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inexpensive 100% solar-house heating with warm air collection
7 apr 2003
most of harry thomason's houses had a trickle collector roof and a large
rock bin with a water tank inside to store and distribute solar heat, but
"house no. 4" had a polyethylene film "pancake heat store" under the floor
for heat storage and distribution. the film available 30 years ago had
pinholes, but it has improved. israeli greenhouses now use water-filled
poly film ducts on the ground to store solar heat.

putting ducts on shelves in a box vs under a floor would make it easier to
control possible leaks and to solar heat and insulate the shelves. this 
could work on a slab with no underfloor space. with a low first cost and
a low operating cost, a simple heating system like this could be suitable
for habitat for humanity houses in the northeast.

a 32'x40' 1-story house with r24 walls and ceiling and 108 ft^2 of r4 windows
and 30 cfm of natural air leakage (0.18 ach, 7 times the 0.025 ach swedish
standard), would have a thermal conductance of about 30 btu/h-f for air leaks
plus 1280ft^2/r24 = 53 btu-h-f for the ceiling plus 108/4 = 27 for the windows
plus 1044/24 = 44 for the walls, a total of 154 btu/h-f. 

nrel says january is the worst-case month for solar house heating in phila,
with 30 f average days with an average daily max of 38. with an average 65 f
indoor temp, the house above needs 24h(65-30)154 = 129.4k btu. a frugal
electrical usage of 300 kwh/month could provide 34.1k btu of that. with no
sun, it needs 95.3k btu/day, or 476.3k btu for 5 30 f cloudy days in a row. 

we might collect solar heat in warm air from a low-thermal-mass sunspace
or thermosyphoning clear corrugated polycarbonate "solar siding" on the
south wall and store it in a 4'x8'x8' tall box with a 4'x8'x4' water tank
below and 12 4'x8' shelves above which act as an air-water heat exchanger
with a slow-moving air to water thermal conductance of about 12x4'x8'x1.5x2
= 1152 btu/h-f.

for shelves, we might drape a 100' length of 30" round poly film greenhouse
duct (about $60) in a zigzag over 100' of 5' wide 2"x4" mesh welded-wire
fencing (about $50), with a 2x4 and an anti-syphoning hole at each end
to make the water depth 2". a low-power pump would circulate water between
the shelves and the tank below, with plywood walls and a 12'x16' piece of
epdm rubber folded up like a chinese takeout box for a liner and a 42 gallon
pressurized galvanized tank for domestic hot water, as in thomason's systems. 

the house needs (65-30)154-1421[elec] = 3970 btu/h on an average day. the
shelf water needs to be 3970/1152 = 3.4 f warmer than the air in the box to
provide this heatflow. with natural convection and a 6' height difference
between a 8 ft^2 supply vent with a 2-watt motorized damper and an 8 ft^2
return vent and a dt box-room air temp diff, cfm = 16.6x8ft^2'xsqrt(6dt),
using an empirical chimney formula... cfmdt = 3970 makes dt = 5.3 f, so
the shelf water temp needs to be at least 70+3.4+5.3 = 78.7 f to keep
the house 70 f. 

the box contains about 4'x8'x4'+4'x8'x2' = 192 ft^3 of water with about
192x64 = 12,288 btu/f of thermal capacitance. if it stores heat for 5 30 f
cloudy days in a row, 476.3k = 12,288(twa-78.7), and the water temp twa
needs to be at least 117.5 f on an average day. 

nrel says 1,000 btu/ft^2 of sun falls on a south wall on an average jan day
in phila... 420 falls on east and west walls, and 190 falls on a north wall.
with 50% solar transmission, 12 ft^2 of windows on north and west walls and
36 and 48 on east and south would collect 0.5(12x190+12x420+36x420+48x1000)
= 35.2k btu/day.

