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

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

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/m 2 Mean monthly irradiance in April at BYU is ≈265 W/m 2 We will measure at noon so the irradiance should be around 1000 W/m 2

5. Theoretical Analysis Energy Balance q rad,abs – q rad,emit – q conv = 0 αG – εσT s 4 – h conv (T s - 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 α w ≈.5 ε w ≈.98 α b ≈.9 ε b ≈.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 T w and T b Ambient Air Temperature T ∞ Free convection coefficient h conv

10. Actual Setup JFSB, 3 rd 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 –T w = 21.6°C –T b = 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/m 2 K

14. Solution G = [ε s σT s 4 + h conv (T s - T ∞ )]/α s White –G= (.98*5.67e-8*(273+21.6) 4 +20*(21.6-19.8))/.5 –G= 910 W/m 2 Black –G= (.98*5.67e-8*(273+35.1) 4 +20*(35.1-19.8))/.9 –G= 900 W/m 2

15. Conclusion At 12:30 pm, the irradiance at BYU is ≈ 900 W/m 2. 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.

17. 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.

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