"TokaMundo" wrote in message
...
On Tue, 02 Aug 2005 00:45:43 GMT, "daestrom"
Gave us:


"John Fields" wrote in message
. ..
On Sat, 30 Jul 2005 10:50:24 -0700, John Larkin
wrote:

On Sat, 30 Jul 2005 09:39:58 -0700, John Larkin
wrote:


At higher frequency AC, current in a wire tends to avoid the center
and crowd near the surface, "skin effect."


Hmmm...

Copper does have a weak Hall effect. And the current through a round
wire does make a circular/transverse magnetic field. So, at very high
DC currents, is the current density a bit non-uniform?

---
I would think that simple thermal effects would cause charge to flow
closer to the surface just because that part of the conductor would
be cooler, ergo lower resistance than the hotter interior.


An interesting point. *IF* the current density is uniform across the
conductor, then the heat generated would be uniform in each unit
cross-section. And a uniform heat generation in a cylindrical rod leads
to
a parabolic temperature profile, the highest exactly at the centerline,
dropping of as you move outward along any radial line.

Of course, in an AC line, the current density isn't uniform, so neither is
the heat generation. So when it comes to skin effect, it tends to lower
the
peak, centerline temperature.

Now, given that both copper and aluminum are excellent heat conductors, it
might be interesting to calculate how big a temperature profile could be
expected, and from this calculate the variation in resistivity.

I suspect the work has been done before, and that the difference is rather
modest for all but the largest cylindrical conductors.

For AC at this frequency there is nil skin effect.


That depends on one's definition of 'nil' I guess.

Current in a wire will heat the wire evenly if it is of one
material.

Not quite. If by 'heat the wire evenly', you mean heat is generated equally
in each unit of cross-section, yes. Since the resistivity of the material
is a constant, and if the current density is uniform throughout, then the
amount of I^2R losses in each unit cross-section is the same. But the
material in the center will be a higher *temperature* than that around the
periphery. It's simple really, the heat generated in the center must be
conducted to the circle of material surrounding it. The heat from the
center, combined with the heat generated in the circle of material must now
be conducted to the next circle of material surrounding that. And so on...
So the material just under the surface has heat generated directly in it,
*PLUS* all the heat generated in interior material conducted into it. For
uniform heat generation throughout the material, it is simple integration to
show that the temperature profile is a parabolic with the apex at the
centerline and temperature falling off as one moves further from the center
to the outer surface.

So the *temperature* profile throughout the conductor is far from 'even'.
If the material has a positive temperature coefficient of resistivity (as do
both copper and Al), then the resistence of the central core is higher than
the outer surface. The exact amount of temperature difference is a function
of the electrical resistivity and thermal conductance of the material.

daestrom