The numerical simulation of the induction heating of three-dimensional metal bodies by moving inductors can be problematic from several points of view when using standard FE or BE schemes. In this paper we describe the main difficulties and propose an alternative modelling approach based on the reformulation of the Maxwell's equations into a system of second-kind Fredholm integral equations. These equations for the eddy currents are coupled with the heat transfer equation with non-linear temperature-dependent material parameters. Mathematical analysis of the existence and uniqueness of solution to the continuous as well as discrete problem is provided and convergence of the numerical scheme is shown. An illustrative numerical example is presented.
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