Conduction with Phase Change: Moving Boundary Problems

There are many applications in which a material undergoes phase change such as in melting, freezing, casting, ablation, cryosurgery, and soldering. Conduction with phase change is characterized by a moving interface separating two phases. Such problems are usually referred to as moving boundary or free boundaryFree boundary problems. They are inherently transient during interface motion. The motion and location of the interface are unknown a priori and thus must be determined as part of the solution. Since material properties change following phase transformation and since a discontinuity in temperature gradient exists at the interface, it follows that each phase must be assigned its own temperature function. Furthermore, changes in density give rise to motion of the liquid phase. If the effect of motion is significant, the heat equation of the liquid phase must include a convective term. However, this effect can be neglected in most problems.