3D topology-optimized fins for vertical PCM melting systems with conduction, temperature gradients, and natural convection

This study develops a three-dimensional topology optimization method for the melting process in vertical latent heat thermal energy storage systems, aiming to achieve efficient heat transfer and stable output for airborne high-power cooling applications. The optimization is carried out using the variable density method under both constant and gradient wall temperature conditions. Conductive topology optimization is governed by the heat diffusion equation, while convective topology optimization employs the incompressible Navier–Stokes equations coupled to the thermal convection–diffusion equation through the Boussinesq approximation. To reduce model complexity while preserving key morphological features, optimized geometries are represented as Non-Uniform Rational B-Splines surfaces for direct use in geometric operations and numerical simulations. Melting simulations are performed using the enthalpy-porosity method. Geometrically processed optimized fins from different governing equations and thermal boundary conditions are compared with one another, as well as against straight and pin fins of equal volume and maximum fin length, with slightly larger heat transfer areas. Results show that incorporating realistic wall temperature gradients and natural convection markedly improves the thermal performance of topological fins, with natural convection being particularly effective. These factors reduce melting time by up to 8.68% and decrease average and maximum temperature variances by 26.54% and 25.35%, respectively. Compared with geometrically favorable straight and pin fins, the optimized topological fins achieve up to 38.51% faster melting and reductions of 74.86% and 80.47% in average and maximum temperature variances. This work highlights the potential of three-dimensional topological fins and provides design guidance for practical applications.