Heat transfer with solid-liquid change of state

The liquid-solid state change of a pure material is characterized by the transformation, at constant temperature, of a liquid phase into a solid phase, or vice versa. This reversible reaction is accompanied by a consumption (fusion) or restitution (solidification) of energy: the enthalpy of mass of fusion (or latent heat of fusion). The aim of this article is to review what we know about heat transfer with a change of state in a phase-change material (PCM) where both liquid and solid phases are present.

Since Stefan's seminal work in 1891 on the thickness of the polar ice cap, heat transfer problems involving solid-liquid changes of state have been named after this physicist. These problems are of considerable importance in many technical applications and natural processes: we might mention the evolution of ice floes, food freezing, biocryogenics, molding, continuous casting, crystal growth, nuclear reactor safety, thermal control of spacecraft, thermal storage, and so on. It's also worth recalling that the first metallurgists in the Middle East cast in clay, then replaced clays with precision-grained sands and metal molds to increase casting precision. Lost-wax casting, which enables the production of parts with extremely fine details, was already known to the Egyptians in the Middle Ages. This wide range of applications explains the impetus behind the research carried out in this field over many years to better understand the dynamics of these processes.

In this article, we will present the main methods developed to solve these problems and the main results obtained. Although this presentation is essentially devoted to purely thermal aspects, we will refer to couplings with matter transfer in change-of-state processes in multi-component systems. However, we will only consider equilibrium change-of-state phenomena here, without taking into account supercooling or rapid solidification phenomena, or the physics of nucleation.