Mathematics and Computers in Simulation 61 (2003) 239–247 On a fieldless method for the computation of induction-generated heat in 3D non-ferromagnetic metal bodies Ivo Doležel a,∗ , Pavel Šol´ ın b , Bohuš Ulrych c a Institute of Electrical Engineering of the Academy of Sciences of the Czech Republic, Dolejškova 5, CZ-182 02 Prague, Czech Republic b TICAM, The University of Texas at Austin, ACE 6.412, Austin, TX 78712, USA c Faculty of Electrical Engineering, University of West Bohemia, sady Pˇ etatˇ ricátn´ ık˚ u, CZ-306 14 Pilsen, Czech Republic Abstract 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. © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved. MSC: 31A10; 45F15; 35K05; 35K55 Keywords: Induction heating; Heat transfer equation; Second-kind Fredholm integral equation; Collocation schemes 1. Introduction Mathematical modeling of the induction heating belongs to relatively well explored disciplines. The model consists of two second-order (generally non-linear) partial differential equations of the elliptic and/or parabolic types, whose solution yields distribution of the electromagnetic field, eddy currents, corresponding Joule losses and consequent temperature rise of the heated body. Sometimes, however, certain difficulties have to be overcome for obtaining correct results. We can mention, for example, the temperature dependent parameters of the materials involved, specific arrangements of the heaters etc. Nevertheless, in most geometries the field equations supplemented with correct boundary conditions may ∗ Corresponding author. Tel.: +420-2-8658-3069; fax: +420-2-8689-0433. E-mail address: dolezel@iee.cas.cz (I. Doležel). 0378-4754/02/$ – see front matter © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved. PII:S0378-4754(02)00080-0