ABSTRACT
This chapter describes numerical methods for solving heat transfer problems involving liquid-to-solid phase change, which is mostly important in materials processing. Materials processing problems often involve phase transformations from liquid to solid, solid to solid, or gas to solid. Transport phenomena significantly affect the morphology and the velocity in phase transformations, and therefore the quality of the resultant materials. Heat transfer problems involving melting or solidification are generally referred to as phase change or moving boundary problems, and also as Stefan problems. The latent heat associated with the phase change is evolved at the solid/liquid interface when liquid is transformed to solid. The coordinate transformation technique can be extended to multi-component phase change problems in which the material does not have a distinct solid/liquid interface; instead melting or solidification occurs over a temperature range. The solid and liquid phases are separate by a two-phase moving region, the ‘mushy zone’.
