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.

翻译：本文研究含移动非磁性导体的多组分系统中的感应加热问题。电磁过程采用涡流模型描述，传热过程由对流扩散方程控制，两者通过受约束的焦耳热源实现耦合。引入时间离散方案对相应的变分系统进行数值求解。借助雷诺输运定理，证明了所提方案的收敛性以及变分问题的适定性。通过数值实验评估该数值方案的性能。