Re: [ATM] undercorrecting?

["Arjan te Marvelde" <arjan.te.marvelde@hetnet.nl>]

Heat loss due to radiation is determined by the law of Stefan-Boltzmann:

P = e*s*A*(T^4 - Tc^4)

Where:
  P is the effective radiated power [W/m^2]
  e is the materials' emissivity
  s is Stefans' constant (5.7 10^-8 W/m^2 K^4)
  A is the objects' area [m^2]
  T is the objects surface temperature [K]
  Tc is the temperature of the surroundings.

The interesting parameters here are e and Tc. The emissivity of polished
aluminium is about 0.04, the equivalent radiative temperature of the night
sky is generally taken as 200K (not the 3K background radiation because of
the atmosphere that's in between!).
Assuming an ambient temperature (equal to the object temperature) of 293K,
and 'grey body' radiation, the effective heat loss due to radiation is
approximately:
  E= 13 W/m^2
This has to be compared with the heat transfer due to forced air cooling,
which is about 100W/K.m^2, or to free convection, about 10W/K.m^2.

When I plug this in my FlexPDE mirror cooling model (10"x3/4" plate), the
front side indeed cools under ambient temperature, but only by 0.015K. The
undercorrection expected to result from this is, in my opinion, negligible.

For those who want to dig further, see also
 http://www.electro-optical.com/bb_rad/emissivity/emisivty.htm and
 http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

For those interested in modeling with FlexPDE, I can send the model upon
request.

Arjan te Marvelde

_______________________________________________
ATM mailing list http://www.atmlist.net/