Numerical Modelling of Induction Heating for Two Dimensional Geometries

We present both a mathematical model and a numerical method for simulating induction heating processes. The aim is to determine the temperature field in a workpiece surrounded by an inductor when the inductor total current is known. We assume that all the conductor (the inductor and the workpiece to be heated by eddy currents) are cylindrical and infinite in one direction. Thus the induction heating problem can be studied in a plane orthogonal to the invariance direction. By considering the temperature in the workpiece and the complex potential in the whole plane as unknowns, we derive a model which involves the coupling of a non linear diffusion problem for with a non homogeneous Helmholtz problem for We give some theoretical results about existence and unicity of a solution, and we describe in detail a method for the numerical resolution. The numerical scheme we propose consists in a semi-explicit Euler scheme for the time discretization and a coupling between a finite element method with a regular boundary element method for the space discretization