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

The paper studies convective heat and mass transport driven by a uniform internal energy source coupled with the solid fraction in different partial air-saturated porous domains. Each domain is bounded by the top and bottom impermeable thermally conductive surfaces. The linear stability analysis is performed and the disturbance equations are derived and numerically solved. The critical internal Darcy-Rayleigh number and wave number are found and compared for three distinct domains. The first domain is an air-porous-air one, where the heat-generating porous matrix is between the upper and lower air layers. In the second air-porous domain, the air layer overlays the porous medium. In the third porous-air 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, one achieves a 40-fold reduction of the critical Darcy-Rayleigh number in the APA domain by increasing the depth ratio from 0 to 0.5. It is by 14 times in the AP domain and is only by 3.5 times in the PA domain. The destabilizing effect enhances with increasing the solid fraction.