Thermal treatment of ferromagnetic pieces at medium frequency

The paper is a continuation of the research reported by the authors regarding the eddy-current heating analysis of a ferromagnetic piece heating equipment. The previous results were dedicated to circular conductors, whereas, in the present paper bars of any the cross-section shape are considered. The electromagnetic field depth of penetration being sufficiently small in comparison with the other geometrical dimensions of the bar, we will take into account only a zone in the vicinity of the bar surface, having a thickness of five times the depth of penetration. Along this depth, the problem is one-dimensional and a combined numerical and analytical approach will result in an extremely efficient procedure for the analysis of the electromagnetic field problem coupled with the thermal diffusion one.