Heat transfer mechanism of topologically-optimised fin structures in latent heat storage units

Latent heat storage is pivotal in advancing the development of intermittent and fluctuating renewable energy sources, but it usually suffers from poor heat transfer performance. Topological fins have been proven effective and feasible in improving heat transfer within latent heat storage units. However, the heat transfer mechanism of topological fins, mainly when natural convection is involved, has yet to be thoroughly investigated. A two-dimensional model of a latent heat storage unit coupled with topology optimisation is established using the enthalpy-porosity approach and considering natural convection with experimental validation. The optimal fins for different unit sizes and operating times are explored. Box-counting dimension (fin complexity) and fin surface area per length are employed to characterise the topological fins, while the Nusselt number is used to reveal the heat transfer mechanism between fins and phase change materials. It is found that in the cases of the same unit volume, topological fins in the narrowest unit tend to develop complex branching structures with a 40 % larger surface area per length compared to the base design with a tube radius of 20 mm, which compensates for the deficiencies in the convective heat transfer by increasing the heat exchange area. Increasing charging time results in simpler fin branches and smaller surface areas, hindering the convective heat transfer at the early stage until large-scale natural convection develops. For discharging time longer than 1200 s, the Nusselt number decreases again after an initial rise, leading to the extension of non-uniform fins toward the middle of the latent heat storage unit, with a 17.8 % increase in surface area per length that enhances heat conduction. Additionally, response surface methodology is incorporated into topology optimisation to improve the manufacturability of the optimal fins, enabling cost-effective designs while maintaining superior heat transfer performance.