Chapter 10: Radiation

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Chapter 10 Radiation
Figures from Intro. to Env. Biophysics (Campbell
and Norman) and Fundamentals of Heat and Mass
Trsfr. (Incropera and Dewitt)
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Black Body Radiation
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Definitions

• a.     Radient flux (W) The amount of radiant
  energy emitted, transmitted, or received per unit
  time
• b.    Radiant flux density (F, W m-2) Radiant
  flux per unit area
• c.     Irradiance (W m-2) Radiant flux density
  incident on a surface
• d.    Radiant emittance (W m_2) Radiant flux
  density emitted by a surface

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Solid Angles
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Hemispherical vs Direction Radiation
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Example Calculate PPFD from 500 W m-2 of PAR
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• a.     Absorptivity a(l) The fraction of
  incident radiant flux at a given wavelength that
  is absorbed by a material.
• b.    Reflectivity r(l) The fraction of
  incident radiant flux at a given wavelength
  reflected by a material
• c.     Transmissivity t(l) The fraction of
  incident radiant flux transmitted by a material

Filter
r(l)
Emissivity e(l) The fraction of blackbody
emittance at a given wavelength emitted by a
material.
e
a(l)
t(l)
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Assessing Interaction between Radiation and Matter

• Need to know
• Radiant flux density as a function of l
• Transmission of intervening medium
• Absorptive response as a function of l for the
  receiver

• Consider
• Sun Atmosphere Leaf
• Growth Chamber Glass/Water Leaf
• Soil Glass Window Infrared Thermometer

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Lamberts Cosine Law
Irradiance on a surface from a parallel beam of
light depends on its orientation with respect to
the radiation
Radiation
Radiation
Radiation
q
q
Projected area
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Bouguers or Beers Law

• Radiation moving through a homogenous medium
• Attenuates beam
• Decrease in flux density described by

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Terrestrial Spectral Emittance (W/m2/um)
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0
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Black Body Radiant Emmitance

• Calculate energy emitted from object either ?
• Integrate energy emitted at each wavelength
• Follows Stefan-Boltzmann Law
• s Stefan-Boltzmann Const.

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Calculating Non-BB Radiant Emittance
Fsr

• All bodies emit radiation
• Total Radiation is a sum of
• Radiant Emittance at each solid angle
• Multiplied by the fractional emittance compared
  to a BB

Fsr
Fsr
Fsr
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Radiant Emmittance of Non-BB

• Integrate over entire spectrum where e(l) is
  spectral distribution of emissivity

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Simplified Non-BB Radiant Emittance Gray Bodies

• Requires
• Temperature of object
• Emissivity of object
• Fraction of radiation the object will emit
  compared to BB
• Although Emissivity is l dependent, well
  simplify and use e that is constant with l
• e are available in table form

Surroundings
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Long Wave Emissivity of Sky
La Sky Thermal
Lg Ground Thermal
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Radiant Fluxes
Sd - Solar Diffuse
Sb - Solar Beam
La Sky Thermal
Loe Emitted Outgoing Thermal
Sr - Solar Reflected
Lg Ground Thermal