Hi everyone
On this matter of "the heated rod, quenched or held in air":
The punch line is my bet would be on a perceptual thing like the sense of touch perceiving more temperature ("heat") in the held end of the rod, once away from the ambience of heat near the forge and now near the ambient coolness of the quench bath. Heat transfer in solids has long demonstrated itself to be simply behaved, so bets are not high on an explanation of heat really "racing away" up the rod away from the quench bath.
More detail:
Heat conduction in a solid like iron is a well-behaved (simply, orderly, regularly) physical process - about as regular as you meet in physics (?).
In my Doctoral work on hydrogen movement ("diffusion") in the weld zone of structural steel welds, heat flow was very much in immediate proximity of view, as heat *conduction* and mass-transfer *diffusion* follow the same mathematics. If there is a constant condition, like a steel plate 1inch thick, with boiling water on one side (100degC) and water with ice in it on the other side (0degC), after a while everything will settle down and there will be a constant flow of heat from hot to cold. In effect, the mathematics of more complicated situations simplifies-out and you get the expression for
*steady-state* heat transfer (or mass-transfer). In steady state heat transfer the property of the material (the iron) which affects rate at which heat passes through it is the
*thermal conductivity*.
But that is not your situation. You are in the more general situation of changing conditions. This is known as *unsteady state heat conduction*. And *thermal conductivity* does not appear to the observer in itself. In unsteady-state conductive heat transfer you "observe" a material characteristic called the *thermal diffusivity". This is a composite the thermal conductivity and the heat capacity. Obviously, with a heat flux, some will "stay around" and some will "pass on by" (heat cap. and th. cond., resp.).
Units of thermal diffusivity, by the way, are "metres-squared per second".
One way to visual heat transfer is atoms "vibrating" in the hot part and "knocking against" neighbouring cooler atoms, passing on vibration and making these affected atoms "hotter". These in turn will "knock against" their neighbours; and so on, so on... Now don't use these visualisation like a crowbar to lever and attack at physicists talking about "phonons" and things like that - using another analogy - your "lever" has no "fulcrum"! But "vibrating atoms" gets you a long way. Certainly engineering qualification of heat transfer.
The reason for conjuring up this analogy is - these "vibrations" and "knocking against" have a certain "stiffness" and quenching in water a bar of iron does not do anything much to the "physical constants" you might derive. We are back to the "simply behaved" point.
The maths of heat flow will show that the held end of the bar will always be at a lower temperature at a given time when the hot end of the bar is quenched than it would be if the bar were "in air", cooling by convection of air and radiation to anywhere. That doesn't stop the held end of the bar getting hotter for a while, even after the hot end of the bar has gone into the quench water - with the heat "thermally diffusing" up there - but that temperature at time will be lower than for the "free" bar, as I said. I can know that because heat "flows downhill from hot to cold" in a simple regular way - it's just a simple relaxation downwards.
Hope this helps.
Richard Smith