Total Energy Balance During Thermal Charging of Cylindrical Heat Storage Units: Thermodynamic Equilibrium Limit

The local energy balance at the liquid-solid front has been widely used in the literature. However, depending on the initial state of the system, the boundary conditions, and the thermodynamic properties of the phase change material, the local energy balance can lead to inaccuracies. The total energy balance has been applied to phase change processes; however, discrepancies have been reported regarding the dynamics of the melting front obtained through this approach. In this work, the concept of thermodynamic equilibrium is used to determine the exact liquid-solid coexistence state in adiabatic systems. Thermodynamic equilibrium of saturated mixtures is used to validate the proposed energy balance. We found that the melting front position obtained from a local energy balance can be underestimated by as much as $37.4\%$ when compared with the equilibrium value. In contrast, the interface position estimated by the total energy balance was in good agreement with equilibrium, with relative differences between $0.082\%$ and $0.11\%$. Finally, a melting experiment using paraffin RT50 was conducted in a thermally insulated cylindrical unit. The experimental front position was underestimated by the local energy balance, with differences between $2.4\%$ and $6.9\%$, while the total energy balance showed smaller discrepancies between $0.28\%$ and $5.71\%$.