The problems of transient heat transfer of electroconductive bodies in the electromagnetic field

Abstract

The article deals with issues related to the analysis of transient propagation of the temperature field in electrically conductive bodies under the influence of an electromagnetic field. The action of the electromagnetic field on electrically conductive bodies is manifested in two versions: the possible movement of the body and a change in its temperature in accordance with the Joule-Lenz law. The energy of the electromagnetic field is used in various technological operations, including in the sense of changing the temperature of the processed objects. The use of the temperature effect of an electromagnetic field is typical, for example, for technological operations such as induction heating. A calculated study of the unsteady temperature field in this case allows us to select rational structural and operational parameters of the technological operation. In addition, it is known that a change in body temperature leads to the appearance of thermal deformations, which makes a certain contribution to the stress-strain state and can affect the working life and durability of technological equipment. Thus, the topic of the article is relevant in practical and scientific aspects. In the analysis of real structures, the features of their geometry and operating conditions require the use of numerical analysis methods. Analytical calculation methods, which most often allow obtaining approximate results, can be used as evaluative for simplified calculation models. In technological operations of induction heating of massive cylindrical billets, a spiral multi-coil inductor is very often used. The article considers the task of analyzing the spatio-temporal distribution of temperature in a cylindrical billet, which is heated by an external multi-turn inductor. The problem is considered in an axisymmetric formulation. The spatial-temporal distribution of the basic characteristics of the electromagnetic field is preliminarily determined. An analytical solution to the problem is presented, which was obtained by the Laplace transform method, under the assumption of unlimited workpiece, its ideal electrical conductivity, as well as neglecting the real heat transfer conditions at its boundary. The numerical solution of the problem is obtained by the finite element method and is devoid of these simplifications. The analysis of the influence of the size of the inductor on the nature of the distribution of the temperature field in the workpiece is carried out.