Numerical solution for discharging of PCM mixed with nano-powders

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.

Automated summary

The numerical procedure based on Galerkin technique was used to model the freezing process of water inside an enclosure with elliptic and triangular cold surfaces. The results showed that the freezing time can be reduced by increasing the volume of nanoparticles or the shape factor, and this effect can be further enhanced by increasing the concentration of alumina.