Gas Radiation
MEL 725
Power-Plant Steam Generators (3-0-0)
Dr. Prabal Talukdar
Assistant Professor
Department of Mechanical Engineering
IIT Delhi
Radiation in absorbing-emitting
media
• When a medium is transparent to radiation,
radiation propagating through such a media
remains unchanged
• However gases such as CO, NO, CO2, SO2,
H2O and various hydrocarbons absorb and emit
radiation over certain wavelength regions called
absorption bands
• We will discuss a very simple analysis of
radiation exchange in an absorbing and emitting
medium, exchange between a body of hot gas
and its black enclosure
Beer’s Law
• If Io is the intensity of radiation at the source and I is the
observed intensity after a given path, then optical depth τ is
defined by the following equation:
S
⎛
⎞
I
= exp⎜ − β λ (s)ds ⎟
⎜
⎟
Io
⎝ 0
⎠
∫
I / Io = e
−τ
Extinction coefficient β is a function of
temperature T, pressure P,
composition of the material
(concentration Ci of the i th
components)
and wavelength of incident radiation
β
s
Characterization of Participating Media
•
•
Absorption: attenuation of intensity
Emission: augmentation of intensity
•
Scattering →
– In-scattering: augmentation of intensity
– Out-scattering: attenuation of intensity
Equation of Radiative Tranfer
• Increase in Intensity of radiation per unit length
along the direction of propagation is
dI λ (s)
ds
dI λ (s) ⎛ emission per ⎞ ⎛ absorption per ⎞
⎟⎟ − ⎜⎜
⎟⎟
= ⎜⎜
ds
⎝ unit volume ⎠ ⎝ unit volume ⎠
dI λ (s)
= κ λ I b λ (T ) − κ λ I λ (s)
ds
The boundary condition for this equation is
I λ (s) = I λ (0) at s = 0
Transmissivity, Absorptivity and
Emissivity
• Solution of Radaitive Transfer Equation with the
assumption that κ λ and Ibλ(T) are constant
everywhere in the medium, gives
I λ (s) = I λ (0)e − κ λ s + (1 − e − κ λ s )I bλ (T )
At the boundary surface
S = L, intensity will be
I λ (L) = I λ (0)e − κ λ L + (1 − e − κ λ L )I bλ (T )
This is due to external
irradiation
Self emission
Negligible emission
• If the emission of radiation by the medium is
negligible in comparison to the contribution to the
externally incident radiation, we get Ibλ(T) = 0
and then the solution becomes,
I λ ( L ) = I λ ( 0) e − κ λ L
• Then the spectral transmissivity
I λ ( L)
τλ =
= e − κλ L
I λ ( 0)
Spectral absorptivity
• If the medium is non-reflecting,
• And the spectral absorptivity αλ
over the path L is
• When Kirchhoff’s law is
applicable, the spectral
absorptivity αλ is equal to
spectral emissivity ελ
• For no externally incident
radiation,
τλ + α λ = 1
αλ = 1 − e
− κλ L
ε λ = 1 − e − κλ L
I λ (L) = (1 − e − κ λ L )I bλ (T )
Absorption and Emission
Properties of Materials
• Absorption and emission characteristics of
gases are quite different from those of solids
• The absorption (or emission) of radiation by
gases does not take place continuously over the
entire wavelength spectrum; rather it occurs
over a large number of relatively narrow strips of
intense absorption (or emission)
• In semitransparent solids, the absorption
spectrum is more or less continuous
Spectral Absorptivity
Radiation Exchange between a Gas
Body and its Black Enclosure
• Assumption:
– Entire gas body is isothermal
– Enclosure wall is black
• Consider a hemispherical body of gas at uniform
temperature Tg and walls are at temperature Tw
• The intensity of spectral radiation Iλ(L) striking the
surface element dA as a result of the emission of
radiation by the gas along the path L is determined from
I λ (L) = I bλ (Tg )(1 − e
−kλL
)
Spectral Emissivity of Gas
• The spectral radiative heat flux qλ because of
incident radiation from the entire hemisphere
2π π / 2
qλ =
∫ ∫I
λ ( L) cos θ sin θdθdφ
φ=0 θ=0
= πI bλ (T g )(1 − e − κ λ L )
= E bλ (T g )(1 − e
− κλ L
q λ = ε λ E bλ ( Tg )
)
Spectral emissivity of gas
for the path length L
Mean Beam Length
• The simple expression for the hemisphere of gas is not
applicable for other geometries
• A concept of mean beam length is introduced for
engineering calculations
• This is an equivalent path length L which represents the
average contributions of different beam lengths from the
gas body to the striking surface
• In the absence of information available, mean beam
length is approximately calculated as
V
L ≅ 3.5
A
Where A=total surface area of the enclosure
and V = total volume of the gas
Chart for Equivalent path length
Emissivity Charts
• Hottel measured gas emissivity εg and presented
emissivity charts for gases such as CO2, H20,
CO, ammonia, SO2, etc. as a function of
temperature and product term PiL, where Pi is
the partial pressure (in atmospheres) of gas i in
the gas mass and L is the beam length.
Charts
Calculation of Radiation exchange between a Gas
Body and Its enclosure
• The net radiative heat exchange Q between
the gas mass at temperature Tg and its black
surroundings at temperature Tw is
Q = Qe − Qa =
4
σA(ε g Tg
4
− α g Tw )
W
Problem
• A flue gas at Tg=1000K and total pressure PT = 2 atm
containing 10 percent water vapor by volume flows over
a tube bank arranged in an equilateral triangle array,
having a tube with Diameter D = 7.6 cm and a spacing S
= 2D. The tubes are maintained at a uniform temperature
Tw = 500K and considered black. Calculate the net
radiation heat exchange between the gas and the tubes
per square meter of tube wall surface