Thermal Stability of Micropolar Fluid Layer in the Presence of Horizontal Magnetic Field Under Variable Gravity

This research paper explores the thermal stability of a thin layer of non-conducting, incompressible micropolar fluid, which is heated from below and subjected to a uniform horizontal magnetic field under a varying gravity field. The study derives a dispersion relation for a flat fluid layer situated between two free boundaries, employing a linear stability analysis theory and a normal mode analysis method. The investigation examines the impact of different factors, including the magnetic field, coupling parameter, micropolar heat conduction parameter, and micropolar coefficient, on the onset of stationary convection under variable gravity. The results are presented in graphical form, validating the Principle of Exchange of Stability (PES). Additionally, the study establishes sufficient conditions for the non-existence of overstability. This research contributes to the understanding of thermal stability in micropolar fluids under varying gravity and magnetic fields, offering valuable insights for future studies in this area.