In order to reduce the disparity between energy supply and demand, thermal energy storage (TES) is a vital part of energy systems. A wide range of technologies, including solar thermal power generation, HVAC systems, and industrial processes, use phase change TES systems, such as Horizontal Shell and Tube Latent Heat Storage Systems (LHTES). Though the heat transfer (HT) efficiency faces a challenge. This paper presents the proposed angled fin (rectangular with a U-shaped tip) and mixed fin design to improve the melting performance of lauric acid as phase change material (PCM) in a horizontal shell and tube LHTES. To study the melting behavior of lauric acid, a PCM in a finned LHTES unit, a two-dimensional model of the melting HT process is created and numerically solved. The development of the melting front, temperature variations within the domain, the impact of natural convection, various fin configurations, and Stefan number are all used to study the melting behavior of PCM. The fins design is optimized by the PCM's entire melting time. We find that the LHTES unit with angled fins (rectangular with U-shaped tip fins) melts at a quicker pace and has a more uniform temperature distribution and PCM velocity because of the higher HT surface area of fins.