A thermal non-equilibrium model with Cattaneo effect for convection in a Brinkman porous layer

Abstract

This paper aims to investigate the onset of thermal convection in a layer of fluid-saturated Brinkman porous medium taking into account fluid inertia and local thermal non-equilibrium (LTNE) between the solid and fluid phases with Cattaneo effect in the solid. A two-field model is used for the energy equations each representing the solid and fluid phases separately. The usual Fourier heat-transfer law is retained in the fluid phase while the solid phase is allowed to transfer heat via a Cattaneo heat flux theory. It is observed that the Cattaneo effect has a profound influence on the nature of convective instability. In contrast to the standard Brinkman convection with LTNE model, instability is found to occur through oscillatory convection depending on the value of solid thermal relaxation time parameter which in turn depends on other parametric values. The instability characteristics of the system are analyzed in detail for a wide range of parametric values including those for copper oxide and aluminium oxide solid skeletons.