Natural Convection in Horizontal Fluid-Superposed Porous Layers Heated Locally From Below

Abstract

This paper reports numerical studies of steady two-dimensional natural convection in fluid-superposed porous layers heated locally from below. The numerical simulation is based on the Darcy-Brinkman-Forchheimer model for the porous layer and focuses on the parametric domain in which the flow is well established, i.e., the overall Rayleigh number is several orders of magnitude larger than the critical value. An emphasis is placed on revealing the effects of two dimensionless parameters on the overall Nusselt number: the porous layer-to-cavity height ratio (η = Hm/H) and the heater-to-cavity base length ratio (δ = LH/L). Calculations cover η = 0.25, 0.5, 0.75, δ = 0.25, 0.5, 1, and overall Rayleigh numbers from 103 to 106. For a fixed height ratio, overall Nusselt numbers increase with a decrease in the heater length. For a given heater length ratio, overall Nusselt number increases with an increase in the height of the overlying fluid layer. Recirculating flow is confined primarily to the overlying fluid layer with some penetration into the upper part of the porous layer. The present results represent an extension of the well studied problem of buoyant convection in superposed layers with a fully heated lower surface.