A numerical scheme for solving an induction heating problem with moving non-magnetic conductor

Abstract

This paper investigates an induction heating problem in a multi-component system containing a moving nonmagnetic conductor. The electromagnetic process is described by the eddy current model, and the heat transfer process is governed by the convection-diffusion equation. The two processes are coupled by a restrained Joule heat source. A temporal discretization scheme is introduced to numerically solve the corresponding variational system. With the aid of the Reynolds transport theorem and a density argument, we prove the convergence of the proposed scheme as well as the well-posedness of the variational problem. Some numerical experiments are also performed to assess the performance of the numerical scheme.