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re: selection of heat source
14 nov 1997
i wrote (describing one way to heat a house in the tennesee mountains): 
>> you might consider adding a lean-to sunspace onto the south side of the
>> house. mine is 32' long and 12' deep and 16' tall, made from about $500...

randall jameson  wrote from austin tx:

>how about this on a smaller scale?

"smaller scale" may be a problem, if the object is heating a house... 
some weather data and arithmetic can give a sense of proportion here.
solar heating is easy in austin, with an average outdoor temp of 49 f
in january, an average daytime high of 59, and an average of 1200
btu/ft^2/day of sun that falls on a south wall.

>maybe a small insulated box 6 ft. tall x 4 ft. wide by 4 ft. deep.

that might be a small water heater, with 6'x4' of solar aperture that
collects an average of about 24k btu per day of heat in the winter,
equivalent to about 1 quart of oil per day.  

>with a 55 gal barrel filled with water inside.

if the sun shines on the drum during the day, and the glazing has no
night insulation, this system would lose lots of heat back out through
the glazing at night. that wouldn't happen if the drum were heated with
solar warmed air, and airflow stopped at night, leaving the drum completely
surrounded by insulation at night. but then, the drum would not have
enough surface area to be efficiently heated by the warm air. the air in
the collector would be very hot compared to the drum water, so the heat loss
from the collector to the outside world would be high. we need smaller
water containers with a total surface on the order of 10x the glazing
area for that sort of system, something more like 5 gallon paint pails
with lids, or 1 gallon milk jugs, like the meinels: 

   in our home solar heating system we used water as the thermal storage
   medium for an air-transfer unit, the water being contained in 1000
   one-gallon polyethylene bottles stacked so that air could flow between
   them. they worked satisfactorily until some desert pack rats invaded
   the storage bin, making nests of the insulation and chewing holes
   in the water bottles. 
                                 p 468, _applied solar energy_, by
                                 aden b. meinel and marjorie p. meinel
                                 addison-wesley, 1976

>the south side of the box is angled to meet the sun for dec 22nd with
>some type of plastic cover. 

that gives you about 16% more sun than a vertical south wall in austin,
maybe not worth the trouble, since it's easier to build vertical walls,
and they can be cooler in summertime, with overhangs.

a single layer of plastic might make an r1 cover with 24ft^2/r1 = 24
btu/h-f of thermal conductance. r8 walls might add 144ft^2/r8 = 18 to that,
making a total conductance of 42 btu/h-f. if the plastic transmits 90% of
the sun, which falls on the drum, the box might gain 1200x24ft^2x0.9 = 26k
btu on an average day. if it provides no hot water or heat for a home, ie
the solar energy that flows into the box on an average day equals the heat 
energy that flows out, and the average temperature inside the box were t,
26k = 24h(t-49)42, so t = 49 + 26k/(24x42) = 75 f. fairly cool. 

this temperature would be slightly higher if the water container surface
(say 240 ft^2 of it, vs 25 ft^2 for a 55 gallon drum) were heated by
sun-warmed air during the day, and lost little heat at night:

        26k = 6h(t-49)24ft^2/r1  (south wall, day)
           + 18h(t-49)24ft^2/r8  (south wall, night)
           + 24h(t-49)144ft^2/r8 (other walls, night)
            = (t-49)(144+54+432) = 630(t-40), so

          t = 49 + 26k/630 = 90 f.

this would actually be a bit warmer, since days are warmer than nights,
and this box is better insulated at night. 

>with a duct for going into a window and a duct that comes from the
>window to the bottom of the box.
the box could be smaller without the drum, say 6'x4'x6" thick, with a layer
of black aluminum window screen in the middle, with room air flowing in
at the bottom, up between the screen and the cover, sideways from south to
north through the window screen and back into the house from the space behind
the screen at the top of the box. this box might not have any insulation
at all, just wooden sides: a 1x6 picture frame glued on edge to the south
wall of the house with a can of spray foam, after attaching the boards with
a few angle brackets. it might collect 26k btu/day of heat again, with a
500 cfm window fan (eg grainger's $60 36 w 4c688 or a $12 20" box fan) in
series with a cooling thermostat in the box and a heating thermostat in the
house (eg grainger's $14.05 2e158a thermostats for both), the air to the
north of the screen might have a temperature of about 70 + 26k/(6hx500) 
= 78 f, so the box might lose 6h(78-59)24ft^2/r1 = 2.7k during the day, and
no heat at night, for a net gain of about 23k btu/day, ie a solar collection
efficiency of about 90% with an electricity consumption of about 36wx6h
= 0.2 kwh/day, ie about 2 cent's worth.  

if the box has no fan, just a couple of one way dampers made from dry
cleaner bags, the airflow would be less, and the temperature inside the
box would be greater, and the heat loss from the box would be greater, and
the amount of house heat collected would be less. one empirical formula 
says the airflow in a chimney h feet tall with a temperature difference
of dt f from top to bottom and vent holes with area av ft^2 at top and
bottom has 16.6avxsqrt(hxdt) cfm of airflow, ie 41 x sqrt(dt) with 6' of 
height and 2 1 ft^2 vents, which transfers roughly 41 dt^1.5 of heat
into the house. with a glazing to outdoor loss of (t-59)6/r1 btu/h-f and
a solar input of 1200 btu/hr, a 6' x 1' chimney has 41(t-70)^1.5 + (t-59)6 
= 1200, so if t = 80 f, the heat that moves into the house is 41(10)^1.5
= 1300... something seems screwed up here. air heaters have more twists
and turns and less airflow than chimneys... for now, let's say you can
double the solar collection efficiency with a fan. 

heat storage won't help much in a small system that only makes the usual
house heating system run a bit less. this is more of a toy than a solar
house heater, and it only serves one purpose, vs a sunspace containing a
picnic table. an austin house might need 400 btu/h-f to stay warm, eg
24h(70-49)400 = 200k btu on an average january day, about 10x the output
of this system. something more like a $300 sunspace 8' tall and 32' wide.  

>the barrel and the inside of the box are painted black.

so the sun shines directly on the drum, and the drum stores heat all day
and loses heat back through the glazing all night...

>would this do any good? that is would it be worth the trouble? 

it wouldn't make a very good water heater, with a max temperature of 75 f.
it might be a better $100 house heater, saving $25 per year of oil or gas,
with some black aluminum window screen inside instead of a 55 gallon drum.
you might make it bigger, and dry fruits and vegetables inside, or make beef
jerky, or put a chair inside to make some sort of sweat lodge or sauna, or
combine it with a doghouse or a tiny greenhouse or a storage shed... 


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