Contrary to the isothermal freezing of a pure metal, a liquid alloy freezes partially and gradually until its temperature drops to an eutectic temperature and then the remaining liquid freezes isothermally at that temperature (the solidus temperature) [4]. Thus, there is a “mushy” region between the solid and the liquid and the three regions are separated from each other by two isothermal surfaces, one at the solidus and the other at the liquidus temperatures. Inside the intermediate phase, the gradual freezing of liquid generates heat (so an extra term is added to the heat conduction equation there). At the solidus temperature the remaining liquid freezes releasing latent heat (hence a Stefan condition there), while at the liquidus temperature no latent heat is generated (so the heat fluxes simply balance each other). On the fixed boundary (the outside) we assume the temperature to be prescribed. Heat sources or sinks are also allowed inside.