Thermal expansion effects on the one-dimensional liquid-solid phase transition in high temperature phase change materials

Heat transfer characteristics of phase change materials (PCMs), such as the absorbed sensible and latent heat, during melting of the solid phase at constant pressure are analyzed. A model is proposed, where thermal dilation is incorporated by applying total mass conservation to materials with temperature dependent densities. A different energy-mass balance equation at the interface is obtained and shown to be a consequence of the proposed general mass conservation. Several authors have found solutions to the melting or solidification process by considering temperature dependent thermodynamic variables. In these works; however, the densities in each phase are assumed to be equal and constant. Other authors have studied the effect of having phases with different densities, but neglect the contributions of thermal dilation. To the authors knowledge, the impact of temperature dependent densities on the dynamics of the phase transition, has not been addressed. In our work, the proposed energy-mass balance equation at the interface, couples the total mass of the liquid or solid phase, to the net heat flux variation by means of an integro-differential equation. The solution of this equation and the general mass conservation presents some challenges from the numerical point of view. Semi-analytical and numerical methods are used to solve the proposed model for two types of PCMs. The solutions obtained from the proposed model are compared with predictions from other models. Depending on the type of material, it is observed that thermal expansion effects can have a significant impact on the thermal energy stored during melting.