In this study, a numerical model to analyse the charging and discharging characteristics of a horizontal shell and tube type Latent Heat Storage (LHS) prototype is presented. The system comprises of Sodium Nitrate as phase change material (PCM) in the shell side and flow of air as heat transfer fluid (HTF) in the tube side. The effective heat capacity approach is followed while solving the fluid flow and energy interactions in the PCM. The design is optimized by modifying a cylindrical shell into a conical shell heat exchanger system. The optimized values of diameters at inlet and outlet of the conical shell are found to be 98.6 mm and 54 mm, respectively having a cone angle of 3.4. A performance comparison is made with a cylindrical shell system of equivalent storage capacity. 3-D numerical simulations performed on the proposed system revealed that an innovation in the design leads to enhanced heat transfer rate caused by uniform melting throughout the system. Further, the conical shell model is numerically simulated for various operating parameters such as inlet HTF velocity and temperature. Also, the effect of fins attached on the HTF tube on the performance of the system is analysed. With the advent of advanced heat exchanger design, there is a greater scope of obtaining higher heat transfer rates employing the proposed conical shell and tube LHS system.