Voltage and Current Excitation for Time-Harmonic Eddy-Current Problems

Abstract

We want to give a systematic presentation of voltage or current intensity excitation for time-harmonic eddy-current problems. The key point of our approach resides in a suitable power law, that permits to understand the role of voltage excitation. We also enlighten the influence of the boundary conditions on the proposed formulations.

Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace

“…In order to impose the current intensities across the inductors and to avoid relaxing the Faraday's law as we did in previous sections, the authors of [2] propose to modify the Ohm's law as follows (24) Notice that, in this way, the current density is divided into two parts: σ E and a source term which is distributed in the coils Δ k . Then, by using the Faraday's law in R 3 , we notice that Eq.…”

“…(11) In Remark 2.2, we will detail another alternative to impose the current intensities, based on the modification of the Ohm's law in Δ. This option has been proposed, for instance in [2], in the context of bounded domains.…”

A formulation of the eddy current problem in the presence of electric ports

“…We want also to note that the choice of the correct boundary condition for the electric field on D is a delicate problem: for instance, imposing E D × n D = 0 on D is not possible. In fact, as proved in [5], Theorem 1.1, solving (23) with this boundary condition on D , instead of εE D · n D = 0, would furnish a solution of the eddy current problem with assigned J e and E × n = 0 on ∂ . Since this solution is unique, it cannot satisfy an additional condition like a prescribed voltage or current intensity.…”

“…On the common interface between the two models, the boundary data for the domain where the eddy current model is considered are either input current intensities or voltages. For a general description of these type of problems, see, e.g., [5,12,16,19,20,22].…”

“…In fact, for the eddy current problem (1) and (2) with boundary conditions (8) the electric field E C and the magnetic field H are uniquely determined (see [5], Theorem 1.1); hence, if J = 0 they are both vanishing.…”