Natural Convection in a Stably Heated Corner Filled With Porous Medium

Abstract

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.