Melting-solidification trade-offs in PCM rectangular enclosures through multi-step and steady-state topology optimization

This study investigates the performance trade-offs between melting and solidification in a rectangular phase change material (PCM) enclosure equipped with topology-optimized extended surfaces. Two topology-optimization design strategies are explored: a steady-state approach for solidification and a multi-step iterative procedure for melting. The solidification design ( S ) is obtained under steady-state conduction conditions, reflecting the dominance of conductive heat transfer during this transition. In contrast, the melting design ( M ) accounts for the coupled effects of conduction and natural convection by iteratively alternating between steady-state topology optimization and transient PCM simulations. Each iteration is stopped at a prescribed melt fraction, progressively adapting the design domain to the evolving phase change interface, say by using a multi-step approach. The two strategies yield markedly different geometries: the solidification-oriented design ( S 1 ) features symmetry and conduction-focused branches, whereas the melting-oriented designs ( M 1 -M 3 ) progressively enhance natural convection. Topology-optimized designs significantly outperform conventional straight-fin geometries in both solidification and melting. Solidification-optimized designs ( S 1 ) complete solidification in 298 min and sustain high early heat flux but show slower melting (110 min). Melting-optimized designs ( M 3 ) achieve faster melting, M 3 –5% (5% metal) completes in 85 min, while increasing the metal content to 10% in M 3 –10% reduces melting time by further 23 min relative to M 3 –5%, retaining about 97% of effective storage capacity. Higher metal fractions (>15%) accelerate melting only marginally while reducing latent heat storage, identifying the M 3 –10% as the optimal design compromise under the specific material properties and boundary conditions considered.