Cattaneo-Ltne Effects on the Stability of Brinkman Convection in an Anisotropic Porous Layer

Abstract

The stability of Brinkman local thermal nonequilibrium anisotropic porous convection under the impact of Cattaneo law of heat conduction in solid is investigated. In the analysis, anisotropies in permeability and thermal (solid and fluid phases) conductivities are highlighted. Condition for stationary onset and oscillatory onset is obtained by carrying out linear instability analysis. A novel result is that the instability occurs through oscillatory mode against the stationary convection perceived in the absence of Cattaneo effect. The relative magnitudes of governing parameters on the initiation of oscillatory instability are delineated in detail. The thermal and mechanical anisotropies inflict stabilizing and destabilizing effects on the onset, respectively. The influence of mechanical anisotropy, thermal anisotropy of fluid, thermal relaxation time parameters and the Darcy number is to broaden the size of convection cells whereas thermal anisotropy of the solid and the Darcy-Prandtl number demonstrate a mixed behaviour. A first order amplitude equation is derived separately for steady and overstable modes by performing a weak nonlinear stability analysis using a modified multiscale method. Depending on the values of governing parameters, it is seen that the stationary mode bifurcates subcritically and supercritically, while the oscillatory mode always bifurcates supercritically