Electrothermics

1.1. Introduction

In induction heating of conductive and semi-conductive materials, electromagnetic, thermal, and sometimes flow phenomena are present simultaneously. These phenomena are governed by Maxwell’s equations, the heat transfer equation, and the Navier–Stokes’ equation, respectively.

In most cases, these equations are mutually coupled by one or more parameters. The electromagnetic and thermal equations are linked by electromagnetic conductivity, magnetic permeability, and induced power. The coupling between the thermal equation and that of flow is done by the density and fluid velocity, and the link between the electromagnetic and flow equations is due to electromagnetic forces.

These phenomena are often governed by partial differential equations where the unknown is either a scalar or a vector quantity, dependent on spatial coordinates and time. In most cases, numerical methods are used to solve these equations. Nevertheless, in certain simple cases and for the understanding of the involved physical phenomena, analytic methods are also used.

In this chapter, we present different local formulations of the phenomena acting in the context of induction heating. For ease of reading, we limit ourselves to the electromagnetic and thermal equations and deal with the problem of flow in Chapter 2, in which we study inductive plasma.

We also study the problem of solving these equations using analytic, semi-analytic, and numerical methods. Particular attention is given to two numerical ...