Analytical solutions to a one-dimensional finite-domain model for stratified thermal storage tanks

A set of analytical solutions to a one-dimensional finite-domain model is obtained to analyze the charging process in stratified thermal storage tanks. An approximate but practically acceptable short-time solution which is compactly expressed in terms of well-defined functions is preferred to the mathematically exact but long-time solution. From the order of magnitude analysis on the series solution, all the higher order terms other than the zeroth order one are truncated, and the resultant solutions prove to be almost exact for the practical charging time range. The earlier Cabelli's solutions based on the semiinfinite domain are found to be a subset of our solutions for which the adiabatic end condition is imposed. In view of the generality and completeness of the model and analysis, it is expected that the present solution may serve as a rigorous theoretical reference for related works. (C) 1996 Elsevier Science Ltd.