Authors & Affiliations
Gladyshev Yu.A.1, Kalmanovich V.V.1, Seregina E.V.2, Stepovich M.A.1
1 Tsiolkovsky Kaluga State University, Kaluga, Russia
2 Bauman Moscow State Technical University (Kaluga Branch), Kaluga, Russia
Gladyshev Yu.A. – Associate Professor of the Department of Physics and Mathematics, Docent, Tsiolkovsky Kaluga State University.
Seregina E.V. – Associate Professor of the Department of automatic control systems, Cand. Sci. (Phys.-Math.), Bauman Moscow State Technical University (Kaluga Branch).
Stepovich M.A. – Professor of the Department of Physics and Mathematics, Dr. Sci. (Phys.-Math.), Professor, Tsiolkovsky Kaluga State University.
In the paper, the problem of mathematical modeling of the stationary heat transfer process in a multilayer medium possessing cylindrical symmetry is considered. For modeling, the matrix method and the method of Bers generalized powers were used together. The proposed method has many applications. One of objects of the application of the developed approach can be a fuel element of the nuclear reactor.
The proposed matrix method is reduced to successive multiplication of second-order functional matrices. Their components at each point are determined by the physical and geometric parameters of the current layer. This method can be applied to an arbitrary number of layers. The use of the ap-paratus of Bers generalized powers made it possible to obtain in a single analytical form the solution of the problems of heat and mass transfer in a medium with various types of symmetry (shear, axial or central), also to take into account the dependence of the layer parameters on the coordinate.
Previously, we used these methods to simulate both stationary and non-stationary heat and mass transfer in a multilayer planar medium with a shear symmetry. In this paper, some of the possibilities of this methods are demonstrated by example of modeling the heat distribution in a fuel element of the nuclear reactor. In particular, the possibility of taking into account the dependence of the heat conductivity coefficient of a material on its temperature is considered. For this it is proposed to artificially break the medium into layers so that on each of them the temperature difference is relatively small so that the value of the coefficient of heat conductivity on the layer can be considered constant.
A more general spatial problem is also briefly considered. In solving this problem, the methods are used together with the classical Fourier method.
The joint application of the matrix method and the apparatus of Bers generalized powers can be promising for solving transport problems in a multilayered medium, including nonlinear ones.
mathematical modeling, matrix method, Bers generalized powers, heat and mass transfer, axial sym-metry
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