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wrote:
Duane C. Johnson wrote:

daestrom wrote:

If there's 'no air gap' then the emissivity of the
foil becomes pretty much irrelevant.

I agree.

Nick, can you give us citations pro or con?

Table 2 on page 22.2 of the 1993 ASHRAE HOF covers air gaps down to 0.5",
with a footnote a: ... Thermal resistance R = 1/C, where C = Hc + EeffHr,

This is a bit offtrack, but about attic insulation...

From your calculations of a typical EeffHr (radiation coefficient) of
..04555 this would give a maximum effective R value of 22 no matter how
thick the insulation. Thicker would get you closer to it but there are
diminishing returns.

Also, not knowing the Eeff of a paper barrier, it would certainly be
higher than .05

Hc is the conduction- convective coefficient, EeffHr is the radiation
coefficient ~ 0.00686Eeff[(Tm+460)/100]^3, and Tm is the mean temp of
the air space... For extrapolation from Table 2 to air spaces less than
0.5 inches (as in insulating window glass), assume Hc = 0.159(L+0.0016Tm)/L,
where L is the air space thickness in inches and Hc is heat transfer
through the air space only.

So, the surface conductance is the sum of its radiation conductance
EeffHr and Hc, which becomes a lot larger than EffHr as L decreases.
For instance, with Eeff = 0.05 (1 foil) at 50 F, EffHr = 0.0455 (R22 :-),
but Hc = 0.159(L+0.08)/L, ie 0.17 (R5.8) for L = 1", 0.29 (R3.5) for 0.1",
1.43 (R0.7) for 0.01", and 12.9 (R0.08) for L = 0.001".

L Hc EffHr U = Hc+EffHr R = 1/U

1" 0.17 0.0455 0.2155 4.6
0.1" 0.29 0.0455 0.3317 3.0 (surprisingly large)
0.01" 1.43 0.0455 1.4755 0.7
0.001" 12.90 0.0455 12.9455 0.1

Each foil can count, on double-foil foamboard, but 2 facing foils with
an air gap only reduce the combined emissivity from 0.05 to 0.03 (1/Eff
= 1/E1+1/E2-1) OTOH, 2 foils may retain inert gas longer than 1 foil.

Notes b and c say

Values apply for ideal conditions, ie air spaces of uniform thickness
bounded by plane, smooth, parallel surfaces with no air leakage from
the space... Thermal resistance values of multiple air spaces must be
based on careful estimates of mean temp differences for each space.

A single resistance value cannot account for multiple air spaces; each
space requires a separate resitance calculation that applies only for
the established boundary conditions. Resistance of horizontal spaces with
heat flow downward are sustantially independent of temp diff [and large,
eg R8.17 for e = 0.05 with 3.5" and a 50 F mean and 30 F temp diff.]

Nick