Can Irradiance be Found Using Properties of Paint?

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• Can Irradiance be Found Using Properties of Paint?

Jennifer Quincy, David Miller, Jake Edmunds
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Objective

• Verify solar irradiance at BYU experimentally.

SWKT
CLYDE
WILK
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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.
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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

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Theoretical Analysis

• Energy Balance
• qrad,abs qrad,emit qconv 0
• aG esTs4 hconv(Ts - T8) 0

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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)

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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.

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Material Properties

• aw .5
• ew .98
• ab .9
• eb .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.

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Unknown Values

• Irradiance G
• Steady State Temperatures Tw and Tb
• Ambient Air Temperature T8
• Free convection coefficient hconv

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Actual Setup

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

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Observations

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

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Measured Temperature

• Steady State Temp
• Tw 21.6C
• Tb 35.1C
• Ambient Temp
• T8 19.8C

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Convection

• For convection (vlt20 m/s) we used
• h  10.45 - v  10vv
• The light breeze was 1 m/s
• h 20 W/m2K

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Solution

• G essTs4 hconv(Ts - T8)/as
• White
• G (.985.67e-8(27321.6)420(21.6-19.8))/.5
• G 910 W/m2
• Black
• G (.985.67e-8(27335.1)420(35.1-19.8))/.9
• G 900 W/m2

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Conclusion

• At 1230 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.

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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 e and a.

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References

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