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re: hot water for storing heat
21 aug 1996
dan settles  wrote:

>hi nick,

hi dan :-)

>i keep forgetting to ask about this, but why do you use 130 degree f as
>your target temperature?

howard reichmuth, pe, who more or less invented the copper cricket, the
ecotope (pragtree farm) parabolic concentrating greenhouse, etc, told me
that it would be pretty tough to get any higher temp than that. another
good solar engineer, fred dubin, pe, from nyc of all places, told me the
same thing.

let's see. full sun is about 300 btu/ft^2/hr = 0.174x10^-8x(t+460)^4
for a non-selective surface. for a selective surface with emissivity e,
this would be
               300 btu/ft^2/hr = 0.174x10^-8xex(t+460)^4 the surface temperature of a layer of dark paint in the sun with e = 1
would be 184 f, i think, if it were insulated on the shady side, and had no
cover in front, and the surroundings were cold, and the only heat loss were
by radiation.

i suppose the surface temp of a layer of glass would be about the same,
if it had a still airspace underneath, then the black paint. the glass would
just heat up like the black paint did, until the re-radiated ir power equalled
the solar power input, if the incoming solar power had no other place to go. 

if the surroundings were at temp ta (f), eg 30 f, not absolute zero, and
the plate were a black body, this equation would become

      300 btu/ft^2/hr + 0.174x10-8(ta+460) = 0.174x10^-8(t+460)^4 or
      300 btu/ft^2/hr + 0.174x10-8(30+460) = 0.174x10^-8(t+460)^4, or
      300 btu/ft^2/hr + 100 btu/hr         = 0.174x10^-8(232+460)^4,
ie the plate temp would go up from 184 to 232 f, because the plate
would be heated by the surroudings as well as the sun.

if the plate had an emissivity of 0.7, we might have

      300 btu/ft^2/hr + 100 btu/hr = 0.174x10^-8x0.7(297+460)^4.
if we moved some air under the glazing, and heated some drums full of 120 f
water inside a solar closet, with the solar closet air heater glazing exposed
to the inside of an 80 f sunspace, we would have an average glazing temp of
ta = 100 f, and with a glazing emissivity of 1 (glass is 0.88), we might get
a useful heat output of approximately q, where 

   300 + 0.174x10-8(80+460)^4 btu/hr = 0.174x10^-8(100 f + 460)^4 + q, or

   300 + 148 btu/hr = 171 + q, so q = 267 btu/hr,

and the 171 btu/hr of heat lost from the closet glazing surface would go
into the sunspace air, which would heat the house. remove the sunspace and
expose the solar closet air heater glazing to 30 f air, and the closet glazing
temp becomes (120+30)/2 = 75 f, so we get

   300 + 0.174x10-8(30+460)^4 btu/hr = 0.174x10^-8(75 f + 460)^4 + q, ie
   300 + 100 btu/hr = 143 + q, so q = 257 btu/hr,

and the 43 btu/hr of net loss from the glazing is lost to the outside air...

at this lower temperature, the convective loss from the glazing may be larger
than radiation loss, especially since the outside air will be moving, vs the
fairly still sunspace air. let's see: if the closet glazing is like a window,
with moving 30 f outside air on one side and still 120 f air inside, it will
have an r-value of about 1, so we might figure the convective loss as

   (120-30)1 ft^2/r1 = 90 btu/hr, vs 143 - 100 = 43 btu/hr, net.

at what temperature does convective loss equal radiative loss? 

              (t-30)1 ft^2/r1 = 0.174x10^-8((t+30)/2+460)^4 - 100

at t = 80 f         50        >             122             - 100          
      100           70   about the same     171             - 100
at about 100 f, in this case. so if the air heater temp is more than 100 f,
we might use the radiation formula, and if it's less, we might use the r1
arithmetic. or we might combine them, in a big complicated quartic equation,
with u = 1.5 + v/5 as the u-value for the airfilm on each side of the glazing,
with moving air at v mph... mathematicians might enjoy that.

iron, copper and tin oxides are somewhat selective (e ~0.7), and darker
than aluminum oxide. i wonder how to make galvanized iron rust in less
than 20 years... :-) h. tabor wrote about slightly more complicated ways
of making galvanized iron selective.

>is this the maximum safe temperature for the
>plastic in the collectors or in the 55 gallon drums,

i don't know. i'd guess the max is higher. depends on how high you stack 'em.
i did try filling up a plastic paint pail with a lid with 130 f water, and
jumping on it, when demon told me that was stupid :-)

>or is there some other element in the solar closet design that doesn't
>hold up well to warmer temperatures?  

i think it's worth using a small fan to make closet collection more efficient,
and my favorite grainger fan for this, the 4c688 560 cfm fan, 10" diameter,
36 watts, about $60, has an upper temp limit of 149 f.

i'd use polycarbonate vs polyethylene glazing for the solar closet, because
it is almost as good as glass at blocking longwave ir, 1% vs 77% transmission
for 80 f ir... and putting some black window screen under the glazing reduces
ir loss.

>good luck with the youth hostel project.

thanks. the only thing that's holding it up at the moment is a possible
administrative nightmare. we are meeting with architect eric on sunday (who
recently installed all the single pane windows in the cabin), who will be
doing a lovely "rendering" for the project, as a part of the admin smoothing
process. what we build, of course, might be quite different :-)

>if i lived a couple hundred miles closer i'd come over and volunteer...

there's a place to stay :-)


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