<p>In current research, a mathematical framework was developed to model and analyze the solidification process within a thermal energy storage system. The governing equations have been formulated and solved using the Galerkin finite element method, ensuring high computational accuracy. In the derivation of the mathematical model, buoyancy effects have been neglected to simplify the analysis, resulting in a final system of two coupled equations. The transient terms in these equations have been discretized using an implicit numerical scheme to enhance stability and computational efficiency. To accelerate the freezing process and intensify the overall thermal performance of the unit, two key enhancement strategies have been incorporated: (1) the introduction of hybrid nanoparticles within water and (2) the consideration of thermal radiation effects. The accuracy of the proposed mathematical approach has been validated against previously published numerical and experimental studies, demonstrating strong agreement with existing results. The findings of this study reveal that the integration of hybrid nanoparticles and radiation effects improves the penetration of cold energy, leading to a notable decrement in the freezing time. Specifically, the loading of additives results in a 5.77% reduction in the solidification time, while the consideration of radiation effects further decreases the freezing time by an impressive 30.48%. This study not only fills a crucial research gap in PCM-based thermal enhancement techniques but also offers a foundation for future experimental and numerical investigations aimed at further optimizing cold storage technologies.</p>