MATHEMATICAL MODEL OF THE MELTING OF MICRO-ASPERITY ARISING IN CLOSED ELECTRICAL CONTACTS

Nauryz T. Juraev D.A.
June 2023 Roman Science Publications and Distributions

Stochastic Modelling and Computational Sciences
2023 #3 Issue 1 39 - 57 pp.

In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization af-ter instantaneous exploding of micro-asperity. Melting of the micro-asperity which considered as material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component could be modeled by making use of Stefan problem in case of generalized heat equation. The process of arc erosion in electrical contacts caused by vaporization and ejection of liquid metal particles can be described using mathematical models. Refractory contact materials such as tungsten, molybdenum, and zirconium can undergo erosion due to the thermocapillary (Marangoni) effect, which is influenced by the temperature dependence of the surface tension coefficient. The mathematical model considers phenomena occurring in the melted pool’s surface layer. Careful selection of contact materials and control of current pulse parameters can maintain the contact material’s thermal stability. In this regard, similarity variable transformation is applied for solving the equation, which leads to reduction of generalized heat equation to nonlinear ordinary differential equation. It is needed to calculate temperature solution of the liquid phase and melting isotherm location. Solution uniqueness and existence is proved by employment of fixed point Banach theorem.

fixed point theorem , incomplete gamma function , nonlinear thermal coefficients , similarity solution , Stefan problem

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Internatinoal School of Economics, Kazakh-British Technical Uni-versity, Department of Mathematical Modelling and Mathematical Physics, Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
Department of Scientific Research, Innovation and Training of Scientific and Pedagogical Staff, University of Economics and Peda-gogy, Karshi, 180100, Uzbekistan

Internatinoal School of Economics
Department of Scientific Research

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