Chapter 11' Fundamental of Thermal Radiation

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Chapter 11. Fundamental of Thermal Radiation

• 11-1 Introduction
• Cooling capacity is comparable to natural
  convection.
• Important in space applications.
• In this chapter, we will study
• - Electromagnetic wave and Thermal
  radiation
• - Blackbody radiation its emissive
  power
• - Thermal radiation properties
• emmissivity
• absorptivity, reflectivity,
  transmissivity
• - Kirchhoffs law

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11-2 Thermal radiation

• Electromagnetic wave covers a very wide wave
  length, varying from less than 10-10 µm (1µm
  10-6 m) of cosmic ray to 1010 µm of electrical
  power wave.
• Thermal radiation is a small portion of
  electromagnetic wave. It is due to the surface
  temperature above absolute zero degree
  concentrates in the wave length range from 0.1 to
  100 µm.
• Does not require any medium in between
• Visible portion of electromagnetic wave in the
  range of 0.4 to 0.76 µm
• Infrared range is from 0.76 to 100µmmilitary
  applications
• Ultraviolet lies between the wave lengths 0.01 to
  0.4µm , wave in this range can kill microorganism
  and cause sunburns.
• Micro wave is in the range 102 to 105 µm.

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11-3
Blackbody radiation

• Blackbody is an ideal or perfect emitter and
  absorber of thermal radiation. It absorbs all
  incident radiation. At a specified temperature,
  it emits more energy per unit area than
  non-blackbodies.
• It emits radiation energy uniformly in all
  directions.
• The spectral distribution of emissive power per
  unit area of a blackbody follows Planks
  distribution law. It is a function of temperature
  and wave length.
• where C1 3 .742x108 W.µm4/m2
• C2 1.439x104 µm.K
• T absolute temperature, K
• ? wave length, µm
• The blackbody emissive power over the entire
• wave length is called--Stefen-Boltzmann
  law
• where s is Stefen-Boltzmann constant
  5.67x10-8 W/(K4 m2)

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11-3 Blackbody radiation

• Wiens law the wave length at which the peak
  occurs

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11-4 Radiation properties

• Absorptivity, Reflectivity, and Transmissivity
• Irradiation The radiation power incident on a
  surface per unit surface area is called
  irradiation, G (W/m2)
• The radiation power incident on the surface can
  be divided into 3 fractions
• - absorptivity, a
• - reflectivity, ?, and
• - transmissivity ?
• Opaque surface, ? 0,
• a ? 1
• black surface a 1.
• ? ? 0

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• Directional distribution of emissive power
  
• - Real surface directional distribution
  of emissive power is not
• uniform.
• - Diffuse surface uniform--independent of
  direction.
• - Gray surfacethe radiation properties are
  independent of wave
• length and direction.
• Emissivity
• The ratio of the emissive power per unit
  area of a surface at given
• temperature to the emissive power per unit
  area of a black
• surface at the same temperature is called
  emissivity.

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• Directional distribution of emissive power
  
• - Real surface directional distribution
  of emissive power is not
• uniform.
• - Diffuse surface uniform--independent of
  direction.
• - Gray surfacethe radiation properties are
  independent of wave
• length and direction.
• Emissivity
• The ratio of the emissive power per unit
  area of a surface at given
• temperature to the emissive power per unit
  area of a black
• surface at the same temperature is called
  emissivity.

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• 11-5 Kirchhoffs Law
• Consider a small, gray surface object of area A
  in a large enclosure at temperature Tc, the
  energy
• absorbed by the small object is
• Note the large enclosure can be considered
• as an block surface, because it absorbs all
  radiation energy emitted from the small object.
  G is the irradiation incident on the small object
  from the enclosure. The energy emitted by the
  small, gray object is
• e and Tso are the emissivity and temperature of
  the small object. At equilibrium, the
  temperatures of the two surfaces will be equal
  and the energy received is equal to the energy
  emitted, we have
• The above is called Kirchhoffs law

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The following pages will not be taught
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Spectral Emissivity

• Spectral emissivity
• The ratio of radiation energy at wave length
  of any surface per unit area to the
  radiation energy of a black surface per unit area
  at the same at the same temperature and wave
  length length is call spectral emissivity, or
  
• The radiation energy per unit area of the surface
  is
• For black surface
• For a gray surface
• For a real surface
• It various with the wave length
• The radiation energy per unit area of a
  real surface can be obtained by knowing its
  spectral emissivity distribution, or taking an
  average value

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11-5 Kirchhoffs Law

• Consider a black and a gray surface of identical
  area A, the two surfaces are put very close to
  each other. The black surface has a temperature
  Tb and the gray surface has a temperature T. The
  total radiation energy arriving to the gray
  surface is
• The radiation energy absorbed by the gray
  surface is Black
• 
  T
  Tb
• 
  Gray
• The energy emitted by the gray surface is
• At equilibrium, the temperatures of the two
  surfaces are equal and the energy received of the
  gray surface is equal to the energy emitted, we
  have
• Absorptivity is equal to emissivity is
  called Kirchhoffs law

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11-5 Kirchhoffs Law

• Consider a small, gray surface object of area A
  in a large enclosure
• at temperature Tc, the energy absorbed
• by the small object is
• Note the large enclosure can be
  considered as an block surface, because it
  absorbs all radiation energy emitted from the
  small object.
• G is the irradiation incident on the small
  object from the enclosure.
• The energy emitted by the small, gray
  object is
• e and Tso are the emissivity and
  temperature of the small object
• At equilibrium, the temperatures of the two
  surfaces will be equal and the energy received is
  equal to the energy emitted, we have
• The above is called Kirchhoffs law

G
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• The following pages will not be taught.

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• Directional distribution of emissive power
  
• - Real surface directional distribution
  of emissive
• power is not
  uniform.
• - Diffuse surface uniform--independent of
  direction.
• Spectral emissivity
• The spectral emissivity of a block surface
  is defined to be 1 and it is independent of wave
  length. The ratio of the spectral emissive power
  of any surface at a given temperature to the
  spectral emissive power of a black surface at the
  same temperature wave length is called spectral
  emissivity. The spectrum emissivity of a gray
  surface is independent of wave length.

blackbody
?
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11-3 Blackbody radiation

• The contribution of emissive power per unit area
  from wave length 0 to any value ?1 is
• the integration is tedious. We normalized
  the result by dividing the emissive power of all
  wave length
• Its value is shown in table 11-1. The emissive
  power per
• unit area from wave length ?1 to ?2 is

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11-3 Blackbody radiation

• Table 11-2

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Example11-2 Emission of radiation from a light
bulb

• Given T 2500K, Bulb is blackbody
• Find The fraction of radiation in the visible
  wave range and the wave length at the peak
• Solution ? 0.4µm to 0.76µm
• (a)
• ?1T 0.4 x 2500 1000µmK
  f?1 0.000321
• ?2T 0.76 x 2500 1900µmK
  f?1 0.053035
• f?1 to ?2 f?2 - f?1 0.053035
  0.000321 0.0527135
• it is about 5 of radiation in the
  visible wave range
• (b) T 2500K
• (?T)max 2897.8 µmK ?? 1.16µm

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11-5 Radiation properties

• The total emissive power of a real surface is
• The total emissivity of the real surface is
• Calculation the average emissivity for a
  specified spectrum emissivity distribution in red
• Emissive power for a gray surface

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Example 11-4 Emissivity of a surface emissive
power

• Given
• Determine the average emissivity