Nah... The thermal conductivity of a film coefficient for air is not the
same as the thermal conductivity of air. The thermal conductivity is only
relavent in a very thin layer against the surface (much less than 10 mm).
Moving outward, the viscosity and velocity of the air become dominant.
Given the film coefficient of air against a vertical surface of about 25
W/(m^2-K), I make it out to only be about 8,000 C. ;-) Having forced air
convection (or a good 'stiff' wind) can improve the film coefficient to
almost 200 W/(m^2-K) (down to 1,000 C ;-). Water cooling can be as high as
5000 to 10000 W/(m^2-K) (as low as 20 C).
I did hedge my number with "very roughly", figuring I could be 2
orders of magnitude off and still make the point.
But larger wires, and those of Al can develop such a gradient more easily.
And true, boiling heat transfer can be several orders of magnitude better,
but one then has to worry about exceeding the critical heat flux (also known
as 'departure from nucleat boiling', 'boiling transition', or 'dryout').
Whether the water is circulating or not, and how far the bulk water
temperature is from saturation also become important (i.e. becomes a real
engineering nightmare).
A spiral of #10 bare copper wire in a plastic garbage can full of
water makes an impressive dummy load, up until the water gets hot
enough to melt the plastic can. Then the hot water gets loose. Keep a
good chair handy.
The industry has a long history of success using pressurized hydrogen. Most
large generators and their connections to step-up transformers are cooled
this way. Much better cooling than plain air, allowing much higher current
densities. And with the same material properties, stronger temperature
gradients.
Except all of the H2-cooled gen-xfmr leads that I've seen use hollow
conductors with H2 forced through the center as well as surrounding the
outside. Similarly, the water-cooled conductors that I've seen are those
found in generators and the water flows down the center of the hollow
conductor. Not much of a temperature profile when the cross-section is
mostly cooling water ;-)
True, but one usually designs to avoid melting, much less boiling.
Fact is, in 60hz applications, the usual design restrictions regarding
skin-effect overshadow any problems with centerline temperature concerns.
Perhaps engineers working with high-current DC applications are more
concerned with the temperature gradient issues. But I suspect it is still
small for good thermal conductors like copper.
I jumped into this fray when 'TokaMundo' said, "In a wire,....would show the
wire at the same temp from center to outer surface". I think we agree this
is wrong. And I agree that the temperature gradient is not severe for
conductors made of Cu or Al under normal circumstance such as air cooling.
But *some* gradient *must* exist, otherwise the centerline temperature must
increase (due to heat generated and not conducted away) until a gradient
begins to conduct heat away as fast as it's created by the electric current.
Wonder how bad it is for graphite rods used in electric furnaces? Of course
graphite has a much higher melting temperature so it can withstand a strong
gradient. But graphite, with its lower thermal conductivity and higher
resistivity, probably develops a very strong gradient. Coupled with the
temperature coefficient of resistivity, it might make for an interesting
current distribution. Even for DC applications.
True. But below the melting point, it isn't hard to approximate the
variance with a low-order polynomial using temperature alone as the
independent variable. I would think this would make it relatively easy to
incorporate into the integration. Haven't tried it though, so who knows???
daestrom
My conclusion from this thread is that skin effect can be important at
60 Hz in entirely practical situations, and thermal gradients in
copper or aluminum conductors are inconsequential unless the current
is high and the cooling novel. We're doing some thermocouple stuff
just now (a simulator module and a complementary measurement gadget,
for jet engine testing) so thermal stuff is on my mind.
I've done a little superconductive/cryo work, where things are very
different. Here, the thermal conductivity of metals changes radically
as a function of temperature, so the net heat flow of, say, a
stainless or manganin leadwire from 4K up to to room temp is
determined by a complex integral (the bottom line of which,
fortunately, you can just look up.)
Yeah, the Toka guy is weird. He insists on crudely insulting anyone
who disagrees with him, and he's usually wrong. Some people seek and
need public humiliation: Usenet pain sluts, as it were.
John
