Impact of couple stress fluid on thermal convection in a rotating porous medium

This study aims to investigates the impact of couple stress fluid on thermal convection in a rotating horizontal porous medium heated from below. A combination of linear stability and weakly nonlinear stability analyses is employed to explore how the couple stress parameter, rotation, and porosity affect the onset of convection and subsequent heat transfer behavior. In the linear regime, the critical Rayleigh number is computed to delineate stability thresholds under various physical conditions, with higher values indicating greater resistance to convective onset. The weakly nonlinear analysis, based on a truncated Fourier series expansion and amplitude equation formulation, captures the nonlinear evolution of convection beyond the threshold, providing an expression for the Nusselt number that quantifies convective heat transport. The results reveal that couple stress effects enhance the system stability by increasing the critical Rayleigh number, thereby delaying convection. Rotation introduces an additional stabilizing influence. However, the nonlinear analysis uncovers that once convection initiates, heat transport increases nonlinearly with both the couple stress and rotation parameters. This nonlinear amplification of heat transfer underscores the importance of post-critical behavior in practical applications. These insights are relevant for optimizing thermal regulation in engineering systems and understanding geophysical flows in porous medium.