The techniques for releasing thermal energy accumulated in periods of high availability to meet the demand in periods of low energy supply contribute to the continuity of the cycles involved in thermodynamic processes. In this context, phase change materials are capable of absorbing and releasing large amounts of energy in relatively short periods of time and under specific operating conditions. However, phase change materials have low thermal conductivity and need to be coupled with high-thermal-conductivity materials so that the heat flux can be intensified and the energy absorption and release times can be controlled. This work aims to numerically study the solidification process of a phase change material inserted into a triplex tube heat exchanger with finned copper walls to intensify the thermal exchange between the phase change material and the cooling heat transfer fluid, water, that will receive the energy accumulated in the material. This work proposes the 3D numerical modeling of the triplex tube heat exchanger with finned walls and meets the need for numerical models that allow for the analysis of the full geometry of the latent heat thermal energy storage system and the thermal and fluid dynamic phenomena that are influenced by this geometry. Results of the temperature, liquid fractions and velocity fields during phase transformations are presented, analyzed and validated with experimental data, presenting average errors of below 5%. The total material discharge time was approximately 168 min, necessary for the complete solidification of the phase change material, with water injected into the triplex tube heat exchanger at a flow rate of 8.3 L/min and a temperature of 68 °C. The solidification process occurred more slowly in the same direction as the length of the triplex tube heat exchanger, and from 80% of the material in the solid state, the difference between the solidification time for z = 0 and z = 480 mm was 30 min. The fluid dynamic conditions developed in the latent heat thermal energy storage system promoted a maximum negative heat flux of −6423 w/m2 to the annular internal surface and −742 w/m2 to the annular external surface, representing a heat removal process nine times less intense on the external surface. The total energy released to the cooling heat transfer fluid was 239.56 kJ/kg.