Re: Heat transfer in a dilute gas

On Oct 8, 4:47 am, "boblat...@xxxxxxxxxxxxxx"
<boblat...@xxxxxxxxxxxxxx> wrote:
Hello folks,

I need to find out the heat transfer between two planar surfaces with
a gas in between them. The mean free path of the gas is larger than
the distance between the surfaces.

This sounds like a homework problem but isn't: it's a real
application. I want to place an Si wafer into a "pizza oven"-like
construction (i.e., horizontally between two heated plates) inside a
vacuum system to bring it up to a certain temperature. I need to find
out the time until the process window is reached.

I've already done some calculations on the radiation effects and found
that I'm almost there. A big unknown is the emissivity because the
wafer is coated with metal that undergoes a phase transfer during
heating. So I'd like to add a bit of Argon back pressure to increase
the thermal coupling.

Thanks,
robert

A vacuum is a terrible conductor of heat. It is also terrible at
convection. Radiation varies with the 4th power of temperature, but
it appears that since you want "a certain temperature", that is not a
variable you can play with to improve heat transfer.

IN THEORY...

The thermal conductivity k of a gas is given by

k = (1/2) rho * c-bar * lambda * c-sub-v

where rho is the density,

c-bar is the average velocity,

c-bar = sqrt[ 8 * K * T / (pi * m ) ]

<where K is Boltzmann's constant, T is the temperature again, and m
is the mass of the molecule>

lambda is the mean free path,

lambda = K * T / (sqrt(2) * pi * sigma^2 * P)

<where sigma is (approximately) the average diameter of the molecule
and P is the pressure>

and c-sub-v is the heat capacity per unit mass.

If you can make this equation work for you, then you are ready to take
a course in physical chemistry (the derivation was in chapter 2 of my
old P-Chem text).

IN PRACTICE...

If you can't make this work then your best bet is to follow Uncle Al's
advice and do some empirical measurements. Data trumps theory any
day, anyway.

"In theory, there is no difference between theory and practice. In
practice, however, there is." - Jan L. A. van de Snepscheut

Tom Davidson
Richmond, VA
.

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