Thermal energy storage units based on phase change materials (PCMs) need a fine design of highly conductive fins to improve the average heat transfer rate. In this paper, we seek the optimal distribution of a highly conductive material embedded in a PCM through a density-based topology optimization method. The phase change problem is solved through an enthalpy-porosity model, which accounts for natural convection in the fluid. Results show fundamental differences in the optimized layout between the solidification and the melting case. Fins optimized for solidification show a quasi-periodic pattern along the angular direction. On the other hand, fins optimized for melting elongate mostly in the bottom part of the unit leaving only two short baffles at the top. In both cases, the optimized structures show non-intuitive details which could not be obtained neglecting fluid flow. These additional features reduce the solidification and melting time by 11 % and 27 % respectively compared to a structure optimized for diffusion.

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