Download - 05 Radiation (v1)
ME 144: Heat Transfer
Introduction to Radiation (v 1.0)
J. M. Meyers
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Initial Concepts
Heat transfer by conduction and convection requires the presence of a temperature gradient
in some form of matter.
Heat transfer by thermal radiation requires no matter.
It is an extremely important process, and in the physical sense it is perhaps the most
interesting of the heat transfer modes.
It is relevant to many industrial heating, cooling, and drying processes, as well as to energy
conversion methods that involve fossil fuel combustion and solar radiation
Very important in high speed aerodynamics and reentry aerothermodynamics
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Initial Concepts
Consider a solid that is initially at a higher temperature �� than that of its surroundings ���� ,
but around which there exists a vacuum
The presence of the vacuum precludes energy loss from the surface of the solid by conduction
or convection
This cooling is associated with a reduction in the internal energy stored by the solid and is a
direct consequence of the emission of thermal radiation from the surface.
In turn, the surface will intercept and absorb
radiation originating from the surroundings.
However, if �� > ���� the net heat transfer rate by
radiation ����,�� is from the surface, and the
surface will cool until �� reaches ����.
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Initial Concepts
All forms of matter emit radiation. For gases and for semitransparent solids, such as glass and
salt crystals at elevated temperatures, emission is a volumetric phenomenon
we concentrate on situations for which radiation can be treated as a surface phenomenon. In
most solids and liquids, radiation emitted from interior molecules is strongly absorbed by
adjoining molecules.
Accordingly, radiation that is emitted from a solid or a liquid originates from molecules that are
within a distance of approximately
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We know that radiation originates due to emission by matter and that its subsequent
transport does not require the presence of any matter.
One theory views radiation as the propagation of a collection of particles termed
photons or quanta.
Alternatively, radiation may be viewed as the propagation of electromagnetic
waves.
Regardless, we will use the standard wave properties of frequency and wavelength when
dealing with radiation exchanges.
These two properties are related by
Initial Concepts
=�
�
≡ wavelength
�� ≡ speedoflightinavacuum[2.998 × 10.m/s]
� ≡ frequency
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Initial Concepts
ELECTROMAGNETIC SPECTRUM
A region containing a portion of the UV and all of the visible and infrared (IR) is termed
thermal radiation because it is both caused by and affects the thermal state or
temperature of matter… for this reason, thermal radiation is pertinent to heat transfer.
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Initial Concepts
Thermal radiation emitted by a surface encompasses a range of wavelengths
The magnitude of the radiation varies with wavelength, and the term spectral is used to refer to
the nature of this dependence.
This spectral distribution will vary with the nature and temperature of the emitting surface
A surface may emit preferentially in certain directions, creating a directional distribution of
the emitted radiation.
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Radiation Heat Fluxes
Various types of heat fluxes are pertinent to the analysis of radiation heat transfer
Emissive power, 4 [W/m6], rate at which radiation is emitted from a surface per unit surface
area, over all wavelengths and in all directions. Recall our treatment of radiation emission:
4 = 78�9
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Radiation Heat Fluxes
Irradiation, : [W/m6], rate at which radiation is incident upon the surface per unit surface area,
over all wavelengths and from all directions.
All of the irradiation must be reflected, absorbed, or transmitted, it follows that
; + = + > = 1
; + = = 1
A medium that experiences no transmission is termed opaque, in which case:
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Radiation Heat Fluxes
Radiosity, J (W/m2), of a surface accounts for all the radiant energy leaving the surface.
For an opaque surface, it includes emission and the reflected portion of the irradiation,
? = 4 + :��@ = 4 + ;:
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Radiation Heat Fluxes
Net radiative flux from a surface, (W/m2), is the difference between the outgoing and incoming
radiation�"��� = ? − :
�"��� = 4 + ;: − : = 78��9 − =:
Combining previous relations:
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Radiation Heat Fluxes
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Radiation Intensity
Radiation leaving a surface can propagate in all directions
thus its directional distribution is important.
Radiation incident upon a surface may come from different
directions and the manner in which the surface responds to
this radiation depends on the direction.
These directional effects are quite important in determining
the net radiative heat transfer rate and may be treated by
introducing the concept of radiation intensity.
Due to its nature, mathematical treatment of radiation heat
transfer involves the extensive use of the spherical
coordinate system.
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Radiation Intensity
The differential solid angle CD is defined by a region between the rays of a sphere and is
measured as the ratio of the area CE on the sphere to the sphere’s radius squared:
CD =CE
F6
Mathematical Definitions
The unit of the solid angle is the steradian (sr),
analogous to radians for plane angles.
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Radiation Intensity
Mathematical Definitions
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Radiation Intensity
Radiation Intensity and Its Relation to Emission
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Radiation Intensity
Radiation Intensity and Its Relation to Emission
The total, hemispherical emissive power, 4 (W/m2), is the rate at which radiation is emitted
per unit area at all possible wavelengths and in all possible directions.
Although the directional distribution of surface emission varies according to the nature
of the surface, there is a special case that provides a reasonable approximation for many
surfaces.
A diffuse emitter is a surface for which the intensity of the emitted radiation is independent
of direction, in which case GH,� , I, J = GH,� ( , ):
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Radiation Intensity
Radiation Intensity and Its Relation to Irradiance
The intensity of the incident radiation may be related to
the irradiation, which encompasses radiation incident from
all directions.
