Integral Solutions for Transient Temperature Profiles in Stably-Stratified Open Enclosures

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.