New method for fast heat transfer analysis of PCM cross sections with integrated finned tubes

State-of-the-art Latent Heat Thermal Energy Storage (LHTES) units use extended heat transfer surfaces to compensate for the typically low thermal conductivity of cost-effective phase change materials (PCMs). The analysis of such surfaces currently depends heavily on numerical simulations. However, due to high computational costs, this approach cannot be practically scaled to analyze complete LHTES storage units. To overcome this limitation, this study proposes a computationally efficient alternative for the analysis of PCM storage systems. In this new methodology, finned geometries are characterized using a novel, purely geometric distance-based framework. This approach serves as the foundation for a simplified model that entirely eliminates the need for additional numerical calibration.To achieve this, four distinct longitudinally extruded fin profiles (24-Branch-Star, Organic, Snowflake, and 6-Branch-Star) with identical fin fractions were evaluated. The methodology translates complex 2D fin cross-sections into 1D Cumulative Distribution Functions (CDFs) based on shortest-path heat transfer distances. A simplified transient model for quasi-isothermal fins was subsequently developed and validated against reference 2D numerical simulations. Results demonstrate that the contact perimeter between PCM and fin is inversely proportional to the melting time, whereas the novel average distance between the PCM and the fin exhibits a direct linear correlation with the phase change time. Both parameters are therefore proven to be reliable predictors for the design of finned profiles. Furthermore, the simplified model for quasi-isothermal fins accurately predicted the transient liquid fraction with a mean absolute error of less than 0.026, while delivering speedup ratios between 77 and 183 times compared to the reference 2D numerical simulations. The proposed efficiency metric revealed that highly branched profiles suffer from severe internal conduction limitations due to branch slenderness. Finally, this novel distance framework provides a highly reliable, numerically-independent tool, eliminating computational bottlenecks and enabling the rapid algorithmic optimization of LHTES fin geometries.