Global stability for thermal convection in a couple-stress fluid

We show that the global nonlinear stability threshold for convection in a couple-stress fluid is exactly the same as the linear instability boundary. This 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 the couple-stress fluid is thermally more stable than the ordinary viscous fluid and then the effect of couple stress parameter on the onset of convection is also analyzed.