Global stability for double-diffusive convection in a couple-stress fluid saturating a porous medium

We show that the global non-linear stability threshold for convection in a double-diffusive couplestress fluid 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 effects of couple-stress parameter (F ) , solute gradient (S f ) and Brinkman number (Da ) on the onset of convection is also analyzed.