In this research, a numerical analysis is accomplished aiming to investigate the effects of adding a new design fins arrangement to a vertical triplex tube latent heat storage system during the melting mechanism and evaluate the natural convection effect using Ansys Fluent software. In the triplex tube, phase change material (PCM) is included in the middle tube, while the heat transfer fluid (HTF) flows through the interior and exterior pipes. The proposed fins are triangular fins attached to the pipe inside the PCM domain in two different ways: (1) the base of the triangular fins is connected to the pipe, (2) the tip of the triangular fins is attached to the pipe and the base part is directed to the PCM domain. The height of the fins is calculated to have a volume equal to that of the uniform rectangular fins. Three different cases are considered as the final evaluation toward the best case as follows: (1) the uniform fin case (case 3), (2) the reverse triangular fin case with a constant base (case 12), (3) the reverse triangular fin case with a constant height (case 13). The numerical results show that the total melting times for cases 3 and 12 increase by 4.0 and 10.1%, respectively, compared with that for case 13. Since the PCM at the bottom of the heat storage unit melts slower due to the natural convection effect, a flat fin is added to the bottom of the heat storage unit for the best case compared with the uniform fin cases. Furthermore, the heat storage rates for cases 3 and 12 are reduced by 4.5 and 8.5%, respectively, compared with that for case 13, which is selected as the best case due to having the lowest melting time (1978s) and the highest heat storage rate (81.5 W). The general outcome of this research reveals that utilizing the tringle fins enhances the thermal performance and the phase change rate.