In pursuit of advancing the efficiency of cold energy storage, a uniquely designed curved container has been employed, filled with a water-nanoparticle mixtureQ. The container is equipped with fins, strategically leveraging the enhanced conduction facilitated by the presence of nanoparticles. The simulation of the intricate unsteady phenomena in this study has been conducted using the finite element technique, providing a robust analytical framework. The incorporation of an adaptive grid ensures a refined resolution, particularly in the vicinity of the ice front region. The nanoparticle fraction (ϕ) emerges as a pivotal factor directly influencing the rate of solidifying. The dispersion of nano-powders leads to a noteworthy reduction in completion time, demonstrating a substantial 33.21% improvement. The diameter of the nano-powders (dp) introduces diverse effects on the solidification process, primarily due to its significant influence on the conductivity of the nanomaterial. An in-depth exploration of the impact of dp reveals compelling insights. As the dp increases from its smallest size to 40 nm, there is a commendable 15.12% reduction in the required freezing time. However, a subsequent increment in dp beyond this threshold results in a notable 36.56% increase in the freezing time. The findings presented here not only contribute to the fundamental understanding of freezing processes but also hold practical implications for the design and optimization of cold storage systems.