Global Stability for Thermal Convection in a Couple Stress Fluid Saturating a Porous Medium with Temperature-pressure Dependent Viscosity: Galerkin Method

A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conductingboundary systems. Here, the global nonlinear stability threshold for convection is exactly the same asthe 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 eigenvalueproblems for different conducting boundary systems are solved by using Galerkin method. The effectsof couple-stress parameter F , Darcy-Brinkman number D% a and variable viscosity parameter Gon the onset of convection are also analyzed. The use of Darcy-Brinkman model makes the system thermally more stable than the Darcy model for all the different conducting boundary systems, couple-stressparameter and medium permeability promotes stabilization, and the variable viscosity destabilizes the system.

Keywords:

Couple-stress Fluid , Porous Medium , Global Stability , Temperature-pressure Dependent Viscosity , Different Conducting Boundaries (Free-free , Rigid-free , Rigid-rigid)