Time harmonic induction heating problem (2D)
Hi all,
I’m Damien, a French engineer, currently in my last year of Ph.D. (hoping to defend it in October 2022).
I’m trying to solve a 2d induction heating problem (magnetodynamic) using the time harmonic formulation.
(This is my first post, so I hope to respect the community guidelines)
Problem description
Please find in the picture below the description of my problem :
The domain is composed of the following parts:

Steel cylinder (the load)

Inductor with 3 copper coils

Ambient air
According to the symmetry of the problem, i used the cylindrical coordinate (r, z) in order to simplify the problem.
Also, as the first step, I assume an isotropic medium and therefore omit hysteresis & nonlinear magnetic properties (mu(B, H)).
Methodology
My goal is to compute the temperature evolution over time due to joule heating from eddy current induced in the steel cylinder by the inductor.
My approach is the following:

Solve the time harmonic electromagnetic problem by computing the eddy current distribution in the steel cylinder.

Compute joule heating in the load from the eddy current distribution and set up as a heat source Q for the transient heat equation.

Solve the transient heat equation by computing the temperature evolution in the load.
Issues identification
My trouble is located in the electromagnetic part of the problem.
Some identified tracks :

Assignment of material properties in subregions like **electrical conductivity and magnetic permeability

2D time harmonic model formulation

Variational formulation implementations of the 2D time harmonic model in cylindrical coordinates.

In the computation of magnitudes of interests (eddy current, magnetic flux)
If someone could help me, I will be very grateful ! (Remarks : if someone is interested in the topic, I’m open to a scientific collaboration on the subject. In other words, I would like to publish on the subjects, some helpful contributor will be associate on the paper (with your agreement). Feel free to pm me)
Many thanks in advance for your time and your help !
Best Damien
Please find the code in attachment.
IH_time_harmonic.edp (7.9 KB)