Transcript
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Introduction to Thermal Radiation
Figures except for the McDonnell Douglas figures come from Incorpera &
DeWitt, Introduction to Heat and Mass Transfer or Cengel, Heat Transfer: APractical Approach
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Thermal Radiation
Occurs in solids, liquids, and gases
Occurs at the speed of light
Has no attenuation in a vacuumCan occur between two bodies with a colder medium inbetween
Applications: satellite temperature management, taking
accurate temperature measurements, designing heatersfor manufacturing, estimating heat gains throughwindows, infrared cameras, metal cooling duringmanufacturing, Greenhouse effect, lasers, insulatingcryogenic tanks, thermos design, ice skating rink ceiling
design
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Background
Electromagnetic radiation energy emitted dueto changes in electronic configurations of atoms
or molecules
where P=wavelength (usually in Qm),
R=frequencyIn a vacuum c=co=2.998x10
8m/s
Other media: c=co/n where n=index of refraction
R!P c
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Background, cont.
Radiation photons or waves?
Max Planck (1900): each photon has an energy
of
h=Plancks constant=6.625 x 10-34 Js
Shorter wavelengths have higher energy
P!R! hhe
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Radiation Spectrum
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Types of Radiation
Two categories
Volumetric phenomenon radiation emitted or absorbed
throughout gases, transparent solids, some fluids Surface phenomenon radiation to/from solid or liquid
surface
Thermal radiation emitted by all substances above
absolute zeroIncludes visible & infrared radiation & some UV
radiation.
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Radiation Properties
Magnitude of radiation varies with wavelength itsspectral.
The wavelength of the radiation is a major factor in what itseffects will be.
Earth/sun example
Radiation is made up of a continuous, nonuniformdistribution of monochromatic (single-wavelength)components.
Magnitude & spectral distribution (how the radiationvaries with wavelength) vary with temp & type ofemitting surface.
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Emission Variation with Wavelength
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Blackbody Radiation
Blackbody a perfect emitter & absorber of radiation; itabsorbs all incident radiation, and no surface can emitmore for a given temperature and wavelength
Emits radiation uniformly in all directions nodirectional distribution its diffuse
Example of a blackbody: large cavity with a small holeJoseph Stefan (1879) total radiation emission per unittime & area over all wavelengths and in all directions:
W=Stefan-B
oltzmann constant =5.67 x10-8
W/m2
K4
24 mWTEb W!
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Plancks Distribution Law
Sometimes we care about the radiation in a certain wavelength interval
For a surface in a vacuum or gas
Integrating this function over allP gives us
? A
constantsBoltzmann'J/K1038051
Km104391
mmW1074232
where
mmW1
23
42
24821
2
25
1
!!!!
!T!
PP!P
-
o
o
b
x.k
x.khcC
x.hcC
TCexp
C
TE
4bE TW!
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Radiation
DistributionRadiation is a continuousfunction of wavelength
Magnitude increaseswith temp.
At higher temps, moreradiation is at shorter
wavelengths.Solar radiation peak is inthe visible range.
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Wiens Displacement Law
Wavelength of radiation with the largest
magnitude can be found for different temps
using Wiens Displacement Law:
Note that color is a function of absorption &
reflection, not emission
max
2897.8 m Kpower
TP Q!
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Blackbody Radiation Function
We often are interested in radiation energy emitted overa certain wavelength interval.
This is a tough integral to do!
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Blackbody Radiation Function
Use blackbody radiation function,
FP(often called the fractional
function)
If we want radiation between P1 &
P2,
4
0
T
dTE
TF
b
W
TFTFTF1221 PPPP
!
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More Radiation Properties
Directional distribution a surface doesnt emit
the same in all directions.
Hemispherical refers to all directions
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Angle definitions
zenith angle Uup and down)
azimuthal angle Jside to side)
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Solid Angle
differential solid angle d[!dAn/r2= dA1cosU/r
2=sinU dU dJ
A solid angle is for a sphere what an angle is for a circle
Units: steradians (sr); For a sphere [=4T sr
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Solid Angle, cont.
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Spectral Intensity
IP,e: rate at which radiant energy is emitted at the
wavelength P in the (UJ) direction, per unit area of the
emitting surface normal to this direction, per unit solidangle about this direction, and per unit wavelength
interval dP aboutP
Translation: rate of emission at a given wavelength, in a
given direction, per unit area, solid angle, andwavelength interval
Units: W/(m2srQm)
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Spectral Intensity
, , ,en
dqI
dA d d P P U J
Z P!
1 cosnd d U!
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To solve for dq
Sometimes we know the intensity Ie rather thanthe spectral intensity (i.e., the rate of emission in
a given direction, per unit area and solid angle).
This is IP,e integrated over all wavelengths. Then
, 1, ,edQ I dA d d P P U J U P! &
1,ed I dA d U J U Z ! &
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Total heat flux
To find the total heat flux, we must integrate over
both angles and wavelength.
2 2
,
0 0
0
, ,eq I cos sin d d
q q d
P
P
TT
PP P U J U U U J
P P
g
!
!
&
& &
2 2
,
0 0 0
, ,eq I cos sin d d d
TT
P P U J U U U J Pg
!&OR
spectral heat flux
total heat flux
total heat flux
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Emissive Power
E: amount of radiation emitted per unit area
Spectral hemispherical emissive power EP (often leave
out the word hemispherical) W/m
2
P Rate of emission per unit area of radiation of a given
wavelength P in all directions per unit wavelength interval
Total (hemisperical) emissive power E (W/m2)
Rate of emission per unit area of radiation of all wavelengthsand in all directions; this is emittedq&
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Diffuse emitters
Diffuse emitter: intensity is the same in all
directions; integration is easy!
,
,0
e e
e e
E I and E I
where I I d
P P
P
P T P T
Pg
! !
!
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Irradiation, G
Irradiation: radiation incident on (hitting) a
surface per unit area
Use subscript i
Same equations as E except replace E with G
and IP,e with IP,i(intensity of incident radiation)
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Radiosity, J
Radiosity: all radiation leaving a surface per unit
area, both emitted and reflected
Use subscript e+r
Same equations as E except replace E with J
and IP,e with IP,e+r(intensity of emitted+reflected
radiation)
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Example 1
A small surface of area A1=3 cm2diffusely emits
radiation with an emissive power of 7350 W/m2.Part of the radiation strikes another small surface
of area A2=5 cm2oriented as shown on the board.
a) Find the intensity of the emitted radiation.
b) Find the solid angle subtended by A2
whenviewed from A1.
c) Find the rate of radiation emitted by A1 thatstrikes A2.
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