The major methods of mathematical modelling of solidification and melting problems were captured in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorised. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems. Numerical methods in conjunction with the control volume scheme in the fixed domain can be highly recommended for multidimensional melting and solidification problems.
Key words: Mathematical Modelling, Solidification, Melting, Analytical Methods
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