Integral approximate solution for the charging process in stratified thermal storage tanks

This paper presents the approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks with fluid mixing at the inlet. The temperature is assumed to be a form of the Fermi–Dirac distribution function, which can be separated into two sets of cubic polynomials for the hot and cold sides of the thermal boundary layers. The proposed approximate integral solutions are compared with previous works on approximate analytic solutions and show reasonable agreement. This approach, however, benefits from reduced mathematical complexity as compared with the complicated solution form and unstable convergence of the series solution found in the previous analytic solutions. For the ideal case of no fluid mixing at the inlet, the thermocline thickness is proportional to the square root of time and reversely proportional to the flow rate. However, if the fluid is mixed perfectly in the region near inlet, the thermocline thickness could be thicker as the flow rate increases because of the increased mixing region caused by promoted flow mixing in this region. Thus the optimal flow rate depends on the relationship between the flow rate and the size of the mixing region. 2011 Elsevier Ltd. All rights reserved.