This paper provides a methodology for the solution of certain inverse heat transfer problems with phase changes. It is aimed particularly at the design of casting processes. The idea is to use the inverse method to calculate the boundary flux history that will achieve the velocities and fluxes at the freezing front that are needed to control liquid feeding to the front, as well as yield the desired cast structure. The proposed method also can be applied to predict the freezing front motion using temperature measurements at internal points. A boundary element analysis with constant elements is used here in conjunction with Beck’s sensitivity analysis. The accuracy of the method is illustrated through one-dimensional numerical examples. It is demonstrated that, by using an integral formulation, one can extend all of the current methods for solving inverse heat conduction problems with stationary boundaries, to inverse Stefan problems. Such problems are of great technological significance.

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