We show that the global nonlinear stability threshold for convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity 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. Then the effect of couple stress parameter, variable dependent viscosity and Darcy-Brinkman number on the onset of convection are also analyzed.
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