Theoretical model of the charging process for stratified thermal storage tanks

In order to provide an upper limit of the performance for stratified thermal storage tanks, a theoretical model of the charging process is studied. First, by introduction of reasonable assumptions in addition to the perfect piston flow, an idealized model is developed. Governing equations derived from the model appear to be characterized by the only parameter, Peclet number. Application of the Laplace transform technique to the equations results in a simple closed-from solution for the transient temperature distribution. The model is validated by examining a distinction from a simpler one which is heat conduction between two semi-infinite regions in contact with a moving interface. Temperature profiles for representative cases as well as the effect of the Peclet number on them are illustrated and discussed. Also, the storage efficiency is analytically expressed in terms of the Peclet number. The efficiency by the present model presents similar trends, but is smaller in value in comparison to that by the semi-infinite case. Consequently, the feasible range of the storage efficiency by the present model, which is the difference between the upper and lower limits of the efficiency, becomes more specific. For the convenience of the usage, a simple correlation of the efficiency is proposed as a function of the Peclet number.