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

Abstract

Couple-stress Fluid Porous Medium Global Stability Temperature-pressure Dependent Viscosity Different Conducting Boundaries (Free-free, Rigid-free, Rigi d-rigid) AB S T R ACT A g lobal nonlinear stability analysis is performed for a cou ple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is imp ortant 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 Da and variable viscosity parameter Γ on 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-stress parameter and medium permeability promotes stabilization, and the variable viscosity destabilizes the system.