on an average day, the house needs 95.3k-35.2k = 60.1k btu more heat than
electrical usage and windows supply... 8'x16' of r1 air heater glazing with
90% solar transmission could supply this at an average temp th, where
0.9x1000x128ft^2 = 6h(th-34)128ft^2/r1 + 60.1k, so th = 106 f. 

if the house has 1280 ft^2 of 1/2" ceiling drywall, ie 640 btu/f (or more, 
effectively, if it warms to 80 vs 70 f or has a layer of sand "pugging"
above) and 1100 ft^2 of exterior walls (550 btu/f) and 576 ft^2 of interior
walls (576 btu/f, for both sides) and 1280 ft^2 of 1 btu/f-ft^2 floor and
1280 btu/f of furnishings, its thermal capacitance will be 4326 btu/f. if
it's 70 f at dusk and 60 f by dawn, it stores 4326(70-60) = 43,260 btu.

on an average day, the air heater needs to supply 6h((70-30)154-1421)
= 28.4k btu to keep the house 70 f for 6 hours plus 43,260 btu to heat
its thermal mass from 60 to 70 f minus 35.2k btu from the windows,
a total of 36,460 btu, ie 6077 btu/h.  

with natural convection and a 6' height difference between an a ft^2
supply vent with a 2-watt motorized damper and an a ft^2 return vent,
cfm = 16.6axsqrt(6'(106-70)), using an empirical chimney formula...
cfmdt = 6077 makes a = 0.7 ft^2. we might use a 2 ft^2 damper. 

on an average day, the house needs 18h((65-30)154-1421) = 71.4k of overnight
heat, of which 43.3k comes from its thermal mass, so we need to store 28.1k
btu in the shelves at a rate of 4.7k btu/h. the air near the shelves needs
to be 4.7k/1152 = 4.1 f warmer than the shelf water during charging. at an 
average shelf water temp ts, with the shelves behind 64 ft^2 of their own
glazing behind the 128 ft^2 of air heater glazing and a 4 ft^2 airflow path
in the shelf-heating loop, the air in the shelf heater needs to be dt f
warmer than the air near the shelves, where 4.7k = 16.6x4sqrt(6)dt&^1.5, so
dt = 9.4. with 1000 btu/day of sun passing through two glazings with 90%
transmission, 810x64ft^2 = 6h(ts+4.1+13.5-106)64 + 28.1k makes ts = 154 f,
or maybe less, with radiation loss from the air heater. (our solar closet
air heater reached 157 f on one december afternoon...)

with no water heating, the shelves would cool by 28.1k/4096 = 6.9 f over
an average night and rewarm the following day. the circulating pump might
run just enough to keep the lower tank warm on an average day, and more
on a cloudy day. if all the shelf heat goes into water heating (with an
efficient greywater heat exchanger to turn it back into space heat) and
we turn on the pump when the shelf water is at least 5 f warmer than the
tank water, the pump needs to move p pounds of water per day, where 28.1k
= 5p, and p = 5620 pounds per day or 0.5 gpm. (will harbor freight's $9.99
41198-1rjh 60 gph 110v 0.07a fountain pump last long at 130 f? :-) taco's
$101 60 watt 006-bt4-1 pump (grainger item 5p429) can move 5 gpm with a 6'
head, so it might only run 2.4 hours per day, consuming 52 kwh/year at
a cost of $5. 

the ashrae handbook of fundamentals says the 99% "winter design temp"
in phila is 10 f, which determines the required heating system capacity.
the house needs (65-10)154 = 7k btu/h to stay 65 f on that very cold day,
when the shelf water needs to be 7k/1152 = 6.1 f warmer than the air in
the box, and 7k = 16.6x8ft^2'xsqrt(6)dt^1.5 makes dt = 7.8 f. at 5 gpm,
7k = 5x8x60dtw, so dtw = 2.9 f, and the tank water temp needs to be at
least 65+6.1+7.8+2.9 = 81.8 f on that day. we might turn on the pump
whenever the shelf water temp is 5 f more than the tank water temp or
the shelf water temp is less than 81.8... 


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