10.1 Introduction

This chapter tackles magneto-thermal coupling problems and presents formulations, resolution methods, as well as the applications relating to induction heating (IH) of metallic or fluid (plasma) mediums.

IH is produced thanks to currents induced in a driver subjected to a time varying magnetic induction field. In addition, the interaction between the eddy currents and the induction field produces electromagnetic forces which act on the material. Thus, in the case of a load made up of conductive fluid (plasma), the effects generated by such forces result in gas displacement.

The expression of partial differential equations (PDE) describing the physical phenomena (electromagnetic, thermal, etc.) having a role in IH systems, is obtained from fundamental physics equations and material properties. In the case of electromagnetism, these are Maxwell's equations and electric (conductivity, etc.) and magnetic (permeability, etc.) material characteristics. In the case of thermal phenomena, they are the laws of thermodynamics and the thermal properties (thermal conductivity, specific heat, etc.) of materials. When the load consists of plasma, the flow phenomena must be taken into account using the laws of fluid mechanics.

The solution to these equations allows the field distribution to be obtained. Knowledge of these fields leads to, in addition to understanding the precise behavior of the system (overheating point, zone of saturation, etc.), an accurate evaluation of the global variables (resistance, inductance, power, force, etc.). This resolution requires the use of numerical methods able to take into account the geometric complexity (system of sheet heating, system with cold...