This work aims to improve the efficacy of phase change material (PCM)-based shell-and-tube-type latent heat thermal energy storage (LHTES) systems utilizing differently shaped fins. The PCM-based thermal process faces hindrances due to the lesser thermal conducting property of PCM. To address this issue, the present problem is formulated by adopting the concept of conducting fins. The geometry comprises concentric cylinders, in which the inner cylinder carries the heat transfer fluid (HTF), whereas the outer cylinder contains PCM. Four number fins of different shapes are attached outside the HTF carrying cylinder. The enthalpy–porosity approach is used for modeling the phase change and heat transfer. The investigation is conducted numerically utilizing the finite volume-based numerical technique for the range of control variables such as the shape of the fins (straight, curved, and wavy fins) and various temperatures of the HTF. Furthermore, all the results are assessed with the results of no-fin case. The results show that the melting time drops markedly by 122.2% using a curved fin. This paper shows the capability of geometry modification in enhancing the heat energy storage rate of thermal energy storage systems. The PCM-based latent heat thermal energy storage (LHTES) unit is very effective for sustainable energy solutions through storing and releasing of renewable energy following the supply and demand cycle. Therefore, the outcome of the present study will enrich the knowledge on the design of efficient and compact thermal energy storage systems.