Transient modeling of storage of cold energy in existence of nano-sized additives

In current paper, a novel approach has been applied to improve the efficiency of cold storage with a complex shape. To simulate the solidification, we employed the Galerkin method along with an adaptive mesh. The meticulously developed model, with a focus on conduction as the predominant main term, integrated a homogeneous nanomaterial. We explored the significant impact of powder shapes on system dynamics, presenting comprehensive results to elucidate this influence. The study meticulously investigated two parameters, specifically shape factor (m) and concentration (41)). Moreover, the mesh configuration dynamically adjusted to the location of the ice front, adding a layer of complexity to our methodology. Thorough validation against established benchmarks confirmed the accuracy of our method. The results revealed that utilizing only water led to an extended freezing duration, requiring 220.24 s. Surprisingly, as the concentration (41)) increases from zero to 0.02 and then to 0.04, the overall freezing time decreases by approximately 13.82 % and 26.79 %, respectively.