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.

Thermal stability of a nonuniformly heat generating annular fluid layer

“…[17] where the basic state of convection in a porous annular region was induced by uniformly distributed heat sources. Shaaban and Ozisik [11] obtained a similar jump for negative values of a. The abrupt change in the most dangerous mode at Pr = 10 is shown in Fig.…”

“…Yucel Ozisik [11] and Kolyshkin and Vaillancourt [12] have applied linear theory stability criteria and studied thermal stability with various values of the nonuniformity source parameter. Fluid models with nonuniform heat generation are also used for the analysis of photochemical reactors and the theory of thermal ignition (see [13,14]).…”