Global stability for thermal convection in a rotating couple-stress fluid saturating a porous medium

We show that the global nonlinear stability threshold for rotating in a couple-stress fluid heated from below saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid and the effect of couple-stress parameter, medium permeability, rotation, and Darcy number on the onset of convection is also analyzed.