We obtain the linear instability and nonlinear stability thresholds for a prob-\ud lem of thermal convection in a bidispersive porous medium with a single\ud temperature. It is important to note that we show that the linear instability\ud threshold is the same as the nonlinear stability one. This means that the\ud linear theory is capturing completely the physics of the onset of thermal con-\ud vection. This result contrasts with the general theory of thermal convection\ud in a bidispersive porous material where the temperatures in the macropores\ud and micropores are allowed be different. In that case the coincidence of the\ud stability boundaries has not been proved

We derive linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature when Darcy theory is employed in the micropores whereas Brinkman theory is utilized in the macropores. It is important to note that we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. The coincidence of the linear and nonlinear stability boundaries is established under general thermal boundary conditions.