Posted by Iain McClatchie on November 18, 2005, 7:29 pm
Daestrom> Two surfaces spaced a modest 1/2 inch apart with
Daestrom> emissivity/abortivity of about 0.5, with temperatures
Daestrom> of 460 R and 461 R will have a net radiant flux of
Daestrom> q' = emissivity*Stefan-Boltzmann * (461^4 - 460^4)
Daestrom> = 0.34 BTU/hr-ft^2 (R-value of 3.0).
Seems like the air-gapped foil-backed insulation's R-value is
dependent on the foil temp.
i^4 - (i-d)^4
= -4i^3d +6i^2d^2 -4id^3 +d^4
So the air gap heat flow is just about linear with delta-T, but
goes up as the cube of ambient temp. So while you got an
R-value of 3.0 for the interior of a cold refrigerator, the same
foil against the interior of a house would see an R-value of 2.0.
Seems like the R-value would be a lot higher if the foil faces
the cold side. If it's -30 F outside, R-value of that gap is 3.75.
Posted by nicksanspam on November 18, 2005, 10:09 pm
What 1/2"? Why 0.5? Most materials are closer to 1.
= i^4 -(i^2-2d+d^2)(i^2-2d+d^2)
= i^4 -(i^4-2i^2d+i^2d^2-2i^2d+4d^2-2d^3+i^2d^2-2d^3+d^4)
= 4i^2d-2i^2d^2 -4d^2+4d^3 -d^4
Yes, with a + vs -, if i>>d.
You've just reinvented the "linearized radiation conductance" :-)
G = 4x0.1714x10^-8Tm^3 Btu/h-F-ft^2, where Tm is the mean Rankine temp.
But air spaces also transfer heat by convection and conduction...
That also depends on convection and conduction, which depend on the temp diff
and the direction of heatflow.
Our local college keeps liquid helium for their electron microscope's
superconducting magnet in a Dewar vacuum flask surrounded by liquid
nitrogen, with insulation around that.
H2 boils at 4.2 K. N2 boils at 77.3 K. So 2 mirrors with e = 0.03 would lose
5.67x10^-8x0.03x40.75^3 = 0.000115 W/m^2C by radiation, ie 0.00002027
Btu/h-F-ft^2, ie US R49335, vs an R20 house wall.
Posted by daestrom on November 19, 2005, 6:15 pm
1/2" is just typical spacing between glazing on double-paned windows. It
doesn't factor into radiant transfer if the two surfaces are flat planes
whose area is >> spacing between them. Yes, the emissivity of many
materials are higher than 0.5. But the example (half of which has been
snipped here) compared the radiant heat loss with/without a low-e coating,
versus the conduction of having two films in direct contact. (remember Duane
had questioned why I said that emissivity is 'pretty much irrelavent' if
there is no air-gap).
The absolute temperature of most building materials is >> the delta
temperature between said materials.
The affects of convection and conduction were already discussed. Those
affects far outweigh the effects of radiant heat transfer in most building
applications. Only after reducing conduction with conventional insulation,
and controlling convection by properly designed air-gaps, does the use of
low-e coatings become a significant factor.
Interestingly, the spacing of glazing in double-paned windows is chosen to
minimize both convection currents and conduction. From a conduction
standpoint, a wider gap is better, but a wider gap allows stable currents to
set themselves up between the panes, bad from a convection standpoint.
Knowing the properties and pressure of the fill gas, one can choose a gap
that has the falling gas film on the cold pane interfere with the rising gas
film on the warm pane, and inhibit long-path (full height of pane)
I'm sure you mean the 'He' boils at 4.2K ;-)
Posted by daestrom on November 19, 2005, 3:39 pm
Yes, you have an interesting point. The absolute temperature involved does
make a difference. But contriving a system where you can get the foil to be
coldest isn't easy. You can't just put it on the outside surface,
convection losses would over-shadow any radiant issues. If the air gap is
embedded in the wall, then it will be at some temperature between inside and
outside, depending on exactly where the air gap is in relation to other
materials. I suppose ideally we would put the air gap as close to the
lower temperature side of the construction as possible. That sounds like an
outer surface with a low emissivity foil, then protected from excessive
convection losses by some thin film to form the air gap. Not sure how
practical such a construction would be in a high wind situation though.
Posted by Iain McClatchie on November 19, 2005, 10:33 pm
Daestrom> I suppose ideally we would put the air gap as close to the
Daestrom> lower temperature side of the construction as possible. That
Daestrom> sounds like an outer surface with a low emissivity foil, then
Daestrom> protected from excessive convection losses by some thin
Daestrom> film to form the air gap. Not sure how practical such a
Daestrom> construction would be in a high wind situation though.
I was thinking of foil-faced fiberglass in the wall, with the foil
plywood exterior sheath. Controlling the size of the air gap might be
tough, unless there was some sort of springy plastic spacer in there.
I suppose we could go all the way and use MLI like NASA does (many
many thin aluminized mylar sheets with vacuum gaps between, for
folks who haven't seen that TLA before). Seems MLI would work in
air reasonably well. I assume fiberglass is cheaper per R than MLI.
...but I wonder. To make code's R-19, we're going to have to use 6"
exterior walls with fiberglass. I presume that I could make R-19 with
4" MLI walls, no problem. (Or foam-filled, etc.) 4" construction is
cheaper than 6", and presumably the manufacturers have looked at