Phase change materials (PCMs) are popular for effectively storing thermal energy due to their high thermal energy density and nearly constant operating temperature. However, a restriction for their effective application comes up due to their poor thermal conductivity. The main aim of this numerical investigation is to analyze the potential of two heat transfer augmentation methods, (i.e., metal foam and nano-additives) for a shell and tube. A mathematical formulation considering the extensions of Brinkman and Forchheimer made on the model of Darcy for porous media is validated with experimental data available in literature and used for simulations. The model is used via a commercial CFD code for simulations of heat transfer and phase change evolution during both charging and discharging processes in the heat exchanger. The thermal performance of the heat exchanger is examined through liquid fraction evolution, time for complete cycle and stored energy. The effects of operational and structural parameters including inlet temperature, metal foam material, foam porosity (0.95 and 0.98), pore density (10, 40, and 70 ppi), and nanoparticle volume fraction (0, 1 and 3 vol%) are investigated. Results show that the metal foam material and nanoparticle concentration have a significant effect on the thermal performance of PCM in shell and tube. Metal foam and graphene nanoplatelets reduce the charging and discharging times by up to 96.11% and 96.23%, respectively. Furthermore, lower porosity foam expedites the charging/discharging process whereas the pore density has no noticeable effect. The findings of this study are hoped to be helpful for designing efficient thermal energy storage units.