Onset of convection in fluid layers with nonuniform volumetric energy sources

The thermal stability of a fluid layer with nonuniform distribution of the volumetric energy sources is studied. The conditions leading to the onset of convective motions in the fluid are determined analytically by linear stability theory. The system considered consists of a fluid layer of infinite horizontal extent which is confined between two rigid parallel boundaries and subjected to general convective boundary conditions. The fluid is heated internally by way of absorption of the external radiation penetrating in the fluid body. The effects of the stabilizing and destabilizing temperature differences at the boundaries and the properties of the bounding surfaces are investigated. Optically thicker layers are found to be more stable