At present, Phase Change Materials (PCMs) possess a great utilization in the area where energy is stored thermally as latent heat of fusion. Different researchers have tried different heat transfer improvement methods due to PCMs’ low thermal conductivity, one of which is using fins. In the present study, the effectiveness of straight fins along with Y-shaped fins in the PCM region of a triplex tube heat exchanger has been investigated. A 3D numerical simulation was conducted using ANSYS Fluent software to analyse the heat transfer during the solidification of PCM. A comparative analysis between straight fins and Y-shaped fins, both made from an equal volume of material, has been done to verify which fin gives better results. The results obtained are based on the solidification behavior of PCM. From the study, it was found that using straight fins instead of no fins decreases the solidification time by 52.8%, and for Y-shaped fins, it decreased by 69.2%. After that, it was also observed that the solidification behavior of PCM also significantly depends on the bifurcating angle between the Y-shaped fins.