The Effect of Temperature and Pressure Dependent Viscosity on Thermal Convection in a Rotating Couple-Stress Fluid Saturating a Porous Medium: A Nonlinear Stability Analysis

A conditional nonlinear stability threshold for rotating in a couple-stress fluid heated from below saturating a porous media with temperature and pressure dependent viscosity 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. Then the effect of couple stress parameter , variable dependent viscosity , medium permeability , Taylor number and Darcy- Brinkman number on the onset of convection are also analyzed.