DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD OF A CONTINUOUS ELECTRICALLY CONDUCTIVE BALL WITH SHORT-TERM INDUCTION HEATING

Abstract

A physico-mathematical model for determining the temperature in a ball valve with short-term induction heating is proposed. The ratio of Maxwell's electrodynamics and nonstationary thermal conductivity is chosen for the initial system of equations of this model, which consists of two stages. On the basis of such relations the centrally symmetric problems of electrodynamics and thermal conductivity for a continuous electrically conductive sphere are formulated. The material of the sphere is homogeneous, isotropic and nonferromagnetic. Its physical characteristics are assumed to be constant and equal to their average value in the considered ranges of temperature change. At the first stage, Maxwell's relations determine the vector of magnetic field strength and Joule heat that arises in an electrically conductive sphere due to its short-term induction heating by eddy currents. At the second stage of the heat equation, in which the heat source is the Joule heat, we find the temperature distribution in a solid sphere. The azimuthal component of the magnetic field vector and the temperature are chosen as the determining functions. To construct solutions of the formulated initial-boundary value problems of electrodynamics and thermal conductivity, a polynomial approximation of defining functions over a radial variable is used. The approximation polynomials are chosen so as to take into account the given boundary conditions for the defining functions, both on the surface of the sphere and in its center. This made it possible to reduce the initial initialboundary value problems to the defining functions to the corresponding Cauchy problems to the radially variable characteristics of these functions. General solutions of Cauchy problems with homogeneous nonstationary electromagnetic action are obtained. The action of eddy currents in the unstable mode is mathematically modeled by the electromagnetic action in the mode with a pulse modular signal. This action is given by the values of the azimuthal component of the magnetic field strength vector on the surface of the sphere. The change in Joule heat in time and temperature in the sphere depending on the amplitude-frequency characteristics of the considered unstable electromagnetic action in the mode with a pulse modular signal and the time of its duration is numerically analyzed.