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.

Yeah, when you dunk the rod in water, the relatively small radiative and
convective losses of heat are replaced by a terrifically large conductive
loss of heat.

The extremely quick cooling is why you dunk the bar in water in the first
place.

-Chuck Harris

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