Solidification process modeling for energy storage by means of galerkin method utilizing nano-sized additives

In this study, a numerical method for modeling the freezing process inside a storage enclosure equipped with ψ-shaped fins has been scrutinized. The container features both square and sinusoidal walls, with ψ-shaped fins enhancing the thermal conduction within the system. Alumina nanoparticles, in both blade and cylindrical forms, have been dispersed in the water to investigate the effect of particle shape on the freezing process. The shape factor ( m ) is considered in the calculation of conductivity to capture the impact of different nanoparticle geometries. Additionally, a single-phase model is used for the nanomaterial formulation, with nanoparticle concentrations ( φ ) kept below 0.04 to ensure accurate representation. The results reveal that increasing ( m ) leads to a reduction in solidification time by approximately 7 %. When nanoparticles are dispersed in water, the time required for complete freezing decreases from 275.57 s to 201.95 s, representing a significant improvement. This demonstrates that the presence of nanoparticles can accelerate the freezing process by about 26.71 %. By incorporating ψ-shaped fins and optimizing nanoparticle characteristics, the study provides valuable insights into enhancing thermal conduction and reducing freezing times.