3. Conclusion

We have attempted to take stock of the problems posed by the study of heat transfer in processes involving solid-liquid change of state. Analytical methods and numerous numerical techniques developed in recent years now make it possible to account for phenomena revealed by experiment.

However, this is a very active field of research, and work in progress aims to provide reliable tools for studying industrial processes, while avoiding the systematic use of detailed physical models requiring significant investment from a numerical point of view.

This presentation recalls what has already been learned about heat transfer, but many aspects could not be covered here. Certain transfer modes (turbulent regimes, as in electromagnetic stirring in metallurgy or radiative transfers in materials), certain couplings (competition between thermal gradient...