Thermal convection in a three-layered air-heat-generating porous-air system with internal heat source depending on solid volume fraction

Abstract

<p>We explore the convective instability in a vertically three-layered system that consists of a heat-generating porous sublayer sandwiched between two air sublayers in the gravitational field. The heat source strength in the porous sublayer depends on solid volume fraction linearly. This fundamental study is motivated by the analysis of natural convective air ventilation in the storage aria of agricultural raw materials. The materials make up a porous matrix generating heat due to its biological activity. The heat release strength is proportional to the density of their bulk. To maintain an optimal thermal regime in the storage aria, one should remove heat from the overheated parts of materials timely. The passive convective flow can be controlled by the additional air sublayers with the required depth. In our research we focus on the solid volume fraction and depth ratio effects on the convection onset and scale of convective flows.</p><p>The three-layered system under consideration is bounded by the impermeable thermally conductive plates with equal constant temperatures. So, flows can arise because of heat release that induces non-uniform thermal profile across the sublayers. We apply a linear stability theory to find the threshold internal Rayleigh-Darcy number for the onset of convection. This similarity criterion is defined through heat source strength in the porous sublayer. The numerical simulation is performed by the shooting method.</p><p>It has been shown that marginal stability curves in the three-layered system as well as those in the two-layered system have two minima, i.e. they are bimodal. Either a large-scale convective flow or a local one may generate immediately after the motionless air state has lost its stability. The former penetrates into the porous medium while the latter forms within the upper air sublayer only, where temperature gradient is destabilizing. It has been found that the onset value of both types of flows reduces with increasing a relative depth of the air sublayer. This reduction is accompanied by a transition from the large-scale to local convection. The observed enhancement of convection turns out to be more effective in the three-layered system as compared to that of the system made up of two sublayers. The solid volume fraction demonstrates a similar effect on the convection onset and wavelength of the convective flows induced. Despite the compaction of porous medium due to the growth of solid volume fraction, the onset value decreases and the motionless air state destabilizes. It can be explained by the fact that heat release strengths with increasing solid volume fraction.</p><p>The work was supported by the Russian Science Foundation (Grant No. 21-71-10045), https://rscf.ru/en/project/21-71-10045/.</p>