Skin Effect in Wires.
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jneutron
diyAudio Member

Join Date: Jan 2004
Location: Long Island NY
Quote:
 Originally Posted by Mark Tillotson The skin depth of copper is 8mm or so at 60Hz, why the 2" thick walls?
It drops off slowly. The exponential equations (what almost everybody touts as "skin effect") actually does not describe what happens within a cylindrical conductor. It describes penetration depth for E/M waves that are normal to a flat surface. As the conductor morphs from flat to cylindrical, the fields within fail to fall off as the planar model describes.
If you wish to know the exact skin depth, you need to use
Bessels. And they do not describe skin depth as shallow as the exponential.

Quote:
 Originally Posted by PRR Skin effect is hardly important. As discussed, when wires get hot, you need *surface area* more than *area*. Continue my 1" wire up to 4". By area, it would carry 16X the current; by surface area, only 4X current. So it can only carry 4X the current, if current is limited by heat. Then you want 4X the copper in 16X the area: you want 3/4 hollow. 3.46" ID 4" OD pipe, 0.27" walls. That's just an example from an assumption that a 1" conductor gets hot at high current. JN asserts that 2" walls work for him--- he does bigger stuff than I want to work with. The implication is that conductor 2" thick and cooled on one side is about as thick as is worth doing; any thicker is a waste of copper. At some point we could write an equation comparing lateral thermal resistance to lengthwise electrical resistance, then factor in acceptable temperature and cost of metal (of various shapes).
Well, write the equations... Show the exact solution, but use Bessels, as the exponential is wrong.

I will say, all your discussion of heating, surface area are are spot on. But you are not positioned to even worry about the regime I speak of. So glibly discounting the science... That is not an accurate position. However, the regime discussed is beyond the experience of most so is not a worry..

As a point of interest, my warm to cold feedthroughs traverse the room temp to 4.5 Kelvin domain, and as the copper gets colder the conductivity rises. As that happens the skin depth decreases. At 60 hz the conductivity at 20 to 50 Kelvin increases so much that the skin depth decreases to the .050 inch range, and the current density related dissipation begins to compromise the connections between the copper and superconductor, not a good thing. While we start with a 2 inch diameter copper conductor, by the time it gets to liquid helium temps it's just a 2 inch diameter shell of .050 thickness, resistive wise.
The navy with their superconducting motor drive r and d...the superconducting windmill turbines..all have to worry about these details..me, I just worry about lunch...

Jn
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Last edited by jneutron; 16th May 2019 at 02:45 AM.

 16th May 2019, 12:32 PM #303 audiofan   diyAudio Member   Join Date: May 2003 Location: quebec I found this on internet... quite easy to read .... What Is the Skin Effect? | Reactance and Impedance -- Inductive | Electronics Textbook
 16th May 2019, 06:55 PM #305 Guerilla   diyAudio Member   Join Date: Feb 2018 Location: Aalborg Denmark What a jurney this thread ��

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