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Paint Properties and Solar Irradiance: Experimental Verification at BYU

This study aims to verify solar irradiance at BYU experimentally by painting hollow steel cubes black and white and measuring the temperature inside the cubes. The results confirm that known properties of paint can accurately determine irradiance.

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Paint Properties and Solar Irradiance: Experimental Verification at BYU

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  1. Can Irradiance be Found Using Properties of Paint? Jennifer Quincy, David Miller, Jake Edmunds

  2. Objective: Verify solar irradiance at BYU experimentally. SWKT CLYDE WILK

  3. The Experiment Step 1- Paint hollow steel cubes black and white. Step 2- Place cubes in foam insulation with one face exposed to sun. Step 3- Allow cubes to reach steady state temperature. Step 4- Measure temperature inside of cubes. Step 5-Determine the irradiance G from Energy Balance.

  4. Predictions for April 2007 • Average monthly maximum irradiance in April at BYU is ≈1100 W/m2 • Mean monthly irradiance in April at BYU is ≈265 W/m2 • We will measure at noon so the irradiance should be around 1000 W/m2

  5. Theoretical Analysis Energy Balance qrad,abs– qrad,emit – qconv = 0 αG – εσTs4 – hconv(Ts - T∞) = 0

  6. About Spray Paint • Flat White and Flat Black differ slightly • Flat White 6% Talc, 4% Titanium Dioxide • Flat Black 4% Talc, .4% Carbon Black • Everything else in spray paint is VOCs and solvents that evaporate • Absorptivity will be different, but emissivity will be virtually the same (mostly IR)

  7. Assumptions • Identical and simultaneous setup allows comparison of the results from the two colors. • Foam insulation negligibly participates in heat transfer. • Assumed material constants are accurate. • At steady state, internal air temp of the cubes is the same as the surface temp.

  8. Material Properties • αw ≈ .5 • εw ≈ .98 • αb ≈ .9 • εb ≈ .98 • These properties are very general; they can vary widely even within the same brand of paint. • Only paint intended for aerospace applications has constant and well-researched properties.

  9. Unknown Values • Irradiance G • Steady State Temperatures Tw and Tb • Ambient Air Temperature T∞ • Free convection coefficient hconv

  10. Actual Setup • JFSB, 3rd floor balcony, 12 am, 12 April 2007 • Thermocouples in cubes to measure temp

  11. Observations • Steady state was reached in 30 minutes • Light breeze present • Lightly overcast • Cool ambient air

  12. Measured Temperature • Steady State Temp • Tw = 21.6°C • Tb = 35.1°C • Ambient Temp • T∞ = 19.8°C

  13. Convection • For convection (v<20 m/s) we used h = 10.45 − v + 10√v • The light breeze was ≈1 m/s • h ≈ 20 W/m2K

  14. Solution • G = [εsσTs4 + hconv(Ts - T∞)]/αs • White • G= (.98*5.67e-8*(273+21.6)4+20*(21.6-19.8))/.5 • G= 910 W/m2 • Black • G= (.98*5.67e-8*(273+35.1)4+20*(35.1-19.8))/.9 • G= 900 W/m2

  15. Conclusion At 12:30 pm, the irradiance at BYU is ≈ 900 W/m2. We confirmed this with the BYU ESC Weather Station data. We verified that the irradiance can be accurately be found using known properties of paint.

  16. Recommendations With a known irradiance, absorptivity of a different color paint could be found. Accurately calibrated thermocouples would yield much greater reliability. A transparent box could be used to reduce convection to negligible levels. Find more accurate values for ε and α.

  17. References • Absorptivity and Emissivity www.solarmirror.com/fom/fom-serve/cache/43.html • BYU ESC Weather Station marvin.byu.edu/Weather • Krylon Spray Paint MSDS www.kpg-industrial.com/krylon

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