05 radiation (v1)

ME 144: Heat Transfer

Introduction to Radiation (v 1.0)

J. M. Meyers

ME 144: Heat Transfer | Radiation

J. M. Meyers2

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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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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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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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 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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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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TRANSMISSIVITY

Deals with the of the response of a semitransparent material to incident radiation


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Environmental Radiation


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OUR SUN


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NASA Glenn Research Center


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Some Practical Radiation Studies


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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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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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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

05 radiation (v1)

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