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

TL;DR

This paper develops and analyzes a numerical scheme for simulating induction heating in a system with a moving non-magnetic conductor, coupling electromagnetic and heat transfer models with proven convergence.

Contribution

It introduces a new temporal discretization scheme for coupled electromagnetic and heat transfer problems involving moving conductors, with rigorous convergence proof.

Findings

The scheme accurately simulates induction heating in moving conductors.

Numerical experiments demonstrate the scheme's stability and effectiveness.

Theoretical analysis confirms the well-posedness of the coupled problem.

Abstract

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.