View
224
Download
0
Category
Preview:
Citation preview
7/30/2019 (33) Radiation Fundamentals 2
1/22
FUNDAMENTALS (2)
Prabal Talukdarssoc a e ro essor
Department of Mechanical Engineering
E-mail: prabal@mech.iitd.ac.in
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
2/22
Irradiation Intensity of incident radiation: It
which radiant energy ofwavelength is incident from
e , rec on, per un areaof the intercepting surfacenormal to the direction er unitsolid angle about this direction,and per unit wavelength
Radiation incident from all
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
3/22
Irradiation S ectral irradiation G =
2/2
ddsincos,,I
Total irradiation
0
,
0
2m/WdGG
=0
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
4/22
Radiosit
leaving a surface Emitted and reflected part
2/2
dddsincosIJ
=
re
0
,
00
I +=
For a surface which is diffuse emitter
and diffuse reflector
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
5/22
Spectral Quantities
Integration of a
spectral quantity for
the total quantity.
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
6/22
Blackbod Radiation
,
regardless of wavelength and direction
wavelength, no surface can emit more
Although the radiation emitted by a
ac o y s a unc on o wave eng antemperature, it is independent of direction.
MECH/IITD
a s ac o y s a use em er
7/30/2019 (33) Radiation Fundamentals 2
7/22
Characteristics of an isothermal
Complete absorption Diffuse irradiation
For an interior surfaces
MECH/IITD
Diffuse emission from an aperture
7/30/2019 (33) Radiation Fundamentals 2
8/22
Planck Distribution
given by Planck ashc2 20
= -34
]1)kT/hc[exp(,
0
5b, =
, . .
Boltzmann constants k = 1.3805x10-23 J/K
speed of light in vacuum c0=2.998x108 m/s
CTITE 1==
MECH/IITD
]1)T/C[exp( 2,,
7/30/2019 (33) Radiation Fundamentals 2
9/22
Planck Distribution
with wavelengthAt any wavelength the magnitude of the
emitted radiation increases
with increasing temperature
A significant fraction of the radiation emitted
by the sun, which may be
approximated as a blackbody at 5800K, is
in the visible region of the spectrum.
In contrast, for T
7/30/2019 (33) Radiation Fundamentals 2
10/22
Wiens Displacement LawC1==
Differentiating the above equation with respect to and
]1)T/C[exp(,,
2
5,,
setting the result equal to zero, we get
maxT = 2897.8 m.K
,
power is displaced to shorter wavelengths with increasing
temperature
The emission is in the middle of the visible spectrum ( =0.5 m) for solar radiation, since the sun emits
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
11/22
Stefan-Boltzmann LawC
)T,(E5
1b,
=
Total Emissive power
2
0 2
5
1b d
]1)T/C[exp(
E
=
-
b TE =
.Since this emission is diffuse, the total intensity
MECH/IITD
b b
7/30/2019 (33) Radiation Fundamentals 2
12/22
Radiation in certain wavelen th- ,
under a curve for a giventemperature represents the
o a ra a on energy em e
by a blackbody at that
temperature
We are often interested in the amount
of radiation emitted over some
wavelen th band.
For example, an incandescentlightbulb is judged on the basis of the
radiation it emits in the visible range
MECH/IITD
rather than the radiation it emits at all
wavelengths
7/30/2019 (33) Radiation Fundamentals 2
13/22
a blackbody per unit area over awavelength band from 0 to is determined from
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
14/22
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
15/22
Surface Emission
surface to the radiation emitted by a blackbodyat the same temperature
Spectral directional emissivity ,(,,,T) of a
surface at the temperature T is the ratio of theintensity of the radiation emitted at the
wavelength and in the direction of and to
blackbody at the same values of T and .
MECH/IITD )T,(I
,,,)T,,,(
b,
e,
,
7/30/2019 (33) Radiation Fundamentals 2
16/22
Blackbod and Real Emission
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
17/22
Emissivit
)T,,(IT e
)T(Ib )T,(E
Spectral hemispherical
)T,(E,
2 2/
b,
=
s ncos,,,
2 2/
0 0
e,
,
2/
0 0b,
MECH/IITD
= s ncos,,0
,
7/30/2019 (33) Radiation Fundamentals 2
18/22
Total Hemispherical Emissivit Total )T(E)T( =
emissivityb
Directional
distributions of
total diretctional
MECH/IITD
,
surfaces to be diffuse emitters with an emissivity equal to the
value in the normal ( = 0) direction.
7/30/2019 (33) Radiation Fundamentals 2
19/22
)T(E)T( =
b
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
20/22
Gra /Real Surface
A gray surface should emit as much radiation
as the real surface it represents at the same
MECH/IITD
empera ure. ere ore, e areas un er e
emission curves of the real and gray surfaces
must be equal.
7/30/2019 (33) Radiation Fundamentals 2
21/22
Spectral dependence of
MECH/IITD
7/30/2019 (33) Radiation Fundamentals 2
22/22
The presence of oxide layers may significantly increase the emissivity of metallic
The emissivity of metallic surfaces is generally small, as low as 0.02 for
higly polished gold and silver
.
MECH/IITD
The emissivity of non-conductors is comparatively large, generally exceeding 0.6
The emissivity of conductors increases with increasing temperature; HoweverFor non-conductors it may be both way.
Recommended