Global Stability of a Couple-Stress Fluid in a Porous Medium Using a Thermal Non-Equilibrium Model

We show that the global nonlinear stability threshold for convection in a couple stress fluid with a thermal nonequilibrium model 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 more stable than the ordinary viscous fluid and then the effects of couple stress parameter, interface heat transfer coefficient, Darcy-Brinkman number and porosity modified conductivity ratio on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.