Global stability of natural convection in internally heated inclined fluid layer

Energy stability theory is applied to the study of the nonlinear stability of natural convection in an inclined fluid layer having a uniform internal heat source (sink), with the boundaries of the layer maintained at constant temperatures. The stability limit is found in terms of the thermal Rayleigh number R-1 and the internal Rayleigh number R-2. The region of stability is found in R-1-R-2 plane where the base state is stable against arbitrary perturbations. The Prandtl number Pr of the fluid and the angle of inclination of the fluid layer play an important role in determining the stability region.