GLOBAL STABILITY FOR THERMAL CONVECTION IN A COUPLE STRESS FLUID: RIGID BOUNDARIES

We show that the global nonlinear stability threshold for convection in a couple-stress fluid (and for a rotating couple-stress fluid) is exactly the same as the linear instability boundary. This optimal result is important, because it shows that the linearized instability theory has captured completely the physics of the onset of convection. The eigenvalue problems for the rigid rigid (RR) conducting boundaries are solved by the single-term Galerkin method. The effect of the couple-stress parameter F and rotation parameter TA on the onset of convection is also analyzed.