Re: Very simple question on heat transfer / thermal conductivity

Got the idea... Thanks for your help and for the relevant terms in
english.
Chau!

mmeron@xxxxxxxxxxxxxxxxxx wrote:
In article <1157315353.435053.326060@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "nassurdinhoga" <avinamal2@xxxxxxxxx> writes:
Your comment about clarity is taken into account here (I'll get away
with spelling mistakes though):

Consider the following:

1. A hollow aluminium cylinder with an internal redius Rin, external
Radius Rout.

2. The inside (the "inner cylinder") is isolated - i.e. there is no
heat flux from the cylinder towards
it's axis, only from the air outside into the cylinder.

3. To avoid the nasty parabolic heat equation, I assume the temperature
in this aluminium cylinder does not vary in space - but only in time.

4. Assume the outer temperature is fixed to be Tout = constant. This is
the boundry condition (which is not realy used since there are no
spacial derivitives).

5. Assume the temperature in the cylinder is zeros as innitial
condition. T(t=0) = 0.

6. To make things even simpler, I assume the cylinder to be realy thin,
i.e. Rin and Rout are both "large" and (Rout - Rin)/Rin is fairly
small ( this is used to set 2*Rout/( Rin + Rout) = 1 )

Anyway, to solve this thing, we have to know something about how the
heat flux, driven by the temperature difference Tout-T(t), is
proportional to to that difference.

When we solve this kind of problems whilst considering the spacial
decay in temperature, we use this (phick law?)

Heat flow = jq = -K* @T(x,t) / @x

Where K is the thermal conductivity constant.

Now I would like to replace this expression with something of the form:

Heat flow = jq = -K*( T(t) - Tout )/L

OK, here is the confusion. It is not "replace". The first equation
is valid *within* the cylinder, it is the standard equation governing
conduction. The second is valid *on the boundary*, it describes not
conduction but transfer of heat between the surface and the
surrounding air. The second is independent of the first. Finding
the appropriate coefficient there is a matter for empirical
measurement. Look up the term "film coefficient".

And, yes, the ratio of thermal conductivity and the film coefficient
has dimensions of length. It is called, in some sources, "Biot
length". But it has nothing to do with the geometrical dimensions of
the body under study.

Mati Meron | "When you argue with a fool,
meron@xxxxxxxxxxxxxxxxx | chances are he is doing just the same"

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