Effects of non-Darcian and nonuniform porosity on vertical-plate natural convection in porous media

TLDR: In this paper, the effects of non-Darcian and non-uniform permeability conditions on the natural convection for a vertical plate in porous media were examined analytically.

Abstract: This work examines analytically the effects of non-Darcian and nonuniform permeability conditions on the natural convection for a vertical plate in porous media. The non-Darcian effects, which include the no-slip and inertia effects, decrease the flow and heat transfer rate, while the nonhomogeneity effect enhances the heat transfer. For packed spheres, in particular, the nonhomogeneity in permeability due to the packing of spheres near the solid wall results in a strong flow-channeling effect that significantly increases the heat transfer. The effect of transverse thermal dispersion is also examined. This dispersion effect causes an increase in the heat transfer.