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. 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.

中文翻译：

---

求解移动非磁性导体感应加热问题的数值方案


本文研究了包含移动非磁性导体的多组件系统中的感应加热问题。电磁过程由涡流模型描述，传热过程由对流扩散方程控制。这两个过程通过受限焦耳热源耦合。引入时间离散方案来数值求解相应的变分系统。借助雷诺输运定理和密度论证，我们证明了所提出方案的收敛性以及变分问题的适定性。还进行了一些数值实验来评估数值方案的性能。