On a Novel Closed-Form Analytical Solution for Unsteady Solidification: Theory and Application

Numerical modeling of transient solidification under convective boundary conditions presents a significant challenge because accurately tracking the solid–liquid interface is essential for obtaining a stable solution. Although analytical solutions are generally straightforward to apply, the growing demand for energy storage driven by mismatches between supply and demand in renewable‑energy systems requires reliable predictive tools for Latent Heat Thermal Energy Storage (LHTES) applications. In this work, we compare a classical analytical solution for the transient solidification of pure and eutectic phase‑change materials with a recently derived formulation that provides a complete treatment of the Biot number. The comparison is performed in the context of sizing LHTES reservoirs and selecting appropriate phase‑change materials. The results demonstrate that the new formulation accurately predicts the velocity of the solid–liquid interface, the thermal gradient, and the cooling rate, offering improved reliability over the classical approach.