Thermal Stability of a Vertical Fluid Layer With Volumetric Energy Source

Abstract

The effects of nonuniform volumetric energy sources on the thermal stability of natural convection in a vertical fluid layer are investigated using the linear theory of stability. The neutral states of stability are obtained for four values of Prandtl number, ranging from 0.71 to 100, and for different values of β in the range 0.1 ≤ β ≤ 10. The critical parameters and the energetics of the critical disturbances are determined for each case. For all values of Prandtl number and β studied here, the critical instabilities set in as traveling waves, moving in the direction of gravity. In the low range of Prandtl number, 0.71 to 5, the critical curves approach the same asymptotic value for β ≥ 10. The critical disturbances are found to be buoyancy driven for all Prandtl numbers and β considered here, except for the low range of Prandtl number, for which they become shear driven disturbances as β increases.