Porous convection with Cattaneo heat flux

We study the problem of thermal convection in a horizontal layer of Darcy porous material saturated with an incompressible Newtonian fluid, with gravity acting downward. The constitutive equation for the heat flux is taken to be one of Cattaneo type. Care must be taken with the choice of objective derivative for the rate of change of the heat flux. Here we employ a recent model due to Professor C. Christov as well as one suggested many years ago by Professor N. Fox. The thermal relaxation effect in both classes of heat flux law is found to be significant if the Cattaneo number is sufficiently large, and the convection mechanism switches from stationary convection to oscillatory convection with narrower cells. The transition point is calculated and the convection thresholds are derived analytically.