Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use som sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

Thin metal film subjected to a short-pulse laser heating is considered. The parabolic two-temperature model describing the temporal and spatial evolution of the lattice and electrons temperatures is discussed and the melting process of thin layer is taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.

The article presents a computational model build with the use of artificial neural networks optimized by genetic algorithm. This model was used to research and prediction of the impact of chemical elements and heat treatment conditions on the mechanical properties of ferrite stainless steel. Optimization has allowed the development of artificial neural networks, which showed a better or comparable prediction result in comparison to un-optimized networks has reduced the number of input variables and has accelerated the calculation speed. The introduced computational model can be applied in industry to reduce the manufacturing costs of materials. It can also simplify material selection when an engineer must properly choose the chemical elements and adequate plastic and/or heat treatment of stainless steels with required mechanical properties.