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Re: Trombe wall efficiency



Johnathan Sawyer <jfsawyer@csn.net> writes:

>I am building a house outside Boulder Co with an unvented  16 x 28 ft Trombe
>wall. The masonry wall is 12" thick and the glazing is single pane...

Pretty far into it, huh? 32 tons of masonry... Perhaps it isn't too late to
soup it up by adding some vents, and some insulation between this Trombe wall
and its glazing? :-)

>I am using an expensive ($3.20/sqft) selective coating made by an
>outfit in New Jersey.

I'd be interested to know their name, address and phone number. I wonder
how this $tuff can be attached to a masonry wall. What will the R-value be
at the interface where it attaches, if the selective surface is a metal
film with an adhesive backing? If the interface R-value is not 0 (and it
may be difficult to attach it well to roughish masonry), the film may
heat up a lot more than the wall, when the sun is shining. 

>They claim this coating gives the wall an
>equivalent of a R12 insulation value at night.

Sounds great, altho pricey, but have you asked about the temperature range?
Trombe walls usually have low temperatures, since they lose heat to the
outside world and the inside of the house, 24 hours a day, through fairly
low thermal resistances, and selective coatings usually help with high
temperature radiation losses. The formula for radiation loss is

Ur = 0.174 x 10^-8 A e ((Tw+460)^4 - (Ta+460)^4), where U is in Btu/hr,
     A is in ft^2, e is a number called emissivity, which is close to 1
     for a non-selective surface and perhaps 0.1 for a selective surface,
     and Tw and Ta are wall and outside surrounding temps in degrees F.
     (I may be doing this wrong, and I would be pleased if someone were to
     post better calculations, vs. posting talk about better calculations.) 

This is on top of convection loss, which is roughly R2, with a still
air surface and a single pane of glass and an airspace. R-values are
supposed to include some radiation loss, but roughly speaking, the total
loss per square foot is Ut = Ur + Uc, where Uc is (Tw-Ta)/R2, so if it's
0 degrees F outside, and the wall has temperature Tw, and e = 0.1,

Tw,   Ut,  Uc, Urs, Urs/Ut and Reff (the effective R-value) would be:

70    41   35  6    15%        1.7 = (70F-0F)/41
80    47   40  7    15%        1.7      ...
90    53   45  8    15%        1.7
100   59   50  9    15%        1.7

>I wonder how the thermal calculations will come out using R12 instead
>of R2 heatloss.

Much better, but it seems to me that convection will make up such a large part
of the total heat loss that the real picture will be about R = 1.7, 24 hours
a day, so the wall temp in the above case, with, say 1000 Btu/ft^2/day falling
on the wall, if it were perfectly insulated on the inside, would be such that 

1000 = 24 Ut, so Ut = 42, and the wall would have a temp of about 70F,
according to the above table.

But of course the wall is not perfectly insulated on the inside--the masonry
has a thermal resistance of about R2. Then again it may be warmer than 0 F
outside, most of the time... In this case, it looks to me like the thermal
resistance of the wall doesn't matter much during sunny days, since it will
have about the same temp as the inside of the house. It won't add much heat
to the house, but it won't be a thermal disaster either, unless the sun goes
in for a few days in a row. Another 32 ton car that gets 2 mpg, while going
10 mph, max :-) Perhaps it can still be helped, tho, into the 20th century.

Nick


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