Thermal convection with the Cattaneo–Christov model

We consider the problem of thermal convection in a horizontal layer of incompressible Newtonian fluid with gravity acting downward. The constitutive equation for the heat flux is taken to be one of Cattaneo type. Since we are considering a fluid one has to be careful 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. The thermal relaxation effect 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.