Induction heat flux density induced by wire in a slab

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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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