Energy Stability Analysis of Thermal Convection in an Inclined Fluid Layer with a Temperature-Dependent Internal Heat Source

Abstract A nonlinear stability analysis of thermal convection in an inclined fluid layer with a temperature-dependent internal heat source is performed using the energy method. The effects of the angle of inclination of the fluid layer, the internal heat source parameters, and the Prandtl number on the critical thermal Rayleigh number are investigated. The region in parameter space for which the basic state remains stable to arbitrary perturbations is identified. Comparison of the nonlinear stability boundary with the corresponding linear instability boundary reveals an uncertain stability region, which depends on the angle of inclination of the fluid layer and the internal heat source parameters.