timization of the a Transverse Fl ction Furnace of a Thin Plate

This paper presents the analysis of a transverse flux induction furnace. The originality of the analysis presented in this paper is to use successively three different formulations in order to solve the magneto-thermal coupled problem. The Whitney elements (node based, edge based, facet based and volume based elements) are shown to be a convenient mean to perform naturally that coupling and to fullfil convergence conditions for the iterative solver. Index ternrs - Coupling, eddy currents, electromagnetic heating, finite element methods, induction heating, thermal devices. I. INTRODUCTION Induction fumaces can be divided into two categories: longitudinal flux furnaces and transverse flus furnaces. While a 2D analysis is generally sufficient for longitudinal flux devices ( 11, transverse flux furnaces need a 3D analysis. From a physical point of view, an induction fiirnaxe is a magneto-themial coupled problem. The coupling is due to the Joule losses acting as a source in thermal field equations and to the temperature dependence of the electric conductivity. The latter is neglected in this paper. All the fields involved in tlus 3D coupled magneto-thennal problem are represented with Whitney elements (2). The four kinds of such elements (based on nodes, edges, facets and volumes) are used. The problem is solved in 3 weakly coupled steps. The first step consists in solving the electrokinetic problem by a mixed formulation (3) using facet based elements or by a generalized source magnetic fields using edge based elements (4). The magnetodynamic problem is solved at the second step with the modified vector potential a* using edgc based elements or a h$ fomiulation using edge based and node based elements. The last step consists in solving the temperature problem in the tlun conducting plate by a classical T formulation using node based elements. The thennal source due to Joule effect is represented in ths formulation with volume based elements. An application of transverse flus induction furnace is presented. For technological purposes, an ((as unifomi as possible )) distribution of Joule losses is desired for a suitable heating of the thin plate. A special attention is therefore paid