Stability of a porous Benard-Brinkman layer in local thermal non-equilibrium with Cattaneo effects in solid

The stability of a porous Benard layer of Brinkman fluid under local thermal non-equilibrium conditions and obeying the Cattaneo flux law in the solid is studied. The preference for stationary and overstable linear motions is examined in the whole parameter space of the problem. It is shown that overstability occupies a region within a branch of a rectangular hyperbola-like curve in the first quadrant of the (τH) plane, where τ,H are the Straughan and thermal inter-phase interaction parameters, respectively, so that overstability persists even when H→∞. The Brinkman effect tends to stabilize the layer but enhances the region of preference of overstability in the parameter space. The influence of the other parameters on the critical mode is also identified. The nonlinear development of the amplitude A of the linear wave motions of both stationary and overstable modes is found to be governed by a first order evolution equation. The analysis of the evolution equation shows that the layer can exhibit supercritical instability for both stationary and overstable modes and subcritical instability and stability for the stationary mode depending on the relative magnitudes of the parameters of the problem. The Brinkman effect is found to reduce the amplitude of the supercritical instability while the porosity modified ratio of thermal conductivities and the ratio of thermal diffusivities tend to promote subcritical instabilities. The implication of these results on the nonlinear global stability of the model is discussed.