Inverse method with heat and entropy transport in solidification processing of materials

An inverse formulation is presented for phase change heat transfer with applications in materials processing such as casting solidification. The scheme predicts the proper transient boundary conditions in order to achieve a prescribed solid–liquid interface motion, as well as corresponding desired interface characteristics (i.e. planar interface). In addition to heat transfer, the model considers entropy transport for effective enhancement of the overall formulation. In particular, the second law of thermodynamics is applied in a corrective manner to support stable computations in the event of non-physical numerical results, such as numerical oscillations. Both heat and entropy transport models are implemented in a control-volume-based finite element formulation of the phase change governing equations. Numerical results are presented for sample problems in order to examine the performance of the inverse algorithm. These results indicate promising performance and good agreement with available analytic solutions. In the application problems, numerical stability is achieved with entropy based corrections of computations during solidification.