The paper presents the results of studies obtained with the development of the technology of electron-beam crucible impregnation of metallurgical silicon. It is shown that refining of silicon from background and dopant impurities in electron-beam crucible-free zone melting occurs by zone purification during melting and as a result of evaporation of impurities from the sample surface. The mathematical model and computational experiment were been performed to determine the temperature gradient at different rates of zone melting. It was found the diapason of temperature gradients, which provides the columnar structure of crystallites and the purification of the samplesdue the melting with the zone recrystallization procedure. The level of the resistivity of the ingots increases at the end.
In the work, a mathematical description of thermal processes in laser welding with the use of the classical theory of thermal conductivity was performed. The thermal cycle under the action of radiation on the surface was analyzed using the models of overall heat balance, distributed surface, point, circular and linear heat sources. The modeling of welding process consisted in solving the problem of forming thermal fields in viscoelastic polymer materials at a moving inner heat source. It was assumed that the upper part is transparent to laser radiation and the lower one has a set coefficient of light beam absorption, and their thermophysical characteristics depend on temperature. The equations of thermal conductivity and defining equations were formulated, supplemented by the boundary conditions of convective heat transfer and the initial temperature distribution. For the numerical implementation of certain equations the finite element method was used, which is based on an alternative formulation of the problem. The results of mathematical modeling showed the peculiarities of the formation of thermal fields in the transmission laser welding of polymer films at different parameters of welding mode.
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