Effect of Imperfectly Conducting Boundaries on the Onset of Convective Instability in a Porous Medium with Throughflow

Understanding the onset of convection in porous media is crucial for a range of thermal engineering and geophysical applications. In this study, I explore how imperfectly conducting boundaries affect the stability of a horizontal fluid-saturated porous layer under uniform flow conditions. Unlike classical studies with idealized boundary assumptions, this work incorporates wall heat transfer characteristics to provide a more realistic stability analysis. A normal-mode approach is used to determine critical Rayleigh numbers, with a parametric investigation of heat transfer coefficient, Throughflow, and permeability. The results show that increasing wall conductivity tends to destabilize the system, while throughflow exhibits a dual stabilizing-destabilizing role depending on its strength. Viscous dissipation delays the onset of instability, particularly under strong thermal resistance at the boundaries. These insights highlight the significant role of boundary conditions in convective processes through porous media and offer guidance for thermal management in porous-layer applications.