A volume-shrinkage-based method for quantifying the inward solidification heat transfer of a phase change material filled in spherical capsules

In order to study quantitatively the inward solidification heat transfer of a phase change material (PCM) enclosed in spherical capsules, an experimental method was proposed in this Technical Note, which is based upon measurement on the instantaneous volume shrinkage of the PCM during solidification. The shrunk volume was compensated continuously by an extra amount of liquid PCM preserved in a tube, and the descending height in the tube was recorded to calculate the volume shrinkage. Other quantities of interest, solidification fraction and surface-averaged heat flux for example, were readily reduced as single-valued functions of the volume shrinkage. Using 1-tetradecanol as the PCM, the proposed method was realized in laboratory with a stainless steel spherical capsule having an inner diameter of approximately 60   mm. Parallel tests were carried out for a set of three boundary cooling temperatures. It was shown that the measured descending heights are reproducible and are in agreement with the theoretical maximum values approaching the end of solidification. The experimental results were then discussed with an emphasis on the transient variations of solidification and heat transfer. Correlations were obtained for both solidification fraction and surface-averaged Nusselt number with respect to the product of Fourier and Stefan numbers.