Numerical Solution of Heat Transfer During Solidification of an Encapsulated Phase Change Material

Macro encapsulation techniques have gained considerable attention in latent heat storage systems for solar energy applications in order to improve the overall energy conversion efficiency in solar thermal power plants. However the heat transfer mechanisms that govern the charging and discharging processes at high operating temperatures are still under development and represent an important aspect in the thermal energy storage design process. This study presents a numerical solution of the heat transfer and phase change that occurs during the solidification process of a phase change material (PCM) encapsulated in a spherical container. A transient two-dimensional axisymmetric mathematical model was solved using the control volume discretization approach along with the enthalpy-porosity method to track the melting front. A spherical shell of thickness t, under the gravitational field is completely filled with liquid PCM. For time t>0, a constant temperature boundary condition Tw, which is lower than the phase change temperature of the PCM, is imposed at the outer surface of the shell. A comprehensive analysis is presented in order to assess the role of the capsule size, buoyancy-driven flow in the liquid phase, and shell outer surface temperature on the thermal performance of the system. Results show that with the increase of Stefan number the solidification rate is enhanced. A reduction of 39.25% in total solidification time is predicted when the Stefan number changed from 0.095 to 0.143. Finally a generalized correlation for the solid mass fraction during solidification is obtained based on a combination of Fourier and Stefan numbers and a dimensionless material parameter.Copyright © 2013 by ASME