Institute of Theoretical Engineering and Metallurgy of Far-Eastern Branch of Russian Academy of Sciences, Komsomolsk-on-Amur, Russia:

G. M. Sevastyanov, Researcher of Laboratory “Metal Technology Problems”, e-mail: akela.86@mail.ru

Komsomolsk-on-Amur State Technical University, Komsomolsk-on-Amur, Russia:

V. V. Chernomas, Professor of a Chair “Machines and Foundry Engineering Technologies”
S. B. Marin, Assistant Professor of a Chair “Machines and Foundry Engineering Technologies”

Amur State University of Humanities and Pedagogy, Komsomolsk-on-Amur, Russia:

A. M. Sevastyanov, Acting Head of a Chair of Mathematics

The paper deals with the use of two packages of numerical integration of the differential equations of heat and mass transfer Fourier – Kirchhoff stationary nonlinear boundary value problems arising in modeling of cooling and solidifying metal in the mold of continuous casting, on the example of the process of obtaining a cylindrical billet of aluminum alloy AD31 (АД31). One of the packages examined using finite-difference approximation of the original partial differential equations and implemented by the authors of this work, the second — non-commercial finite element package Elmer FEM company CSC — IT Center for Science Ltd. (Finland). The possibility of designing the cooling system of the mold shells on the basis of the evaporation circuit. A mathematical model of the process includes the conditions of contact and boundary heat transfer on the basis of relations for specific capacity of heat removal during boiling liquids near vertical surfaces as well as the source term in the equation of Fourier — Kirchhoff, due to the phase transition, the functional dependence of which the temperature is based on the analysis of the pseudo chart state of the alloy. Sampling spatial derivatives made by the Central difference scheme for the diffusion term of the equation and, counterflow scheme for the convective term. The rates of pulling the ingot, providing for the design under consideration mold forming a solid phase of a given thickness at the outlet of the primary cooling zone. It is shown that under certain structural and technological parameters of the stationary evaporative cooling takes place at the level of sub-critical heat flux density, which is a necessary condition for the stabilization process.

The work was supported by the Ministry of Education and Science of the Russian Federation in the framework of the basic tasks of the state in the sphere of scientific activity, the project No. 2559 “Mathematical modeling of thermomechanical processing of materials”.
The authors thank Peter Raback (Helsinki University of Technology), for advice on the use Elmer FEM in problems of heat and mass transfer in systems with phase transitions.

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