The present study has investigated the latent heat energy storage inside two-tube converter systems with PCM materials. Additionally, the effect of fin placement on energy storage efficiency in two-pipe converter systems, with the help of fin design in geometry, was investigated and optimized. The designed geometry is 3D and with axial symmetry for the whole geometry and fins. The time-dependent model was used to predict the melting process of TR58 paraffin as PCM material, and copper metal was utilized as fin during the simulation. The needle-shaped fins were used at angles of 0°, 45°, 90°, 135°, and 180° with respect to the top of the geometry so as not to prevent the natural convection of PCMs during phase change. The results of the presence of fins were compared with the condition without fins, and it was found that the presence of fins can increase the speed of phase change by 36.51%. The optimization results revealed that 81.24% of the final efficiency of all fins could be achieved with optimal angles and a 50% reduction in the number of fins. Moreover, findings indicated that in addition to the angle of the fins, the style of their arrangement is effective in improving their performance.