The preservation of thermal energy is a significant problem that needs to be resolved. In the present energy demand situation, effective storage of available energy will be a technique to manage the gap between the demand and supply. Solar energy is one such energy, which is an easily obtainable and renewable source of energy. Still, the maximum employment of solar energy is not readily possible without the implementation of the thermal energy storage system (TESS). This TESS can be an integral part of solar applications, thus TESS acts as a reservoir of energy to deliver the energy requirement at all times. Hence, it is an appropriate system to unite the energy source, i.e., the sun and the applications. Thus, the TESS is very vital in solar applications. The main objective of this work is to design and analyze the vertical shell and tube type TESS using water as heat transfer fluid (HTF) and paraffin wax RT58 as phase change material (PCM), which is subjected to change its phase at 46 °C to 68 °C from solid to liquid when exposed to higher temperatures, and its operating temperature range is 60 °C to 80 °C. Here, PCM (RT58) is enclosed in the tubes of the shell and tube storage unit. The property of the high specific heat capacity of PCM is tested for utilization of latent heat storage that can be used any time as required. Temperature measurements are taken using a T-type thermocouple along with an indicator and a series of experiments were conducted to study the effects of PCM in TESS. PCM encapsulated heat exchanger performance is investigated for both charging and discharging cycles with 85 °C inlet water temperature and a constant flow rate of 0.04 kg/s. To analyze the melting characteristics of PCM, simulation is carried out using ANSYS Fluent in the workbench, and comparative simulation studies are carried out for quadrilateral and triangular node shapes for better accuracy with experimental data. The heat energy stored in the charging cycle is 302.327 kJ for 100 min duration, and in discharging cycle is 295.8 kJ for 56 min duration. The HTC and Nusselt number were also calculated for both the charging and discharging cycle. It is evident from the present work, that the PCM can act as a better alternate for energy storage medium compared with the present solar energy storage methods, ensuring the correct adaptability of PCM for the particular application. The heat transfer rate can be increased further by using more amounts of different PCM or PCM composite with higher latent heat and also by providing better tank insulation. In future work, emulsification of nanomaterial in the PCM or in the HTF, and implementation of finned tube profile can increase the overall performance of TESS.