Stability analysis of a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model

A nonlinear stability threshold for convection in a couple stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple stress fluid parameter (F), temperature and pressure dependent viscosity (Γ), interface heat transfer coefficient (H), Darcy-Brinkman number (D˜a) and porosity modified conductivity ratio (γ) on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient (H) is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.