Coupled Effect of Solid Fraction and Internal Energy Source on Convective Heat Transport in Three-Layered Air-Porous-Air Domain: Comparison With Different Two-Layered Domains

Abstract

This paper studies convective heat transport driven by a uniform internal energy source coupled with the solid fraction in the partial air-saturated porous domains bounded by the top and bottom impermeable thermally conductive surfaces. The consideration of the coupled effect distinguishes our work from the papers of previous authors. We provide a comprehensive numerical study of internal convection and compare results of the linear stability analysis for three distinct domains. The first domain is air-porous-air (APA), where the heat-generating porous matrix is between the upper and lower air layers. In the second air-porous (AP) domain, the air layer overlays the porous medium. In the third porous-air (PA) domain, the air layer underlays the porous medium. The bimodal marginal stability curves and regime map with a demarcation line between the local and large-scale convective flows are obtained only for the APA and AP domains due to the division of each domain into the upper unstably stratified and lower stably stratified parts. The local convection cannot originate in the PA domain because the air layer belongs to the lower stably stratified part. A remarkable destabilizing effect of additional air layers has been revealed. For example, at the fixed solid fraction of 0.1, we achieve a 40-fold reduction of the critical Darcy-Rayleigh number in the APA domain by increasing the depth ratio from 0 to 0.5, and by 14 times in the AP domain and only by 3.5 times in the PA domain. The destabilizing effect enhances with increases in the solid fraction.