15. Radiation Introduction
Transcript of 15. Radiation Introduction
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15. RADIATION HEAT TRANSFER
Heat conduction and convection - always a fluid which
transfers the heat (gas, liquid, solid) – motion of atoms ormolecules
Heat conduction and convection is not possible in a vacuum
In most practical applications all three modes occurconcurrently at varying degrees
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A hot object in a vacuum
chamber looses heat by
radiation only
Unlike conduction and convection, heat
transfer by radiation can occur between two
bodies, even when they are separated by
a medium colder than both of them
c o n v
e c t i o
n
r a d i a t i o n
What will be a final equilibrium temperature of the body
surface?
Can you write an energy balance equation between the body andsurrounding air and the hot source (fire)?
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Theoretical foundation of radiation was establishedby Maxwell
Electromagnetic wave motion or electromagnetic radiation
Electromagnetic waves travel at the speed of light c in a
vacuum
Electromagnetic waves are characterized by their frequency f
or wavelength λ: λ=c/f
c=co /n co light speed in a vacuumn refraction index of a medium (n=1 for air and
most gases, n=1,5 for glass, 1,33 for water)
In all material medium, there is attenuation of the energy
In a vacuum there is no attenuation of the energy
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Electromagnetic radiation covers a wide range of wavelengths
Radiation that is related to
heat transfer –
Thermal radiationλ from 0,1μm to 100 μm
As a result of energy transition
in molecules, atoms andelectrons.
Thermal radiation is emitted by all matter
whose temperature is above absolute zero.
Everything around us emits (and absorbs)
radiation.
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• Thermal radiation includes entire visible (0,4 to 0,76 μm)
and infrared light and a portion of ultraviolet radiation.
• Bodies start emit visible radiation at 800K (red hot)
and tungsten wire in the lightbulb at 2000K
(white hot) to emit a significant amount of
radiation in the visible range.
• Bodies at room temperature emit radiation in
infrared range 0,7 to 100 μm.
• Sun (primary light source) emits solar radiation –
0,3 to 3 μm – almost half is visible, remaining is
ultraviolet and infrared.
• Body that emits radiation in the visible range is
called light source.
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Spectral and Directional Distribution
Radiation characteristics vary
with wavelength and direction
• Monochromatic or s pectral : Characteristics at a given λ
• Total : Integrated values over all wavelengths
• Directional : At a given direction
• Diffuse radiation: Uniform in all directions
• Hemispherical : Integrated values over all directions
The assumption of diffuse radiation will be made throughout
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Emissive Power E , Irradiation G and
Radiosity J
• Emissive Power (zář ivost):
Radiation emitted from a surface
• Spectral emissive power λ E :
λ E
per unit area per unit wavelength,
= rate of emitted radiation
mW/m2μ
• Total emissive power E :
, E = Integration of λ E over all values of λ2
W/m :
( ) ( )∫∞
=
0
, λλ d T E T E
∫∞
=0
λλd E E
λ
λ
10.1Fig.
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• Irradiation: Radiation energy incident on a surface
• Spectral irradiation λG :
λG per unit area per unit wavelength,
= rate of radiation energy incident upon a surfacemμW/m
2−
• Total irradiationG :
G = integration of λG over all values of λ :
( ) ( )∫∞
=
0
, λλ d T G T G
• Radiosity: The sum of emitted and reflected radiation
• Spectral radiosity λ J :
λ J = rate of radiation leaving a surface per unit area per
unit wavelength, mμW/m2−
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In the above definitions, summation in all directions is
implied although the term hemispherical is not used
• Total radiosity J :
( ) ( )∫∞
=
0
, λλ d T J T J
J = integration of λ J over all values of λ :
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Characteristics of blackbody:
(1) It absorbs all radiation incident upon it
(2) It emits the maximum energy at a given temperature
and wavelength
(3) Its emission is diffuse
Planck's Law
λb E = spectral emissive power of a blackbody:
( )1)/exp(
,2
51
−
−
T C
C T E b
λ
λλλ C 1 and C2 are constants
Blackbody Radiation
Blackbody: An ideal radiation surface used as standardfor describing radiation of real surfaces
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Planck's Law
Blackbody Radiation
2879,6 T λmax =
Maximum emitted energy at
specific temperatures given by
Wien law:
Note - by qualitative judgment -
energy emitted in visible range
for 2000 K – tungsten wire in
a light bulb.
