On a closed-form solution of natural convection in a cavity partially filled with a porous medium

This study deals with the steady flow structure and temperature field in a rectangular cavity including a layer of porous medium adjacent to the heated side, with uniform heat flux from the sides. The Navier-Stokes and energy equations in the Boussinesq approximation are written with an extra term accounting for the Darcy effect within the porous medium. After correct scaling and numerical integration, we derive a closed-form analytical solution in the case of an infinite vertical slot, which is then compared to the numerical results. (C) Academie des sciences/Elsevier Paris.