Asian Journal of Pure and Applied Mathematics

This study examines the combined effects of Hall current and Soret diffusion on the unsteady natural-convection magnetohydrodynamic (MHD) flow of a viscous, incompressible, electrically conducting Jeffrey fluid through a porous medium in the presence of thermal radiation and chemical reaction. The governing nonlinear equations for momentum, energy, and species transport are transformed into a dimensionless system and solved numerically using a sixth-order Runge–Kutta method coupled with a shooting technique. The resulting velocity, temperature, and concentration profiles are analysed graphically for different parameter values. The numerical simulations are implemented in Maple. The principal novelty of the study lies in the simultaneous consideration of Hall current and thermo-diffusive Soret effects in unsteady Jeffrey-fluid flow through a porous medium under radiative and chemically reactive conditions, thereby providing a more comprehensive description of coupled momentum, heat, and mass transport. The analysis reveals that increasing the Hall parameter enhances the velocity profiles, whereas the opposite trend is observed with increases in the viscosity ratio and chemical reaction parameter. Thermal radiation elevates the temperature profiles, whereas increasing the frequency of oscillations suppresses them. Furthermore, concentration decreases with increasing Schmidt number but increases with an increase in the chemical reaction parameter. These results have significant practical implications for solar-physics applications, including solar-cycle dynamics and sunspot development, as well as for the design of MHD sensors and rotating MHD induction energy generators. The study provides valuable insights into optimising heat and mass transfer in porous-media systems where electromagnetic and thermo-diffusive effects are dominant.