A Unified Heat Transfer Coefficient for Phase Change Time Prediction Across Biot Number Regimes

This paper introduces a novel, closed-form analytical model for predicting phase change times that effectively bridges the gap between lumped-capacitance and moving-boundary formulations. The model is valid across an extended Biot number range of 0.01≤Bi≤20.01≤Bi≤2, addressing the challenging intermediate regime where internal and external thermal resistances are comparable. At the core of the formulation is a physically derived global heat transfer coefficient UU, obtained from first-principles thermal resistance analysis. This coefficient incorporates geometry-specific ΦΦ factors for planar, cylindrical, and spherical configurations, eliminating the need for empirical fitting. The model explicitly separates sensible and latent heat contributions, enabling both physical insight and computational efficiency. Validation against high-resolution numerical solutions of the Stefan problem demonstrates that the model maintains errors below 5% for Bi ≤ 1 and below 15% for Bi=2, significantly outperforming existing lumped-capacitance extensions limited to Bi < 0.2. The framework is further applied to water solidification with supercooling, successfully predicting the non-monotonic relationship between solidification time and temperature, including a minimum near −12C consistent with experimental observations. Key strengths of the model include: A closed-form expression suitable for rapid parameter sweeps and system optimization Applicability to multiple geometries without reliance on numerical simulation Incorporation of supercooling effects via an effective phase change temperature derived from energy balance The work provides practical tools for the design and optimization of phase change material systems in thermal energy storage, cryopreservation, electronics cooling, and climate modeling. All numerical codes, datasets, and derivations are made publicly available to ensure reproducibility and further research.