Thermal radiation 0,1 to 100 μm
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Stefan-Boltzmann Law
Based on:
• Experimental data by Stefan (1879)
• Theoretical derivation by Boltzmann (1884)4T E b σ =
b E = total blackbody emissive power (all wavelengthsand all directions), [W/m2]
428-K W/m105.67 − is the Stefan-Boltzmann
constant
It can also be arrived at using Planck's law
Stefan-Boltzmann law
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( ) ( )
4
02
51
0b λb
T σ
d λ1 )T / λC ( exp
λC
dx λ ,T E T E
=
∫ =−
=
=∫=
∞ −
∞
• Stefan-Boltzmann law gives the total radiation emitted from
a black body at all wavelengths from λ =0 to λ =∞.• Often an interest in radiation over some wavelength band –
light bulb – how much is emitted in
the visible range?• We use a procedure to determine E b,0- λ
∫=−
λ
0
b λ λb,0 T)d λ( E (T) E ,λ
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Define a dimensionless quantity f λ(T):
4
λ
0 b, λ
λσ T
(T)d λ E (T) f
∫=
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Want to know how energy is emitted
in the visible range 0,40 to 0,76 μm.
λ1T=0,40.2500=1000 ⇒ f λ1 = 0,000321
λ2T=0, 76.2500=1900 ⇒ f λ2 = 0,053035
f λ2 - f λ1 = 0,0527
Only about 5% of radiation is emitted
in the visible range. The remaining
95% is in the infrared region in theform of heat.
Light bulb.
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Radiation of Real Surfaces
Objective: Develop a methodology for determining
radiation heat exchange between real surfaces.
• Surface radiation properties
• The graybody
• Kirchhoff's law
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Absorptivity a, Reflectivity r , Transmissivity t
G
G
G G E
J
10.2Fig.
rG
tG
Irradiation incident on a real surface can
be absorbed, reflected and transmitted.
Remind: radiosity J (total radiation leaving
the surface) is a sum of
emitted E and reflected rG radiation.
a = total absorptivity = fraction absorbed
r = total reflectivity = fraction reflected
t = total transmissivity = fraction transmitted
G G t rG aG =++
1=++ t r a
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Similarly
1=++ λ λ λ t r a
a λ
= spectral absorptivity
r λ = spectral reflectivity
t λ
= spectral transmissivity
Opaque material: 0== λ t t
Simplification: 1=+ r a
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Emissivity (emisivita, poměrná zářivost)
Total emissivity ε (T):
Ratio of emissive power of a
surface to that of a blackbodyat the same temperature:
( )
( )T E
T E T
b
)(=ε
Spectral emissivity λ :
Ratio of the spectral emissive power of a surface to that
of a blackbody at the same temperature:
( ))
( )T E
T E T
b,
,,
λ
λ λ ε
λ
λ λ =
λ
λ E
10.3Fig.
blackbody
surfacereal
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Kirchhoff's Law
It is much easier to determine emissivity ε than absorptivity a.
By experiments. But how we can determine absorptivity?
Kirchhoff’s law says that under certain
conditions:
( ) ( )T T α ε =Total
( ) ( )T T ,, λλ=Spectral
Kirchhoff’s law is used to determine a λ( λ ,T) from experimental
data on ε λ( λ ,T)
Equality of emissivity and absorptivity
Quite different physical quantities
Just numerical equality
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Graybody Approximation
The graybody concept is introduced to simplify theanalysis of radiation exchange between bodies
Graybody: An ideal surface for which the
spectral emissivity ελ is independent of λ
λ
λ E
10.3Fig.
blackbody
surfacereal
gray body
λ
λ E
10.3Fig.
blackbody
bodygray
approx. 0,75 E b
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Thus: =)(),( T T ελ constant independent of λ
It follows from Kirchhoff's Law that
( ) ( ) graybodya for T T =
NOTE:
(1) Radiation properties ε , a and r are assigned single
values instead of a spectrum of values
(2) Data on ε give r and a for opaque surface.
