Thermal Instability of a Micropolar Fluid Layer with Temperature-Dependent Viscosity

In this paper, the effect of temperature-dependent viscosity on the onset of thermal convection in a micropolar fluid layer heated from below for each combination of rigid (the surfaces with non-slip condition) and dynamically free (the surfaces with stress-free condition) boundaries is investigated. It is shown here analytically that the principle of exchange of stabilities is valid for the problem, which means that instability sets in as stationary convection. The expressions for Rayleigh numbers for each combination of rigid and dynamically free boundary conditions are derived using Galerkin method. The effects of micropolar parameters and viscosity variation parameter on critical wave numbers and consequently on the critical Rayleigh numbers are computed numerically.