Thanks for your response (and Mikko Kiviranta's), as there have been very
few in this (and other newsgroups). I am asking others about their
knowledge of any cases of thermal inductance being observed, because it is
one explanation for an event that I experienced about 20 years ago. I'll
briefly describe the event.
I was holding a 6 foot long piece of rebar (about 1/2" diameter steel rod,
commonly used to reinforce concrete) at arms length while a friend I was
helping was cutting it in half with an oxy-acetylene torch (I think steel
melts at ~1400 C). It was cut in half and both ends were brightly red hot.
After cutting, I moved my hands towards the ends to hold one 3 foot piece in
each hand at the cool end. There was a D-shaped tank (about 12" wide, 3
feet long, 2 feet high, flat of D facing up) filled with water nearby, about
2 inches from the top. So I dipped one of the hot ends in the water
gingerly a few times to cool it at about a 30 degree angle from the floor.
I didn't want to make a lot of steam quickly, as I thought that rapid
cooling might alter the metal somehow and my friend was going to weld the
two pieces to a piece of angle iron afterwards. The steam ball made was
about 4-6 inches in diameter at most as I recall. Within 15 seconds or so,
the 3 foot rod I was cooling became so hot that I couldn't hold it anymore,
so I dropped it into the tank. I was still holding the other rod in my
other hand (still glowing red hot) and it was only slightly warm where I
held it. I cooled it off too and we went about the next step of welding the
two pieces to the angle iron.
I do not have access to a torch or rebar to recreate the event since then,
but I've often thought about what I experienced ever since. I wonder if I
experienced thermal inductance, analogous to an inductive kick in
electronics. I still wonder about it and would appreciate any considered
explanations you may have (or others in this group).
I looked into the case you state regarding the violation of the second law
and found an interesting statement on page 144 of
http://www.tu-harburg.de/mst/deutsch/lehre/mikrosystementwurf/pdf/kap6_eng.pdf
that leads towards "extended irreversible thermodynamics" (I'm still reading
on this). It notes the same thing you stated, and goes on to say:
"Now we can only draw the conclusion that this effect is usually of no
importance for us, but in no way we can conclude that there is no such thing
like a thermal inductance. An apparent contradiction results between
thermal inductance and the second law of the thermodynamics, which states
the well known fact that entropy is always increasing. By this it is
usually concluded, that a heat flow ?th is directed along the gradient of
temperature. On the other hand, due to the relation (see text) a constant
heat flow can appear at a thermal inductance also if the temperature
difference disappears, which apparently contradicts the statement of the
second law of thermodynamics. The above consideration shows that the
phenomenon of thermal inductance is of importance, if we consider a
high-speed process, for example the heating by short-time laser pulses.
Classical thermodynamics assumes slow changes, so that the system is in a
quasi-stationary status. By inclusion of an additional state variable (i.e.
the flux of energy), it is possible to introduce a definition of entropy,
which is in accordance to the second law of thermodynamic, whereby the
contradiction is eliminated. This theory is call extended irreversible
thermodynamics."
Post by Gerard Westendorp[..]
Post by s.morraSo it appears that thermal resistance and thermal capacitance but no
thermal inductance phenomena have been observed. Does anyone know of any
cases where thermal inductance has been observed?
If you had thermal inductance, you could let heat flow from a hot
thermal capacitance (A) to a cold thermal capacitance (B). When the
temperatures become equal, the flow in the inductance would cause
additional heat to move to move from A to B, this time against
the temperature gradient. That would violate the second law
of thermodynamics.
This would be OK if the inductive energy were not thermal, but
for example mechanical.
Oscillations related to heat are observed, for example
in Rayleigh's 'singing flame' and Rijke tubes. But the 'induction'
in these system is actually mechanical energy storage, although
the mechanical energy has been converted from thermal energy.
Thermal energy is by definition energy that is at least locally
in thermal equilibrium. As soon as energy is stored in a form
that allows you to do work, it is not thermal energy anymore.
Gerard