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re: overnight heat storage
2 jul 2002
>what's the min r-value for a 32x32x16' house with 8% of the floorspace
>as r4 windows with 50% solar transmission and 0.2 ach and 300 kwh/month
>of internal heat gain...
 
with 96 ft^2 of south windows and 32 on the east and west and 16 on the
north and a 1024 ft^2 ceiling and 848 ft^2 of walls with r-value r, its
conductance g is 1872/r plus 176ft^2/r4 = 44 btu/h-f for windows plus
about 32x32x16x0.2/60 = 55 for 55 cfm of air leaks, ie g = 99+1872/r. 
 
on an average jan day in phila, the sun gives 0.5(96x1000+64x420+190x16)
= 63k btu of heat, with 34.1k more from electrical use. if 24h(65f-30f)g
< 97.1k, we can heat the house with windows alone, and r113 insulation :-)

we might make an air heater by glazing the entire south wall with
a single layer of r1 polycarbonate with 90% solar transmission over 
an air gap and insulation behind the non-window areas and keep the house
70 f for 6 hours on an average day. a square foot of air heater at say,
80 f for 6 hours would gain 900 btu on an average day and lose about
6h(80f-30f)/r1 = 300, for a net gain of 600, so the non-window part of
the south wall could contribute another 160ft^2x600 = 96k btu of heat.
if 24h(65f-30f)g < 193.1k, we need r14 walls.

a square foot of air heater on an east wall gains 380 btu/day and loses
about 3(80-30) = 150, for a net gain of 230. "solar siding" on east and
west walls could add 448ft^2x230 = 102.1k btu. if 24h(65f-30f)g < 295.2k,
we need r7.4 walls. we might use r8, eg 2" dri-vit over concrete, making
g = 99+1872/8 = 333 btu/h-f. with 1421 btu/h of internal (electrical)
heat gain, the house can keep itself 65 f when it's 60.7 outdoors.

the 2896 ft^2 of walls and slab might contain 4344' of 4" pvc pipes on
8" centers with elbows for easy cleaning. with 4550 ft^2 of pipe area,
the concrete-to-still-air conductance would be about 1.5(2896+4550)
= 11,169 btu/h-f. with 8" thick walls and slab and a net concrete volume
of 1552 ft^3, c = 38,790 btu/f, so the internal time constant rc = 3.5 h,
and c/g = 116 hours. if the concrete warms to tmax after 6 hours in 70 f
air and cools to tmin after 18 hours, tmax = 70-(70-tmin)exp(-6/3.5) and
tmin = 30+(tmax-30)exp(-18/116), so tmin = 63.2 and tmax = 68.8, and it
can store (68.8-63.2)c = 215.5k btu, vs the 18h(65-30)g = 209.8k the house
needs for the night, ignorning the internal gain. we might get by with
fewer pipes or less concrete, especially if the sunspace is warmer than
80 f, and the air that enters the pipes near the ceiling is warmer than
80 f, and it leaves the slab to enter the sunspace. 

r. h. turner et al describe (in "thermal storage in the walls of a solar
house," journal of solar energy engineering, nov., 1994, vol. 116, pp
183-193) tests of a 2x4 wall section with 4 3" sealed water pipes in each
16" cavity storing about 9.4 btu/f per square foot of wall, ignoring the
drywall, with active charging and passive discharging... 5 4" pipes in
a 24" 2x6 wall cavity could store 14 btu/f-ft^2. an 8" concrete or block
wall with 4" pipes on 8" centers can store 13.4 btu/f-ft^2. 

conventional walls are colder than room air in wintertime.
storing heat and coolth in radiant walls can make people
comfortable at lower and higher room air temps... 

nick




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