Thermal convection in double porosity media

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores due to cracks or fissures in the solid skeleton. The linear instability and nonlinear stability thresholds for a problem of thermal convection in bidispersive porous media with a single temperature are obtained and we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is able to capture completely the physics of the onset of thermal convection.