Publication

Abstract : Quantifying heat transfer in nonlinear convection remains a fundamental challenge. This study investigates the combined effects of throughflow and quadratic drag on thermal convection in a rotating porous medium subjected to gravity modulation, using both linear and weakly nonlinear stability analyses. The flow within the porous medium is described by the Forchheimer-extended Darcy model, and the governing equations are formulated under Boussinesq approximation. A normal mode analysis is applied to derive the linear stability equations, while the Galerkin weighted residual method is employed to determine the critical Rayleigh number for the onset of convection. Near the instability threshold, a weakly nonlinear analysis yields a Ginzburg-Landau amplitude equation, which is used to explore the nature of bifurcation and heat transfer characteristics. Contour plots of streamlines, isotherms, and vorticity fields demonstrate the deformation of convection cells induced by throughflow. The results reveal that the Taylor number, throughflow, and quadratic drag parameter have a stabilizing influence by delaying the onset of convection, whereas an increase in the Darcy-Prandtl number enhances heat transfer and promotes instability. The findings advance an understanding of heat transfer mechanisms relevant to geothermal energy, rotating filtration, and porous thermal management systems.