Induction heat flux density induced by wire in a slab

AI Thread Summary
The discussion focuses on calculating the induction heat flux density generated by an infinitely long wire in a thick slab. The user is exploring two approaches: one based on induced currents from H-field circulation and another using a 2D model to determine the linear density of the electric displacement field (EDF). Concerns are raised about the limitations of electromagnetic field penetration and the potential divergence of the EDF integral. The user seeks validation of their methods and welcomes alternative solutions. The overall goal is to accurately simulate induction heating in the specified setup.
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TL;DR Summary: How to calculate induction heat flux (density) induced by an infinitely long wire in an infinitely large slab.

Hi,
I have to simulate induction heating caused by a straight long wire in a thick slab of material (no strict limitations).
To make it, in the best case I should calculate heat flux density. The heat source is a Joule heating in a slab. This way the task concludes in finding induced currents.

I have attached on the foto below task description and two approaches to solve it.

In the first approach I am calculating induced currents from H-field circulation. I am not sure in this solution as a limitation in EM field penetration depth is not occured, and I am not really experienced in electromagnetic engineering.
The second approach is based on a 2D model and aimed to find linear density of EDF. I am also not sure in it. Especially I have doubts that integral for EDF is divergent without limitations.
I want you to check my solutions, please!
May be you have another approaches to solve it, they are super welcome!

Best wishes for you!!!

Images consist of 3 Pages.
1. Task description. 2. First approach to solve. 3. Second approach to solve
 

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