Mathematical Models of Electromagnetic Interaction of Field Sources with Conducting Body

The chapter deals with mathematical models for studying the electromagnetic interaction of field sources with a conducting body. In the general case, the presented exact analytical solution of the field conjugation problem on a flat interface between media can be used as a mathematical model for finding the electromagnetic field. The solution has no restrictions on the geometric configuration of the external field sources, the properties of the media and the frequency of the field used. The approximate model is based on the expansion of the exact solution into an asymptotic series. The model is valid for processes in which the product of the field penetration depth and the relative magnetic permeability of the conducting medium does not exceed the distance between the field sources and the media interface. An even simpler mathematical model of a locally two-dimensional electromagnetic field is valid in the case of a close location of the field sources and the conducting medium. The model can be used to study processes with strong interaction between field sources conducting body, for example, in induction heating devices of conducting bodies. Mathematical models are considered for induction devices of heat treatment by a high-frequency field of moving conducting strips, the thickness of which significantly exceeds the field penetration depth. It is assumed that the field is created by an inductor without a ferromagnetic core in the form of current contour in the general case of a spatial configuration. Using the model of the locally two-dimensional field, the value of the surface density of energy flux into the metal strip is analyzed. It is shown that the value of this energy differs significantly for sections of the strip passing under the edge of the inductor contour and the rest of it. The mathematical model of heat transfer is substantiated, in which the temperature is uniform throughout the thickness, and the process is considered adiabatic in the longitudinal directions.