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a translucent solar window collector?
16 aug 1996
thermal shades are nice for windows on winter nights, but they are usually
opaque, so we have to open them to get solar heat and light into a room in
the morning, and close them again at night. if they are closed all day, they
don't provide daylight, and they prevent heat loss at best, vs collecting
solar heat... 

full sun is about 10,000 footcandles, but a well-lit room is only 50 fc, so
we could attenuate the sun by 200:1 and still have lots of light in a room,
if the whole south wall were a window. or have a 20:1 attenuation with 10%
of the south wall. 50 layers of very thin plastic might have an r-value close
to 50, and an attenuation of 200, and provide diffuse light for a room...

that's a lot of layers. fewer would be less bulky on a roll-up window blind.
should some of them be tinted or reflective? how efficient could 3 layers be?

cathy woodgold is thinking about using 10 layers of thin plastic glazing
inside a south window, with a possible improvement: seal the lower edge and
sides of each layer but leave the top open somehow, so if the air temp inside
a glazing cavity is less than the room temp, the air stays there, but if it's
warmer, it rises into the room... this would reduce the heat loss back out
of the window, by keeping some of the glazing cavities cooler than if they
were all sealed. but a large area sandwich with thin airspaces might have
a thermal resistance from one layer to the next that is a lot less than the
convective resistance for vertical airflow, so leaving the top open might
not help a lot... would it help to seal some of the cavities, with a little
water inside, to try to make heat pipes? would this thing get so hot inside 
that the plastic would melt?

a square foot of collector might look like this, schematically, with
no upward convective airflow:

        90%    90%
         | r1  | r1  | etc |     |     |     |     |     |     |
32 f     |     |     |     |     |     |     |     |     |     |  72 f
         |     |     |     |     |     |     |     |     |     |
300 -->  |     |     |     |     |     |     |     |     |     |  105 -->
btu/hr   |     |     |     |     |     |     |     |     |     |  btu/hr
         |     |     |     |     |     |     |     |     |     |

the equivalent electrical circuit might look like this

         t1    t2    t3    t4    t5    t6    t7    t8    t9    t10
         |     |     |     |     |     |     |     |     |     |
32 --ww--|--w--|--w--|--w--|--w--|--w--|--w--|--w--|--w--|--w--|--ww-- 72
         ^     ^     ^     ^     ^     ^     ^     ^     ^     ^
         |     |     |     |     |     |     |     |     |     |
         i1    i2    i3    i4    i5    i6    i7    i8    i9    i10

ie a string of resistors with small current sources (the sun absorbed
by each glazing) feeding each node...

here's a little basic program that estimates the temperatures of 10 layers of
glazing, with full sun shining in the window, when it's 32 f outside and 72 f
inside, with a us r-value of 1 for each glazing cavity and an absorptance of
0.1 for each glazing, and no reflectance, with still air inside and outside
the house:

10 'calc temps for series glazing
20 i=300'solar input in btu/hr-ft^2
30 t=.9'transmittance of each glazing layer
40 r=1'us thermal resistance of each glazing cavity
50 ta=32'outdoor temp (f)
60 ti=72'indoor temp
70 i(1)=i*(1-t)'sun power absorbed by window (btu/hr)
80 print int(i(1)+.5);tab(6);
90 for n=2 to 9'calc and print sun power sources
100 i(n)=t*i(n-1)
110 print int(i(n)+.5);tab(6*n);
120 next n
130 i(10)=t*i(9)
140 print int(i(10)+.5)
150 te(10)=ti+r*i(10)'thevinin equiv temp of innermost glazing
160 rt(10)=1'thevinin equiv resistance of innermost glazing
170 for n=9 to 1 step -1'calc rest of thevenin equiv temps & resistances
180 te(n)=te(n+1)+r*i(n)
190 rt(n)=11-n
200 next n
210 for n=1 to 9'print thevenin equiv temps
220 print int(te(n)+.5);tab(6*n);
230 next n
240 print int(te(10)+.5)
250 for n=1 to 9'print thevenin equiv resistances
260 print int(rt(n)+.5);tab(6*n);
270 next n
280 print int(rt(10)+.5)
290 tg(1)=ta+(te(1)-ta)/(rt(1)+r)*r'window temp (f)
300 print int(tg(1)+.5);tab(6*1);
310 for n=2 to 9'calc rest of glazing temps
320 tg(n)=tg(n-1)+(te(n)-tg(n-1))/(rt(n)+r)*r
330 print int(tg(n)+.5);tab(6*n);
340 next n
350 tg(10)=tg(9)+(te(10)-tg(9))/(rt(10)+r)*r
360 print int(tg(10)+.5)

the i's above (rounded) are:

 30   27    24    22    20    18    16    14    13    12    (house)

the "thevenin equivalent temperatures" for each glazing layer, looking to
the right (an electrical model that simplifies calculations) are: 

 267  237   210   186   164   145   127   111   97    84

the "thevenin equivalent resistances" for each layer are:

 10   9     8     7     6     5     4     3     2     1

and here are the glazing temperature estimates:

 53   72    87    100   109   115   117   116   109   96

it looks like there is a max temp in the center, which makes sense, because
there are low thermal resistances on each side, but the center glazing isn't
very hot, even in full sun.

this calculation might be expanded to estimate the solar collection efficiency
including glazing reflections, different thermal resistances at the ends,
selective upwards convection from each space, tints, selective surfaces, heat
loss at night, daylighting, summer performance with the shade turned upside
down, etc...

nick



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