Passive convective ventilation in a double air-porous layer with internal heat generation depending on solid fraction

The convective stability of a two-layered system consisting of a heat-generating porous region underlying an air region has been numerically studied. The linear dependence of the heat release on the solid volume fraction is taken into account in the porous region. The equal constant temperature values are fixed on the external impermeable boundaries of the system. The critical internal Rayleigh-Darcy number at which the convection is induced in the system in the form of two-dimensional roll patterns with a given wave number has been determined. The convective flow is possible due to the formation of unstable density stratification in the presence of internal heat release.
Two types of stationary convection, namely, the local and the large-scale convection, have been studied. The local flow arises in the air sublayer and scarcely penetrates into the porous sublayer. The large-scale convection covers both sublayers. The change in the convective regime occurs with the growth of one or another parameter of the system and indicates the variation of the instability type. It is accompanied by an abrupt (by times and tens of times) change in the critical wave number of roll patterns.
Numerical calculations show a decrease in the onset value for both types of convection with increasing solid volume fraction $\phi$ in the porous sublayer and increasing relative thickness d of the air sublayer. The growth of the Darcy number (the dimensionless permeability of the porous sublayer) also causes destabilization of the air motionless state at the given $\phi$ and $d$. The variation of the convection regime from a large-scale flow to a local one occurs with increasing relative thickness of the air sublayer, whereas an opposite transition from the local to the large-scale convection regime is observed with increasing Darcy number.