Stability Analysis in a Rotating Couple-Stress Fluid Heated from Below Saturating a Porous Medium with Temperature-Pressure Dependent Viscosity

Stability analysis is performed for a rotating couple-stress fluid heated from below saturating a porous medium with temperaturepressure dependent viscosity for free-free, rigid-free and rigid-rigid conducting boundary systems. Here, the non-linear stability threshold for convection 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. The eigenvalue problems for different conducting boundary systems are solved by using Galerkin method. The effects of couple-stress parameter F, Darcy- Brinkman number ˜D a , variable dependent viscosity T and Taylor number T_A on the onset of convection are also analyzed. Couple- stresses, rotations and medium permeability promote stabilization whereas the variable viscosity destabilizes the system.