Melting in Shell-and-Tube and Shell-and-Coil Thermal Energy Storage: Analytical Correlation for Melting Fraction

The following study investigated the melting behavior of coconut oil as a phase-change material in shell-and-tube and shell-and-coil thermal energy storage systems. The primary objective was to deepen the understanding of PCM melting dynamics under varying boundary conditions, aiming to optimize TES designs for renewable energy applications. This research addresses a gap in understanding how different heat-transfer configurations and boundary conditions affect melting efficiency. Experimental setups included two distinct heat-transfer surfaces in a cylindrical shell—a copper tube and a copper coil—tested under constant wall temperatures (34 °C for the tube, 33 °C for the coil) and constant heat flux (597 W/m 2 for the coil). Findings reveal that melting under constant heat flux takes approximately twice as long as under constant wall temperatures, underscoring the critical role of heat-transfer conditions in TES performance. The liquid fraction was estimated using two approaches: image-based analysis and the volume-averaged temperature method. The former proved less reliable due to geometric limitations, particularly when the heat-transfer surface was distant from the shell wall. Conversely, the latter yielded higher accuracy, especially in the shell-and-tube setup. Due to the scarcity of correlations for constant heat-flux conditions, the novel contribution of this work is the development of a modified semi-empirical correlation for the shell-and-coil TES system. For this purpose, an existing model, which demonstrated strong alignment with experimental data, was adapted. The findings suggest that slower melting under constant heat flux could benefit applications needing sustained heat release, like solar energy systems. Future work could investigate additional PCMs or novel geometries to further improve TES efficiency and scalability.