Development of numerical code for mathematical simulating of unsteady solidification phenomena in existence of nanomaterial

Abstract

This research zeroes in on improving the freezing process by synergistically employing a wavy wall and fins. To enhance cold penetration, the phase change material (PCM) is enriched with nanoparticles, and a single-phase model is adopted due to the low nanoparticle concentration. The numerical simulations leverage the Galerkin method and the validation procedure affirms the precision of the code, extensively evaluating the impacts of φ (concentration of additives) and dp (particle diameter). With an increase in particle diameter (dp), there is an initial 19.76% decrease in the required time, succeeded by a subsequent 50.56% increase when φ = 0.04. Furthermore, an escalation in φ results in an 11.04%, 40.91%, and 26.36% reduction in completion time for dp values of 50, 40, and 30 nm, respectively. Without the inclusion of powders, the solidification process lasts for 84.8 s. However, with the introduction of the optimal powder size, this duration significantly reduces to 50.1 s. This emphasizes the efficiency improvements attained through the strategic integration of a wavy wall, fins, and PCM infused with nanoparticles.

Keywords

• Mathematical modeling
• Galerkin
• Freezing
• Unsteady phase change
• Completion time
• Nanomaterial