Potential field formulation based on decomposition of the electric field for a nonlinear induction hardening model

Abstract

In this paper we investigate a mathematical model of induction heating including eddy current equations coupled with a nonlinear heat equation. A nonlinear law between the magnetic field and the magnetic induction field in the workpiece is assumed. Meanwhile the electric conductivity is temperature dependent. We present a potential field formulation (the $A$-$\varphi$ method) based on decomposition of the electric field for the electromagnetic part. Using the theory of monotone operator and Rothe’s method, we prove the existence of a weak solution to the coupled nonlinear system in the conducting domain. Finally, we solve it by means of the $A$-$\varphi$ finite element method and show some numerical simulation results.