In this article, the reconstruction of the function describing the boundary conditions along the primary and secondary cooling zones in the 2-D and 3-D continuous casting processes of pure metal is presented. The process is modeled by the inverse Stefan problem, where additional information consists of temperature measurements at selected points of the domain. In numerical calculations, Tikhonov's regularization, a genetic algorithm, and an alternating phase truncation method are used. The featured examples of calculations show very good approximation of the exact solution. The influence of the number and accuracy of measurements are also investigated.

In this article, the possibility of the application of the homotopy perturbation method for solving the two-phase inverse Stefan problem is presented. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of the functions describing the temperature and the heat flux on the boundary when the position of the moving interface is known. The validity of the approach is verified by comparing the results obtained with the exact solution.

The article presents an algorithm of a solution of the two-phase inverse Stefan design problem. Based on the given information about the partial position of a moving interface, a functional was built defining the error of an approximate solution. To find the functional's minimum, a genetic algorithm was used, whereas for solution of the Stefan problem, the alternating phase truncation method was applied. Stability of the procedure was guaranteed using the Tikhonov regularization method. The results obtained corroborate the usefulness of the presented approach.