Can Irradiance be Found Using Properties of Paint?

Jennifer Quincy, David Miller, Jake Edmunds

Objective:Verify solar irradiance at

BYU experimentally.

SWKT

WILK

CLYDE

The ExperimentStep 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.

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

Theoretical AnalysisEnergy Balance

qrad,abs – qrad,emit – qconv = 0

αG – εσTs4 – hconv(Ts - T∞) = 0

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)

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.

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.

Unknown Values

• Irradiance G

• Steady State Temperatures Tw and Tb

• Ambient Air Temperature T∞

• Free convection coefficient hconv

Actual Setup

• JFSB, 3rd floor balcony, 12 am, 12 April 2007

• Thermocouples

in cubes to

measure temp

Observations

• Steady state was reached in 30 minutes

• Light breeze present

• Lightly overcast

• Cool ambient air

Measured Temperature

• Steady State Temp– Tw = 21.6°C

– Tb = 35.1°C

• Ambient Temp– T∞ = 19.8°C

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

Solution• G = [εsσTs

4 + 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

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.

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.

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