Effects of Pressure-Induced Density Changes in the Thermal Energy Absorbed by a Micro-Encapsulated Phase-Change Material

Density changes produced by pressure increments during melting of a spherically confined phase-change material have an impact on the thermal energy absorbed by the heat storage unit. Several authors have assumed incompressible phases to estimate the volume change of the phase-change material and the thermal balance at the liquid-solid interface. This assumption simplifies the problem but neglects the contribution of density changes to the thermal energy absorbed. In this work, a thermal balance at the interface that depends on the rate of change of the densities and on the shape of the container is found by imposing total mass conservation. The rigidity of the container is tuned through the coupling constant of an array of springs surrounding the phase-change material. This way, the behavior of the system can be probed from the isobaric to the isochoric regimes. The sensible and latent heat absorbed during the melting process are obtained by solving the proposed model through numerical and semi-analytical methods. Comparing the predictions obtained through our model, it is found that even for moderate pressures, the absorbed thermal energy predicted by other authors can be significantly overestimated.