Thermally driven shallow cavity flows in porous media: the merged-layer régime

Abstract

An analysis is given of convective motions generated in a shallow rectangular cavity by an applied horizontal temperature gradient; the cavity is filled with a fluid-saturated porous medium. For large Rayleigh numbers R, and for large aspect ratios L, a distinguished limit arises when R = O(L2). In this limit the boundary layers on the horizontal walls merge and completely fill the cavity. The régime is characterized by a non-parallel core flow that provides the dominant structure over a surprisingly wide range of the parameter R/L 2. New results for the merged layer core are compared with the parallel flow convection-dominated boundary layer limit R/L2 → ∞, and with the parallel flow diffusion-dominated limit R/L2 → 0. Heat transfer calculations, which define the dependence of the Nusselt number on R/L2, have also been carried out.