Study of heat sink effects during melting of constrained phase change material inside a spherical enclosure

Abstract

Abstract This paper presents an analytical investigation to study the heat sink effects during melting of phase change material (PCM) encapsulated in spherical container. The heat sink is treated as a negative uniform volumetric heat generation term in the energy equation. The performed exact solution can be used as a reference to validate the numerical simulations and other approximate methods related to thermal energy storage within PCM in spherical capsules. The mathematical model is based on pure conduction in the PCM, subjected to a convection heat transfer at the external surface of spherical shell. The complimentary error function and variables separation method have been used to resolve energy equation in both solid and liquid phases in transient regime. The heat transfer within the PCM was analytically modelled during melting process. The natural convection inside PCM liquid phase was considered via the liquid fraction dependency of the effective thermal conductivity. The results predicted by the current model have been compared with those previously published in the literature, and a good agreement is showed. Then, a parametric study for different Rayleigh number, Biot number, Stefan number and heat dissipation power is conducted. The results show that the complete melting of PCM will not be achieved if the heat sink power exceeds certain limit value, which is strongly depending on Rayleigh and Biot numbers.