Parametric analysis of latent thermal storage unit filled by metal foam: A semi-analytical correlation of melting fraction and full melting time

Integrating metal foam with phase change materials (PCMs) improves heat transfer in thermal energy storage systems. The thermal performance of these composites, however, varies with several geometric and operational factors. Although computational fluid dynamics (CFD) can provide detailed insights into phase-change behavior, its high computational cost makes it impractical for large-scale design and optimization. Therefore, efficient predictive models are necessary for engineering applications of copper foam-paraffin composite materials (CFPCMs) and for supporting their role in sustainable energy systems. This work systematically investigated how six key parameters affected the transient liquid fraction during melting in a shell‑and‑tube CFPCM accumulator, including metal foam porosity, heat transfer fluid temperature, initial PCM temperature, fluid flow velocity, outer‑to‑inner diameter ratio, and height‑to‑inner diameter ratio. After normalizing the parameters and introducing a modified Fourier number that accounts for the effective thermal conductivity of metal foam, we developed an empirical correlation between the resulting dimensionless groups and the liquid fraction using stepwise regression. The analysis reveals that the logarithm of the total melting time is linearly related to the logarithms of the influencing factors. The proposed correlation predicts the transient liquid fraction to within about 15% deviation for liquid fractions from 0.2 to 1.0. For liquid fractions above 0.4, the deviation drops below 10%. The model reliability was confirmed through validation with three independent cases, all showing prediction errors generally within 10% for liquid fractions above 0.4.