A study of buoyancy-driven flow in a confined fluid overlying a porous layer

Two different models to analyze the natural convection in a confined fluid overlying a porous media were compared. The first approach used the Navier–Stokes equation and Darcyʹs law coupled by Beavers and Joseph (B–J) interfacial boundary condition. Instead, the second approach considered the Brinkman extended Darcyʹs law together with the continuity of stress and velocity in the fluid/porous medium dividing surface. The numerical predictions were mainly used to analyze the effects of the Rayleigh and Darcy numbers on the local and average Nusselt numbers of the cold and hot walls. Significant differences between the overall average Nusselt numbers were found when the Rayleigh and Darcy numbers were large enough.