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**A comprehensive numerical model for melting with natural convection.**
*(English)*
Zbl 1190.80044

Summary: A comprehensive and efficient numerical model for melting with natural convection is developed. The model is based on the finite volume approach and temperature transforming model. A new method for solid velocity correction with an explicit update for melting front and buoyancy force (the governing equations are otherwise discretized in fully implicit format) is proposed and shown to be very effective in eliminating inconsistencies found in previous studies. The predictions of the proposed numerical model are compared to previous theoretical, modeling and experimental results, and reasonable agreement is achieved. It is shown that the consistent update technique (CUT) algorithm is much more efficient (CPU time reduce by an order of magnitude) than the SIMPLE algorithm for solving melting problems. Furthermore, it is demonstrated that the central difference scheme is much more accurate than the power law scheme, and that the Richardson extrapolation method provides a powerful tool for grid and time step independence tests as well as discretization error estimates. Finally, it is found that melting phenomena of octadecane and sodium nitrate, both melting in a square cavity with a Rayleigh number of \(10^{8}\) and a Stefan number of 0.1, are essentially identical; such a similarity can be used as a foundation for conducting room temperature experiments to investigate the melting/solidification characteristics of high temperature phase change materials (PCMs). A benchmark solution for the entire melting process of sodium nitrate is provided as well.

### MSC:

80A22 | Stefan problems, phase changes, etc. |

76R10 | Free convection |

76M12 | Finite volume methods applied to problems in fluid mechanics |

80M12 | Finite volume methods applied to problems in thermodynamics and heat transfer |

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\textit{S. Wang} et al., Int. J. Heat Mass Transfer 53, No. 9--10, 1986--2000 (2010; Zbl 1190.80044)

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