In explaining this whole thread to an officemate ("so now here's a
topic to get a bunch of engineer's in a room arguing about") I came up
with these thought models:

For this test case I assumed the "problem" was:
Given a sheet of metal with a hole in it, where the hole is subject to
local heating that is significantly greater (exponentially) than the
temperature of the remaining sheet, will the hole become smaller?  If
not then either the material will expand sideways, or the material
will expand outward and stress the rest of the sheet, or both.  (
alternately the material is pushed into another dimension :-)

So the two test cases are as follows:

Assume an inelastic material with a hole in it.  Place a ceramic liner
inside the hole.  place a metal washer/donut/etc into the ceramic
liner.

Now you have a hole in a chunk of metal inside a hole that's insulated
from the external material which will no expand.

I beleive this is the point that the "hole gets smaller" crowd is
trying to make:  That under certain circumstances a normal sheet of
metal will behave as this model.  In this case if you heat the metal,
then depending on it's thickness it may buckle inside the hole, it may
expand outward (along the axis of the hole).  If the buckling that
occurs is small enough and even enough then it may appear that the
hole has become smaller, but I doubt it will simply be a smaller
version of the original hole - it will have changed shape.
Regardless, a shaft that used to fit will likely no longer fit.

The "hole gets bigger" crowd is simply saying that it would be a very
contrived and improbable situation for a regular sheet of metal to get
in.  It simply would not happen under normal circumstances.

I think of it as an archway in a castle.  The arch may become hot, and
the archway will become larger regardless of the heating of the
adjacent walls.  Either the arch will twist as it expands if it no
longer fits in the wall, or the wall or the arch will fail.  Either
way, the archway does not get smaller unless some sort of structural
failure occurs.

But perhaps I'm taking too simplistic of a view...

Please note that when I say the localized heating is greater, this is
not a linear function.  the heat can drop of very rapidly from the
hole to the edge and still be "even" in the sense that the entire
metal structure can easily withstand the expansion created near the
hole without forcing the hole to become smaller.  The temperature
difference must be huge to create the buckling of the metal structure
near the hole, which I view as a difficult situation to achive, if not
impossible, before reaching a liquid state at the hole.  Maybe if one
circulated liquid nitrogen around the entire sheet of metal about one
inch away from the hole...

-Adam
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