1994 Scoping Analysis
SolarAtticTM Solar Pool Heater
From the handwritten notes of the 11/29/93 "scoping analysis"
Professor Ephraim M. Sparrow, University of Minnesota, Minneapolis, MN.
Heat Supply To Attic Air :
- Direct solar. Use 250 Btu/hr ft2 incident
normal to the sun's rays. The angle of incidence varies throughout a given
day and also depends on latitude and on the season. Use a factor of 0.7 to
account for the non-normal incidence. As a best case, assume that all the
incident solar is absorbed (i.e., d s= 1). If a 1500 ft 2 roof
is everywhere incident by direct solar, then
250 x 0.7 x 1500 = 262,500 Btu/hr.
This would be valid for an unshaded, low-pitch roof. Perhaps
a more typical roof
would be half shadowed. For such a roof, the absorbed solar would be @
- Scattered Solar.
Use 30 Btu/hr - ft 2 as a typical value. For total absorption
on a 1500 ft2 roof
30 x 1500 = 45,000
- Total solar. Range:
175,000 - 307,500
Heat Losses From Attic Roof:
- Convection losses. Assume roof outside surface temperature
is 115 degrees F and that the air ambient is 85 degrees F.
- Convective heat loss equation:
Q conv = T/R,
where R is the thermal resistance without wind,
h @ 0.7 Btu/hr-ft2 -° F.
|| - 85)
| Q conv =
|| = 31,500 Btu/hr
|| (0.7) (1500)
For moderate wind, use h @ 2 Btu/hr-ft 2 -°
Q loss = (115 - 85)/ (1/(2)(1500))
Q loss = 90,000 Btu/hr
- Radiation losses. If the diffuse sky radiation is
characterized by T sky, then,
Q loss = E s A
(T4 -T sky4 )
This equation is for infrared radiation. The emissivity E is
about 0.85 for both
black and white roof surfaces;
s = 0.1712 x 10 -8 Btu/
hr-ft2 -° R4 .
Both T and T sky are in degrees Rankine, °
R = ° F+ 460. Then,
Q loss = (0.85) (0.1712 x 10 -8 ) (1500)
(575 4 - 4604 )
Q loss = 141,000 Btu/hr.
Max Q loss = 90,000 + 141,000
= 231,000 Btu/hr
Min Q loss = 31,500 + 141,000
= 172,500 Btu/hr
Range of losses: 172,500 - 231,000 Btu/hr
Range of solar absorbed: ( a s = 1)
175,000 - 307,500
Conclusion: There are clearly many
cases where the system will work (i.e.
provide = 90,000 Btu/hr), but the combination of a half or
more shadowed roof
and moderate wind will unable the [pool] water heating to be
If you want to "run the numbers," you can download the Acrobat PDF file.