SolarAttic's Scientific Model

IMPORTANT NOTICE


This WWW html translation has not been checked for formula accuracy.
If you want to "run the numbers," download the Acrobat PDF file.

1994 Scoping Analysis
 SolarAtticTM Solar Pool Heater

From the handwritten notes of the 11/29/93 "scoping analysis" performed by
Professor Ephraim M. Sparrow, University of Minnesota, Minneapolis, MN.

Heat Supply To Attic Air :

  1. 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 @ 130,000
Btu/hr.

  1. 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

  1. Total solar. Range:

175,000 - 307,500

Heat Losses From Attic Roof:

  1. Convection losses. Assume roof outside surface temperature is 115 degrees F and that the air ambient is 85 degrees F.
  2. Convective heat loss equation:

Q conv = [Image]T/R, R= 1/hA

where R is the thermal resistance without wind,

h @ 0.7 Btu/hr-ft2 -° F.

So that
(115 - 85)
Q conv = ____1____ = 31,500 Btu/hr
(0.7) (1500)

For moderate wind, use h @ 2 Btu/hr-ft 2 -° F

Then,

Q loss = (115 - 85)/ (1/(2)(1500))

Q loss = 90,000 Btu/hr

  1. 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.

Heat Balance:

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 accomplished.

IMPORTANT NOTICE


This WWW html translation has not been checked for formula accuracy.
If you want to "run the numbers," download the Acrobat PDF file.