Solidification and melting model of phase change material with volumetric shrinkage/expansion void in an annulus

Abstract

A one dimensional analytical model is proposed to analyze the solidification/melting of phase change materials (PCMs) incorporating the shrinkage/expansion void in an annulus. An air-PCM system is considered in this study. Paraffin wax is considered as PCM and filled inside the annulus, while air is considered inside the void. Separation of Variable method involving Bessel's function is employed to obtain temperature distribution for air, solid and liquid domains and to locate interface positions. Stefan condition and mass conservation equation are used at the interfaces. Results obtained from the present model are found to be in good agreement with the existing test results. Effect of various parameters such as density ratio, end wall temperature, and radius ratio on the solidification/melting of PCM have been investigated. The solid-liquid interface moves 76.53% and 70.88% during solidification and 34.26% and 35.32% during melting for density ratio of 1 and 1.16, respectively during a time period of 1400 s. Shrinkage as well as solidification rate increases with decrease in cold wall temperature, increase of radius ratio and increase in Stefan number; while expansion as well as melting rate increases with increase in hot wall temperature, increase of radius ratio and increase in Stefan number. © 2021 Elsevier Ltd