Induction heat flux density induced by wire in a slab

In summary, the study investigates the induction heat flux density generated by a wire placed in a slab. It explores the relationship between the wire's current, the distance from the wire to the slab, and the resulting heat flux density within the slab material. The findings highlight the significance of electromagnetic induction in generating heat and suggest implications for applications in materials processing and thermal management.
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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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FAQ: Induction heat flux density induced by wire in a slab

What is induction heat flux density?

Induction heat flux density refers to the amount of thermal energy generated per unit area within a material when exposed to an alternating magnetic field. This phenomenon occurs due to the induced eddy currents within the conductive material, resulting in localized heating.

How does a wire induce heat in a slab?

A wire carrying an alternating current generates a magnetic field around it. When this magnetic field interacts with a conductive slab placed nearby, it induces eddy currents within the slab. The resistance to these currents generates heat, leading to an increase in the temperature of the slab.

What factors influence the induction heat flux density in a slab?

Several factors influence induction heat flux density, including the frequency of the alternating current, the electrical conductivity of the slab material, the distance between the wire and the slab, and the geometry of both the wire and the slab. Higher frequencies and better conductivity typically result in greater heat flux density.

What are the applications of induction heating in slabs?

Induction heating is widely used in various applications, including metal hardening, melting, and forging processes. It is also utilized in surface treatment, cooking technologies, and in the manufacturing of composite materials, where precise and localized heating is required.

How can the efficiency of induction heating be improved?

Efficiency in induction heating can be improved by optimizing the design of the induction coil, selecting appropriate frequencies, and using materials with high magnetic permeability. Additionally, minimizing air gaps between the wire and the slab and utilizing advanced control systems can enhance the overall efficiency of the heating process.

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