Due to the low thermal conductivity of the phase change material and low thermal diffusion inside the phase change material, this study seeks to improve the melting response of a triple-tube latent heat storage system via employing annular fins by optimizing their structural parameters, including the fin number, location, and dimensions. Natural convection effects are numerically evaluated considering different numbers and the locations of the fins, including fin numbers of 4, 10, 16, 20, and 30 in a vertical system orientation. The fins are attached to the inner and outer sides of the annulus, accommodating the phase change material between the inner and center tubes. The fins' number and location are identical on both sides of the annulus, and the volume of the fins is the same across all scenarios evaluated. The results show that the higher the number of fins used, the greater the heat communication between the fins and the phase change material layers in charge, resulting in faster melting and a higher rate of heat storage. Due to the limited natural convection effect and lower heat diffusion at the heat exchanger's bottom, an additional fin is added, and its thickness is assessed.The results show that the case with equal fin thickness, that is, both original fins and the new fin, performs the best performance compared with that for the cases with an added fin with thicknesses of 0.5, 1, and 2 mm. Eliminating an extra fin from the base of the system for the case with 30 fins increases the charging time by 53.3%, and reduces the heat storage rate by 44%. The overall melting time for the case with an added fin to the bottom is 1549 s for the case with 30 fins which is 85.8%, 34.2%, 18%, and 8.8% faster than the cases with 4, 10, 16, and 20 fins, respectively. This study reveals that further attention should be given to the position and number of annular fins to optimize the melting mechanism in phase-changing materials-based heat storage systems.