On a fieldless method for the computation of induction-generated heat in 3D non-ferromagnetic metal bodies

The paper deals with the mathematical and computer modeling of the induction heating of non-ferromagnetic metal bodies in harmonic electromagnetic fields. One of the main advantages of the presented method is the elimination of the surrounding air from the electromagnetic model, which strongly reduces the necessity of meshing and simplifies the computation. The task is formulated as a non-stationary quasi-coupled problem, with respect to the temperature dependencies of all important material parameters. Distribution of the eddy currents and Joule losses in the metal body is solved by a system of second-kind Fredholm integral equations. Existence and uniqueness of solution for the continuous as well as discrete problem is shown. Convergence results for the numerical scheme are presented. The theoretical analysis is supplemented with two illustrative examples.