Dave Tweed wrote:

> Please forgive me for jumping into this thread late. I assumed that you
> were talking more or less theoretically about round holes in uniform,
> isotropic materials, and applying heat in the general region of the hole.

We started out with the quiz question "what happens to a hole in metal when
you heat the metal?" and there was the obvious answer "it grows, of
course". 

I brought up the idea that the "it grows, of course" requires a number of
assumptions to be fulfilled, and claimed (at this point pretty much
shooting almost in the dark) that there are situations where the hole may
become smaller. 

At that point this wasn't yet theoretical, and the material was assumed to
be steel or iron or similar. As we proceeded to discuss, we elaborated some
conditions and for lack of proper tools for executing enlightening
experiments, the discussion became more and more theoretical.

> Sure, if any of those things apply, some dimensions of the hole will get
> smaller. What's your point?

More or less this is my point. Maybe this is obvious to you, but it isn't
to me, and it doesn't seem to be to many others. So far I seem to have been
unable to convince Tony Smith of that possibility, but this may well be
because I don't really understand that much about the details of the
effects involved. 


> Ah, yes, hypothesizing a container that has no elasticity at all kind of
> changes the universe of discussion. 

I didn't mean to change the universe with that; it's just one aid for
explaining things. I think it doesn't have to change things. If you
simplify the temperature gradient to a cold cylinder outside and a hot
cylinder inside, there will be stress on both (on the outside cylinder
towards increasing size, on the inside cylinder towards decreasing size)
and the inside cylinder will likely grow less than it would if both were
heated uniformly. What the maximum of that reduction is I can't tell... I'm
sure I could calculate it if I spent the time.

> In that case, shrinkage of the hole requires a reduction of modulus, as I
> said before; 

Which happens (see the posted link). One question is whether the reduction
is enough.

> I'll jump back out of this thread now. Please carry on.

No matter whether you jump out or stay in, thanks a lot for your
contribution. It inspired me to research which cleared a few things up in
my head.

Gerhard

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