Approximate analytical model for two-phase solidification problem in a finned phase-change material storage

During the phase change in a phase-change material (PCM) storage system, the solid–liquid interface moves away from the heat transfer surface and the surface heat flux decreases due to the increasing thermal resistance of the molten or solidified medium. Heat-transfer enhancement techniques such as fins and honeycombs have to be used to increase the heat-transfer fraction in the store. The purpose of this paper is to develop a simplified analytical model which predicts the solid–liquid interface location and temperature distribution of the fin in the solidification process with a constant end-wall temperature in the finned two-dimensional PCM store. The storage is initially in a liquid state and its temperature is greater than the solidification temperature of the PCM. The analytical results are compared to the numerical results calculated using the heat-capacity method. The results show that the analytical model gives a satisfactory estimation for the fin temperature and the solid–liquid interface when the length-to-height ratio (λ) of the storage cell is smaller than 6.0 and the fin length is smaller than 0.06 m. The error made in the fraction of solidified PCM is ±10% when the analytical model is used rather than the two-dimensional numerical model.