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Radiation Exchange Between Black Surfaces
Two black surfaces with
areas 1 S and 2 S at
temperatures1
T and2
T
Objective: Determine the net
heat transfer 21Q −& between the two surfaces
21 T T >
1T
2T
1 S
2 S
1 E 2 E
12Q&
1
2
Important factors:• Configuration
• Surface area
• Surface temperature• Radiation properties (for gray body)
• Surrounding surfaces
• Space medium
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The View Factor
(1) Definition and use:
• It is a geometric factor
• Also known as shape factor and configuration factor
The view factor is the fraction of radiation energy
leaving surface S 1 which is intercepted by S 2
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1Q& = rate of radiation energy leaving surface 1, = S 1 E 1
2Q& = rate of radiation energy leaving surface 2, = S 2 E 2
21Q −& = net radiation energy exchanged between 1 and 2
21−F = fraction of radiation energy leaving 1 andreaching 2
12−F = fraction of radiation energy leaving 2 andreaching 1
1T
2T
1 S
2 S
1 E
2 E
21Q −&
1
2
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For black surfaces:
The net energy exchanged between the surfaces 1 and 2:
21-2212-112-1 bb E F S E F S Q −=& (a)
Radiation that leaves the surface 1: 111 b E S Q =&
1121 b E S F −and is intercepted by the surface 2:
222 b E S Q=&
Radiation that leaves the surface 2:
2212 b E S F −and is intercepted by the surface 1:
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If 21 T T = then 21 bb E E = and 12Q&
= 0.
( ) 44212-11212-112-1 T T F S E E F S Q bb −=−= σ &
122211 −− = F S S (b)
Combine (a) and (b) and use Stefan-Boltzmann law
:
4
T E b σ =
Reciprocal rule (vztah recoprocity)
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(2) Rules:
• Reciprocal rule can be generalizedi j j j i i F S F S −− =
• Additive rule: Conservation of energy - see the figure.
( ) 3-12-132-1 F F F +=+
Multiply by 1 S
3-112-113)21 F S F S F S +=+−(1
Use the reciprocal rule
1-331-221-3)+(232 )( F S F S F S S +=+
10.5Fig.
1
2
3
12
3
i
n
(i=1 to n, j=1 to n)
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• Enclosure or summation rule: All energy leaving one
surface must be received by some or all other surfaces
11131211 =nF F F K
ni F n
j
j i ,,3,2,1 1=
1=
K
• Conclusion: ii = 0 for a plane or convex surface and
ii F ≠ 0 for a concave surface
(3) Determination of view factors:
• Simple configurations: By physical reasoning:
n
4
3
2
1
6.10Fig.
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2
1 A 2 A
1
112 =F
Apply the reciprocal rule
211122 −− = F S F S
21212112 /)/( S S F S S F == −−
• Other methods:
• Surface integration method: Can involve tediousdouble integrals
• View factor algebra method: Known factors are used
in a superposition scheme together with the threeview factor rules to construct factors for other
configurations
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View factor for parallel rectangles
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View factor for perpendicular rectangles
with a common side
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Examples of the View factor algebra method:
Determine F1-3 and F3-3
(i) Figure (a): F 1-2 is given in Jícha: P ř enos tepla a látky P ř íloha 2-3a, (př ípad 3 )
Apply summation rule to surface 1
1131211 =F F F
But 11 = 0
∴ 1213 1 F F −
1
2
3
Figure (a)
To determine F 33
apply summation rule to surface 3:
1333231 =F F F
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Symmetry, 3231 F
Thus, 3133 21F −
Reciprocal rule:1-333-11
F S F S =
∴ 3-1313-3 21 F S S F )(−=