Phase change materials are applied in heat storage systems because of their high latent heat. The low thermal conductivity of phase change materials limits the heat transfer rate. Rectangular grille fins, semicircular wave fins, cosine wave fins, and triangular wave fins are designed to enhance the heat transfer rate in flat-plate storage modules. The addition of Al2O3, CuO, and Fe3O4 at 1 %, 3 %, 5 %, and 7 % volume fractions is investigated based on the triangular wave fins to improve the heat storage performance. Compared with the finless structure, the complete melting time of phase change materials is reduced by 4.70 %, 7.10 %, 9.15 %, and 10.71 % in rectangular grille fins, semicircular wave fins, cosine wave fins, and triangular wave fins modules. The heat storage power of a triangular fin module increases by 7.88 % relative to the finless module. The melting time is shortened for all nanoparticles as the volume fraction increases, accompanied by an increase in the average temperature. The melting rate of phase change materials is improved by 16.84 % with the addition of 7 % Al2O3 nanoparticles and triangular wave fins relative to the bare cavity. Compared with pure phase change materials, the heat storage power is improved by 11.11 % owing to the synergistic effect of triangular wave fins and Al2O3 nanoparticles. Enhancement strategies for latent heat storage systems are provided through the synergistic combination of periodic fins and nanoparticles.