The Onset of Darcy–Brinkman Convection in a Porous Layer with Mutual Impact of Thermal Non-Equilibrium and Non-Uniform Temperature Gradients

Abstract

The two-field thermal conditions of local thermal nonequilibrium (LTNE) were used to investigate linear stability of thermal convection in a liquid-saturated, porous layer via the extended Brinkman–Darcy model for different non-uniform basic thermal gradients. The critical values were numerically computed by the Galerkin method for rigid isothermal boundaries. The impact of LTNE and different forms of non-uniform basic temperature gradients on the onset of porous convection was examined. The porosity modified conductivity ratio has no influence on system stability at a small inter-phase heat transport coefficient limit. However, for higher values of the inter-phase heat transport coefficient, an increase in the porosity modified conductivity ratio hastens the onset of convection. An increase in the Darcy number delays the convective motions. The results for different basic temperature profiles are symmetric qualitatively. In addition, the possibility of control of convection by a basic temperature profile was studied in detail.