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A nonlinear stability threshold for convection in a rotating 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 , Taylor number  T A  , Darcy–Brinkman numberD  ˜   a    $\tilde{D}a$   , 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.

journal of non-equilibrium thermodynamics

Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous media with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model