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January 27, 2011


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Frank Walker

Nice one John!

George Storm

Not just "a bit of fun", but a nice illustration that "big" in natural systems often means "slow".
But I still felt the need to work out what the thermal resistance might mean in physical terms. So if we take the block to be about 20x20x10cm high, the thermal resistance given corresponds to the interface being...
. rather thin (about 1-mil or 30-um) if its a good insulator such as expanded polystyrene, or
. a few mm upwards if it's almost anything solid.

But, while we are on educational diversions...
One of the "tools" I find useful in nearly every area of work is knowledge of the relevant scaling laws. That is, what happens if you take a geometrically similar structure with all dimensions scaled linearly.
Of course you need to know where scaling works well and where it is at best a guide; speed of MOSFETs at small geometries is an example of where simple (purely dimensionally based) scaling laws break down.
But in many (maybe most) other situations basic scaling laws work very well. Heat transfer works is one of these, and for most cases right down to nanometer dimensions:- the time constants of thermal systems vary as the square of the linear dimensions.

Naturally we can confuse ourselves when the problem is presented (as originally here) in a mixed format. I.e. the thermal resistance as a "given", whereas thermal mass is calculated from geometry), so we need to 'factor in' that thermal resistance scales inversely with linear dimensions.

Jean-Marc Nogier

The aluminum mass has a temperature gradient between the base plate (bottom) and the ambiant (top).
I am wondering what temperature is reached at say 5*Tau, and where is this temperature located ?

John Dunn

Hi, Jean-Marc.

I actually haven't figured out how to deal with the real life issue of there being a thermal gradient in the aluminum block which is why I assumed that there was zero assumed thermal resistance in the aluminum block itself. For estimation purposes, this was good enough, but clearly incomplete.

Maybe someone can help us out here?

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