Modeling two-dimensional freezing using transfinite mappings and a moving-mesh finite element technique

Freezing phase change problems in conduction heat transfer represent a set of moving boundary problems for which much interest currently exists. In the work presented here, two-dimensional freezing is modeled by incorporating the use of transfinite mappings with a moving-mesh finite element technique. The use of transfinite mapping in a governing interior mesh motion is shown to provide very acceptable results and is demonstrated to be the most efficient general computational technique used to date. The model developed is capable of using either Cartesian or cylindrical coordinates. Both frozen and unfrozen phases may be modeled when conduction governs behavior in both. In the case of freezing of a fluid as it flows through a pipe the usefulness of always having the phase boundary coincident with element boundaries is demonstrated. Results of the model are shown to compare well with analytical and experimental results. A von Neumann stability analysis is performed for the numerical solution and tends to support the observation that the occurrence of a high Peclet number in the moving-mesh model of heat conduction may produce distortions of the numerical solution.