Re: cooling

On Sat, 29 Nov 2003 20:34:08 +0000 (UTC), [EMAIL PROTECTED] (Henry
Allen) wrote:

>So,
>This maybe be a little crazy but I guess that never stopped anyone
>from posting to usenet...
>
>It is well known that the rate of cooling of a volume depends largely
>on the surface area of that volume.  I am curious what happens in the
>limit...
>
>Suprisingly, It is possible to constuct a curve that has an infinite
>perimeter while only containing a finite area (e.g. snowflake curve). 
>And, if you rotate this curve in space, you wind up with a volume that
>has an infinite surface area while only containing a finite volume. 
>So, direct application of most rate of cooling equations would imply
>an infinite rate of cooling. It's entirely possible, then, to
>construct a theoretical object you can hold in your hand that would
>drop the earth to zero kelvin if it came into contact with it.;)  Idle
>speculation on the properties of such an object is amusing, I find...
>
>Granted as atoms have a finite size and all this isn't terribly
>possible, but it does indicate that it's possible to construct
>surfaces with a huge surface to volume ratio- how do the conventional
>heat flow equations break down when you have really enormously large
>surface areas?
>Thanks!
>henry

        It's not quite that simple.  A point on the surface of a
radiating body is basically exchanging thermal radiation with whatever
is in line of sight from it.   A fractal surface mostly only sees
other parts of the same surface, so won't radiate to the black sky any
more effectively than a black, spherical surface.  However,  a fractal
surface could be  pretty good for exchanging heat with a flowing
fluid.

Steve