Thermal convective instability of viscoelastic fluids in a rotating porous layer heated from below

Abstract

Abstract Linear and weakly nonlinear stability analyses of thermal convection in a viscoelastic fluid-saturated rotating porous layer heated from below are studied. The influence of rotation is considered by extending the modified Darcy–Maxwell–Jeffrey model to include the Coriolis force term. The linear analysis results show that if the Taylor number is greater than a certain critical value, the overstable mode disappears and only the stationary convection can set in. This result is different from the case for a Newtonian fluid in a rotating porous medium or for a pure viscoelastic fluid subject to rotation. Finite amplitude solutions of temperature and velocity perturbations are obtained by using a weakly nonlinear analysis. Both the amplitude equations of stationary and overstable convection are shown to be of Laudau type and the bifurcations from the basic states are supercritical. Furthermore, the Nusselt number variations under supercritical conditions are determined for stationary and overstable convection. It is found that rotation reduces the heat transfer capacity for both stationary and overstable convection modes.