Stability analysis in a couple-stress fluid layer with variable viscosity heated from below: Different conducting boundaries

Abstract

The Linear stability analysis technique and non-linear stability analysis technique are applied for couple stress fluid layer with having variable viscosity depending on temperature and pressure. The linear and nonlinear threshold that encapsulates the physics of the onset for convection is found to be same. Eigenvalue problems for free-free (FF), rigid-free (RF) and rigid-rigid (RR) conducting boundaries are solved with the help of a single term Galerkin technique. The couple stress is seen to have a stabilizing impact while the viscosity variation has destabilizing impact on the system.