The spectral irradiation :(W/m2Mm) is defined as the rate
at which radiation of wavelength is incident on a surface,
per unit area of the surface and per unit wavelength
interval C about :
Eq. 12.18
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Blackbody Radiation
1. A blackbody absorbs all incident radiation, regardless of wavelength and direction.
2. For a prescribed temperature and wavelength, no surface can emit more energy than a
blackbody
3. Although the radiation emitted by a blackbody is a function of wavelength and
temperature, it is independent of direction. That is, the blackbody is a diffuse emitter.
As the perfect absorber and emitter, the blackbody serves as a standard against
which the radiative properties of actual surfaces may be compared.
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Blackbody Radiation
Black body emission can be described by the well known Planck distribution:
GH,N , � =2ℎ�P
6
Q exp ℎ�P/ ST� − 1
ℎ = 6.626 × 10VW9J∙s
ST = 1.381 × 10V6WJ/K
�P = 2.998 × 10.m/s
PLANCK DISTRIBUTION
Speed of light
Boltzmann constant
First Radiation Constant:
4H,N , � = \GH,N , � =]^
Q exp ]6/ � − 1
]^ = 2\ℎ�P6 = 3.742 × 10.W∙μm9/m6
]6 =ℎ�P
ST= 1.439 × 109μm∙KSecond Radiation Constant:
Planck constant
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Blackbody Radiation
PLANCK DISTRIBUTION
Log scale
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Blackbody Radiation
PLANCK DISTRIBUTION
Several important features should be noted:
1. The emitted radiation varies continuously with wavelength
2. At any wavelength the magnitude of the emitted radiation increases with increasing
Temperature
3. The spectral region in which the radiation is concentrated depends on temperature, with
comparatively more radiation appearing at shorter wavelengths as the temperature
increases.
4. A significant fraction of the radiation emitted by the sun, which may be approximated as a
blackbody at 5800 K, is in the visible region of the spectrum. In contrast, for T < 800 K,
emission is predominantly in the infrared region of the spectrum and is not visible to the
eye.
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Blackbody Radiation
WIEN’S LAW
The blackbody spectral distribution has a maximum and that the corresponding wavelength max
depends on temperature
b�c� = ]W
The nature of this dependence may be obtained by differentiating Planck’s Law with respect to
and setting the result equal to zero, which leads to:
Where the third radiation constant is ]W = 2898μm∙K
Wien’s Law
According to this result, the maximum spectral emissive power is displaced to shorter
wavelengths with increasing temperature
This emission is in the middle of the visible spectrum ( b�c ≈ 0.5μm) for solar radiation, since
the sun emits approximately as a blackbody at 5800 K.
A tungsten filament lamp operating at 2900 K ( b�c = 1μm) emits white light, although most
of the emission remains in the IR region
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Blackbody Radiation
WIEN’S LAW
IR thermography
temperatures
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Blackbody Radiation
STEPHAN-BOLTZMAN LAW
Determining the total, hemispherical emissive power, using Planck’s Law yields the Stephan-
Boltzman Law
Performing the integration, it may be shown that
where the Stefan-Boltzmann constant, which depends on C1 and C2, has the numerical value:
This Stefan-Boltzmann law enables calculation of the amount of radiation emitted in all
directions and over all wavelengths simply from knowledge of the temperature of the
blackbody.
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Band Emission
To account for spectral effects, it is often necessary to know the fraction of the total emission
from a blackbody that is in a certain wavelength interval or band
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Emission From Real Surfaces
7 , � =4 , �
4N , �
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Absorption, Reflection, and Transmission by Real Surfaces
ABSORPTIVITY
The absorptivity is a property that determines the fraction of the irradiation absorbed by a
surface.
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Absorption, Reflection, and Transmission by Real Surfaces
REFLECTIVITY
The reflectivity is a property that determines the fraction of the incident radiation reflected
by a surface.
Surfaces may be idealized as diffuse or specular, according to the manner in which they
reflect radiation
diffuse specular
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Absorption, Reflection, and Transmission by Real Surfaces
TRANSMISSIVITY
Deals with the of the response of a semitransparent material to incident radiation
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Absorption, Reflection, and Transmission by Real Surfaces
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Absorption, Reflection, and Transmission by Real Surfaces
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Environmental Radiation
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Environmental Radiation
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Environmental Radiation
OUR SUN
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Environmental Radiation
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Environmental Radiation
NASA Glenn Research Center
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Some Practical Radiation Studies
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Some Practical Radiation Studies
A. M. Brandis, et al., “Validation of CO 4th Positive Radiation for Mars Entry,” NASA Ames
Research Center, AIAA 2012-1145
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Some Practical Radiation Studies
A. M. Brandis, et al., “Validation of CO 4th Positive Radiation for Mars Entry,” NASA Ames
Research Center, AIAA 2012-1145
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Radiation Exchange Between Surfaces (Chpt. 13)
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Radiation Exchange Between Surfaces (Chpt. 13)
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Radiation Exchange Between Surfaces (Chpt. 13)
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References
• Bergman, Lavine, Incropera, and Dewitt, “Fundamentals of Heat and Mass Transfer, 7th Ed.,”
Wiley, 2011
• Chapman, “Heat Transfer, 3rd Ed.,” MacMillan, 1974
• Y. A. Çengel and A. J. Ghajar, “Heat and Mass Transfer, 5th Ed.,” Wiley, 2015