This paper introduces a finite element temperature-based model to represent
conduction-advection dominated heat transfer when the material is undergoi
ng phase-change. A fixed domain method is applied, so that the energy balan
ce through the interface does not need to be explicitly accounted for in th
e weak formulation of the problem, obtained either by the standard Galerkin
or Streamline Upwind Petrov-Galerkin (SUPG) procedures. The model is appli
ed to analyze a continuous casting process.