Natural Convection Near a Cold Plate Facing Upward in a Porous Medium

It is shown that the phenomenon of natural convection driven in a porous medium by a cold plate facing upward or by a warm plate facing downward consists of a finite-length boundary layer flow chopped off by the sharp edges of the plate. The heat and fluid flow features of the boundary layer are determined analytically employing scale analysis and integral analysis. The overall heat transfer rate between porous medium and plate is found to vary as Nu/Ra1/3 = 0(1), where Ra is the Darcy-modified Rayleigh number based on plate half-length. The boundary layer features of the flow and the heat transfer effected by it are confirmed in the Ra range 100–700 by numerical solutions of the complete partial differential equations.