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

This paper investigates an induction heating problem in a multi-component system containing a moving non-magnetic conductor. The electromagnetic process is described by the eddy current model, and the heat transfer process is governed by the convection-diffusion equation. Both processes are coupled by a restrained Joule heat source. A temporal discretization scheme is introduced to solve the corresponding variational system numerically. With the aid of the Reynolds transport theorem, 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.