to obtain an accurate analytic solution of the governing equations for the fluid velocity, fluid temperature, and species concentration. This solution is obtained while taking the proper initial and boundary conditions into consideration. With the assistance of the MATLAB program, graphical representations are provided for the numerical values of the main and secondary fluid velocities, the temperature of the fluid, and the concentration of the species. The shear stresses, the Nusselt number, and the Sherwood number are calculated analytically, rendered computationally in a tabular style, and discussed with regard to the most important factors with the purpose of satisfying engineering curiosity. 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 the 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.