Dynamics of Viscous Jeffrey Fluid Flow Through Darcian Medium With Hall Current and Quadratic Buoyancy.

This contribution builds on existing studies by investigating the dynamics of Hall current in Jeffery fluid under radiative heat, convective boundary conditions, Joule heating, and Darcy dissipation. Hall current, an important phenomenon in engineering applications involving strong magnetic fields, highlights the impact of electromagnetic force in examining blood flow rate, determining charge drift velocity, density, and movement, and is used in power generators and high-voltage transformers. This analysis incorporates dissipative and thermal radiative heat and employs the effects of Hall current and Joule heating, resulting from porous medium resistance, to derive the partial differential equations governing the dynamic systems. These equations are then reduced to ordinary differential equations (ODEs) through similarity variables. The Galerkin weighted residual method (GWRM) is employed to examine the dynamics of Hall current and quadratic thermal buoyancy, shedding light on the thermal properties and hydrodynamics of Jeffrey fluid convection within a porous medium. The analysis reveals that in the presence of an applied magnetic field, the contribution of Hall current to flow and heat dynamics induces a magnetic force that enhances fluid motion and negatively impacts heat energy patterns. The imposition of dissipative heat physically increases the fluid temperature, owing to an increase in buoyancy current. The occurrence of thermal radiation, Hall current, viscous dissipation, and Joule heating can efficiently optimize the rate of heat transfer and shear stress. Moreover, the tabular results indicate that Jeffrey fluid, exhibiting higher relaxation time, will experience a lower friction coefficient and heat transfer rate.