ABSTRACT
Mathematical modeling of induction heating processes started in the 1920-1930s [1-3] using analytical and semiempirical methods. The main application was coreless induction melting furnaces. In 1933, K. Reche published an interesting paper with detailed description of a new analytical method and multiple experiments that he conducted to confirm the theoretical results [4]. He considered an induction furnace as a part of a system with periodic structure, i.e., of an infinite set of furnaces with a certain distance between them. The currents in the adjacent inductors had different directions. Solution for the magnetic field and current density in the load had a form of infinite series containing Bessel and Hankel functions of complex arguments. Experiments, performed for a set of the furnace models with equal lengths of coil and charge, showed good matching with calculations. This two-dimensional (2D) method was the most advanced technique of furnace calculation at that time.
