The stably-stratified filling of an enclosure produces an interfacial layer, or thermocline, separating the hot and cold fluid volumes which is transported through the vessel with the bulk flow. The evolution of this interfacial layer is characterized by profile asymmetries and growth rates not explained by simple molecular diffusion. The present paper presents integral solutions to the horizontally-averaged energy equation with variable diffusivities exhibiting these same characteristics. The formulation requires only two parameters in addition to those of the uniform diffusivity case. The solutions are compared to published data to illustrate determination of the empirical constants and show that key characteristics of the model, specifically a constant fill-line temperature and symmetric growth rates, are satisfied for a range of moderate flow rates. At higher flow rates, the layers are seen to exhibit an increasingly higher degree of growth rate asymmetry.
Integral Solutions for Transient Temperature Profiles in Stably-Stratified Open Enclosures
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division February 13, 2001; revision received August 26, 2002. Associate Editor: B. T. F. Chung.
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Homan, K. O. (March 21, 2003). "Integral Solutions for Transient Temperature Profiles in Stably-Stratified Open Enclosures ." ASME. J. Heat Transfer. April 2003; 125(2): 273–281. https://doi.org/10.1115/1.1527911
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