https://doi.org/10.1140/epjp/s13360-022-03173-w
Regular Article
Numerical solution for discharging of PCM mixed with nano-powders
Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia
Received:
23
March
2022
Accepted:
9
August
2022
Published online:
1
September
2022
Numerical procedure based on Galerkin technique has been chosen to model the freezing of water inside the enclosure contains elliptic and triangular cold surfaces. The size of grids near the place where ice exist should be smaller and such time-dependent behavior leads to more accuracy in solution. Since the velocity of liquid water is very slow in freezing, the related terms were neglected in modeling and only temperature equations should be solved. In this equation, variations of solid fraction and temperature respect to time have been involved as well as diffusion term. Validation procedure portrays the good accuracy of proposed model. With adding more volume of nanoparticles, the period of freezing drops around 9.22 and 11.75 when m = 3 and 5.7. Moreover, with growing shape factor up to 5.7, the freezing time decreases by 5.96%. Also, such change can be more effective if concentration of alumina increases.
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