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This study conducts a simulation of the freezing through a container featuring finned sinusoidal geometry. The application of the Galerkin method effectively captures the intricate dynamics of unsteady processes, showcasing a significant enhancement by introducing nanoparticles to augment the system's thermal conductivity—an essential element for optimizing conduction efficiency. The numerical approach underscores the importance of employing an adaptive grid in unsteady scenarios, tailoring the grid based on the solid front's position due to heightened scalar gradients. Various powder diameters (dp) and fractions (ϕ) are systematically investigated, elucidating their distinct impacts on process duration. Results reveal that an initial increase in dp causes to a decrement in period by 19.93%, followed by a subsequent rise of 49.06%, specifically for scenarios with a 0.04 nanoparticle concentration. The incorporation of nanoparticles yields a noteworthy 41.13% decrease in solidification time when optimal powder sizes are utilized. In contrast, the solidification time without additives is 278.95s, reduced to 164.19s with the introduction of optimally sized powders.
Yahya Ali Rothan (Sat,) studied this question.