Thermal Instability of Ferromagnetic Couple Stress Micropolar Fluid with Rotation and Hall Current in Porous Medium

The study investigates the thermal instability phenomena in a ferromagnetic couple stress micropolar fluid within a porous medium, incorporating the effects of rotation and Hall current. The governing equations are derived using the normal mode method to analyze the stability conditions influenced by couple stress forces, micropolarity, magnetic fields, Hall current, and porous media properties. Analytical calculations, numerical simulations, and graphical representations are used to illustrate the results. Thermal instability is a crucial factor in various engineering and natural processes, including geothermal systems and lubrication mechanisms. The microstructural and rotational effects of micropolar fluids introduce unique behaviors that differ from classical Newtonian fluids. Additionally, the inclusion of ferromagnetic properties expands the scope of research applications in bio-fluid mechanics, industrial processing, and nuclear reactor technology. The presence of rotation and Hall currents further contributes to the complexity of magnetohydrodynamic (MHD) flows, which are essential in geophysical and astrophysical studies. This study aims to examine the combined effects of these factors on the onset of convection patterns in porous domains using mathematical modeling and stability analysis. The findings contribute to a deeper understanding of fluid motion and magnetic interactions in complex systems.