Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid

Abstract

The Bénard problem for a thermomicropolar fluid is investigated. Attention is focussed on the possibility of oscillatory convection and on nonlinear energy stability. For a certain sign of the thermal interaction coefficient (compatible with the Clausius-Duhem inequality) we are able to fully analyse the problem. A striking feature is that stationary convection is seen to be likely to be the physically realizable mode whereas oscillatory convection is likely to occur only at very high Rayleigh numbers and then only when the layer is heated from above.