The phase transition heat transfer during the melting and solidification processes of phase change materials (PCMs) was modeled in a shell-tube thermal energy storage unit. For the first time, special attention was dedicated to the heat transfer enhancement on the heat transfer fluid (HTF) side by placing metal foam (MF) inserts in the HTF tube. The MF inserts on the HTF side were placed next to the fin bases to produce the maximum heat transfer enhancement. A two-temperature local thermal non-equilibrium model was applied to accurately model the transient heat transfer in the MF domains. To perform a fair heat transfer analysis and consider the hydrodynamic aspects of heat transfer, the pumping power for driving the HTF fluid was kept fixed. The finite element method with automatic time-step control was used to integrate the model equations. Results show that the insertion of the MF in the HTF tube enhances conduction heat transfer but reduces flow for a constant pump power. Using a small amount of MF provides a good flow rate and a convective heat transfer while using a large amount of MF provides good conduction heat transfer but a poor flow rate and convection. A moderate amount of MF inserts results in poor conduction and a poor flow rate, notably increasing the phase transition time. A 5 % MF insert could provide about a 13 % shorter solidification time compared to a 25 % MF insert. Thus, a well-designed and engineered MF insert configuration on the HTF side can reduce the phase transition time and improve the energy storage power.