Nonlinear thermal convection in a rotating porous medium with couple stress fluid under internal heat modulation

This study investigates nonlinear thermal convection in a rotating porous medium saturated with a couple stress fluid, considering the effects of internal heat modulation. The study of convection in rotating porous medium containing complex fluids is essential for understanding large-scale phenomena, including Earth's mantle dynamics and the development of advanced aerospace and energy cooling technologies. The research employs a two-pronged approach: a linear stability analysis to pinpoint when convection begins, and a weakly nonlinear analysis to explore how convection evolves and transfers heat. The governing equations incorporate the Darcy-Brinkman model for the porous medium and couple stress theory for the fluid, accounting for nonlinear effects. A linear stability analysis using the normal mode approach determines the critical Rayleigh number at the onset of stationary convection. A weakly nonlinear analysis, performed via the truncated Fourier series method, derives the Ginzburg-Landau equation to assess heat transport characteristics. The results indicate that internal heat modulation significantly influences stability and heat transfer, with an increase in the couple stress parameter (9.9%) reducing the Nusselt number (1.6%), leading to a more stable system. Specifically, we find that (1) the critical Rayleigh number increases with higher couple stress parameters, demonstrating enhanced system stability, and (2) the couple stress parameter reduces heat transfer efficiency, as evidenced by a decrease in the Nusselt number. This study advances previous research by incorporating nonlinear effects and internal heat modulation, providing deeper insights into convection control mechanisms in a rotating porous medium.