The problem may be due to the subjectivity of the observer, not a
real effect.
One dimensional heat flow along a bar will be close to the simple
step function
in an infinite one dimensional medium.
The solution is in the form of Gauss's Error Function, and any
cooling can only
reduce the rate of progress and/or amplitude of the heat front.
Unless heat is added
to the cold end of the bar there is no way that it will heat quicker.
The radiation can only be switched off by reducing the surface
temperature
which in turn rapidly reduces the temperature gradient driving the
heat front.
Thats my 2c worth,
Cheers, Neville Michie
On 12/06/2009, at 12:36 PM, Bruce Griffiths wrote:
Perhaps the answer is somewhat more prosaic.
Radiation and convective losses from the hot end of the bar are
significant.
In particular the radiative loss is (as a first approximation)
proportional to the difference of the 4th powers of the bar
temperature
and ambient temperature.
When one modifies the model to include radiative losses near the
hot end
that are in effect switched off by cooling then some overshoot can
occur
at the hand held end of the bar.
Bruce
Bruce Griffiths wrote:
John
That doesn't appear to reproduce what was claimed to have been
observed
at all.
The input is more like a step function that switches from hot to
cold.
This allows the simulated bar to reach a steady state temperature
distribution before decaying smoothly to a lower temperature.
Bruce
J. Forster wrote:
The effect that was described was absolutely NOT a result of thermal
conductivity being a function of temperature.
It was a dynamic effect... a transient condition. The result of
applying a
short heat pulse to a long Time Constant, distributed system.
Do the simulation I suggested hours ago.
-John
==============
Tom
The thermal conductivity isnt constant with temperature.
It also varies between different crystalline forms of the same
material.
This can be seen in more comprehensive tables of thermal
conductivity.
In particular at cryogenic temperatures the thermal
conductivity can
change dramatically (eg in superconductors)
Bruce
Excellent. Not constant; and perhaps not even linear?
If you run across a thermal conductivity table for steel
from say 0 to 1000 C let us know. From that graph we
should be able to calculate what Rex felt when he put the
red hot (1500 F?) end of the 1 inch bar into cold water.
Better yet, if some metal or material has an even more
pronounced thermal conductivity function it would make
a great party trick.
/tvb
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