DESIGN OF 2-DIMENSIONAL STEFAN PROCESSES WITH DESIRED FREEZING FRONT MOTIONS

This paper presents a methodology for the design of two-dimensional solidification processes. It is aimed particularly at the calculation of the boundary flux or temperature for a body that solidifies with a desired motion of the freezing front. Such problems are of particular technological significance, considering that the freezing front motion is directly related to the quality of casting. Solution of these problems can be used to achieve a desired cast structure, to optimize the time of casting, to Prevent choking of the liquid flow, or to control liquid feeding to the contracting front so that cavities and partial solidification in complex castings are avoided. Spatial smoothing and a modification of Beck's future information method are used to solve this ill-posed design problem. A moving and deforming finite-element formulation is employed. The accuracy of the method is demonstrated through several two-dimensional numerical examples.