Journal of Advances in Mathematics and Computer Science

The enhancement of thermal energy storage efficiency using phase change materials (PCMs) plays a crucial role in the development of advanced solar thermal systems. In the present study, a comprehensive numerical investigation is performed to examine the melting behavior, heat transfer characteristics, and thermodynamic performance of PCM nanofluids, including paraffin–Al₂O₃ PCM, PCM graphene, and nano-encapsulated PCM (NEPCM). The transient two-dimensional governing equations are solved using the finite volume method coupled with the SIMPLE algorithm, while the phase change process is modeled through the enthalpy–porosity approach. The influence of nanoparticle enhancement on temperature distribution, melting fraction, stored thermal energy, entropy generation, Bejan number, and thermal efficiency is systematically analyzed. The results reveal that the PCM–graphene nanofluid exhibits significantly improved thermal transport, resulting in faster melting, higher energy storage capacity, and reduced thermodynamic irreversibility compared with paraffin–Al₂O₃ PCM and NEPCM systems. In contrast, the NEPCM demonstrates delayed melting behavior due to encapsulation-induced thermal resistance, although it provides enhanced thermal stability during the discharging period. A multi-objective performance evaluation is further conducted using the overall performance index and Pareto-based optimization framework, which confirms the superior thermo-energetic efficiency of the PCM–graphene nanofluid. The findings of this study provide valuable insights into the optimal selection of PCM nanofluids for high-efficiency solar thermal energy storage and heat management applications.