Mathematical modeling of unsteady process of cold storage within a container filled with nanomaterial incorporating Galerkin method

This research focuses on simulating the freezing involving a mixture of H₂O and alumina nano-powders. It sheds light on the complex relationship between the characteristics of nano-powders and freezing dynamics, offering valuable insights applicable to various fields, including cryopreservation and thermal energy storage. By utilizing the Galerkin approach and incorporating an adaptive grid, the research introduces an elliptic container with a cold surface and strategically placed rectangular fins. The investigation examines how the characteristics of nano-powders, particularly their size (dp) and concentration (ϕ), influence different scenarios. Notably, changes in powder size have a significant effect on freezing time, initially decreasing by approximately 20.22 % before increasing by 19.1 %. Moreover, the sensitivity of powder size decreases with lower powder concentrations. For example, at ϕ = 0.02, an augment in dp primarily reduces the time by about 11.72 %, followed by an increase of 10.98 %. The most substantial improvement occurs when ϕ is optimized, resulting in a remarkable 41.27 % reduction in freezing time.