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re: solar heating for barn
9 feb 2004
duane c. johnson  wrote:

>> > > nrel data indicate december is the worst-case month
>> > > for solar house heating in helena, when 390 btu/ft^2
>> > > of sun falls on the ground and 810 falls on a south
>> > > wall on an average 21.2 f day with an average daily
>> > > high and low of 11.2 and 31.3, for an average daytime
>> > > temp of about (21.2+31.3)/2 = 26.3.
>> in a sense. i didn't explicitly calculate collector efficiency
>> in the rest of my posting, but i did take account of the ambient
>> temp, the r1 glazing with 90% solar transmission, and so on, in
>> calculating the indoor air temp. care to go back and calculate
>> the collector efficiency, ie the net daily heat delivered to
>> the barn divided by the daily solar energy that falls on the
>> outside of the collector?

>if the collector works for 6 hours on an average december day,
>you might have 82.2k = 6h(t-26.3)103ft^2/r1 + 24h(t-21.2)160,
>approximately, which makes the average barn temp t = 40.4 f.
the left side of the equation is the aamount of sun that passes
through the collector glazing on an average december day, and
the right is the heat loss through the collector glazing over
6 hours, when i assumed it was warm and working, plus the heat
loss of the barn. if 82.2k/0.9 = 91.3k btu of sun were to fall on
the glazing and it were to provide 24h(40.4-21.2)160 = 73.7k btu
of useful heat, the collector efficiency would be 73.7k/91.3k = 81%.  

i assumed the barn and outdoor temps were constant and the
air temp next to the glazing was the same as the barn temp,
while the collector was working, ie barn air rises up between
the screen and mesh, then gets heated as it passes from south
to north through the warm mesh. i also assumed the air temp
inside the glazing was the same as the outdoor temp during 
the 18 hour non-collection time.

>to review:
>1 transparent layer.

r1, with 90% solar transmission...

>no air insulator spaces.

i think of that r1 as coming from the slow-moving air layer
near the inside of the glazing. it's really closer to r2/3, with
a moving air layer outside the glazing with less resistance,
depending on wind, and there's radiation loss too, and the 
glazing absorbs some (2%?) of the sun, which lowers the heat
loss from the inside, and each of the two air-glazing interfaces
reflects some (4%) of the sun, and some of that is rereflected
from inside to outside, but i try to make these calculations
really simple. r1, period :-) we can worry about the 2nd decimal
place after our houses are 90% solar heated.

increasing the space between the glazing and screen decreases
the air velocity and inside film conductivity (about 1.5+v/5
btu/h-f-ft^2 for a smooth surface like glass in v mph air,
or 2+v/2 for a rough surface like stucco.)

>ambient temperature is 26f

during the day...

>barn temperature is 40f
>temperature rise is 14f

>not a sophisticated collector but doesn't need to be
>for such a low temperature rise.

bigger might be better.

>i have done some experiments with a test collector that
>operated at 0% efficiency. it was made with 2 glass layers
>and an aluminum flat black painted absorber all spaced
>with 3/4" gaps. i used 6" of iso board insulation.
>this high performance collector has:
>2 layers of transparent glass insulation.
>2 layers of stagnant air insulation.
>stagnant air is the primary transparent insulation.
>this collector can reach a temperature rise of about
>340f above ambient. 


>this is what i call stasis temperature. at stasis
>the collection efficiency is 0% as no heat is being
>if all the heat removed until the absorber temperature
>is the same as ambient the efficiency is 100% although
>not useful.
>most collectors operate between these extremes.
>gary's collector has no stagnant air insulation.

i'd say it has slow-moving air, with some insulation,
we could estimate how much. his 4% vent area keeps 
the temp rise low, which makes it efficient. more vent
area would raise efficiency, but it would also raise
the heat loss at night, with r1 vent vs r19 wall area.

>this would seriously limit the stasis temperature rise.
>my guess is gary's stasis temperature rise would be
>1/4 to 1/3 rd that of my example.

with the vents blocked... crudely speaking, i'd say
a square foot of r1 glazing transmitting 90% of 250
btu/h ("full sun") with no airflow or heat loss or
heat storage behind it would lose dtx1ft^2/r1 to the
outdoors, so dt = 0.9x250 = 225 f. two layers would
gain 0.9x0.9x250 = dtx1ft^2/r2, so dt = 405 f. the 
real temp rise would be less, because of reradiation.

>let's assume the value is 1/3 of 340f or 110f.
>in the case of a 14f rise the collector efficiency
>might be:
>(110f - 14f) / 110f
>  96f        / 110f = 87%

with the vents blocked? :-)

>the part missing in your calculation is losses due to
>re-radiation. in this case radiation loss is not much
>as the collector temperature rise above ambient is low.

the screen also lowers re-radiation.

>i usually make a small test model of a collector
>and cover to see how they perform. this method is
>not rigorous but quite sufficient for me.

it seems more "rigorous" than these calculations, 
but also more work :-)


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