Environmental Engineering Reference
In-Depth Information
E
= ε
E
b
(3.20)
Therefore, it is sufficient to calculate the balance of radiant emission and absorp-
tion of the wall, when we can adopt a gray model in estimating the radiative heat
transfer within an enclosure filled with clear gases.
3.3.1.2 Weighted-Sum-of-Gray-Gases Model
Like a solid medium, gases can absorb and emit radiative energy. Radiation from
gas typically exhibits discrete band emission/absorption in terms of wavelength,
since the interactions between molecules are relatively weak in gases. Therefore,
even if a gas is clear at a certain wavelength, it may behave nonclearly at another
wavelength. A mixed gas generally has different emission/absorption characteristics
depending on the concentration of nonclear gases.
Figure 3.11
shows an example
of the distribution of absorptivity of mixed gas containing CO
2
and N
2
,
9
which varies
with gas temperature and the temperature of radiation source. Thus, it is erroneous
to neglect these features when estimating the radiative heat transfer in a furnace
filled with burned product by using a constant emissivity.
The relationship between the emissivity-path length for an unclear gas can be
expressed by
ε
g
= 1 - exp(-
kL
)
(3.21)
where
k
is the absorption coefficient and
L
is the path length of radiation. Hottel
10,11
showed that the emissivity of a real gas can be represented by the weighted sum of
gray gases, and the emissivity-path length relationship may be approximated by a
series as:
{
}
−
(
)
ε
g
=
a
1
exp
k L
(3.22)
g n
,
n
n
where
a
gn
= 1
(3.23)
,
n
where
a
g,n
is the fractional amount of energy in the spectrum regions where the gray
gas of absorption coefficient,
k
n
. With this expression, the absorption coefficient,
k
n
,
can be made independent of temperature and the temperature dependence of emis-
sivity taken by the weighting factor
a
g,n
.
A luminous flame has a continuous spectrum emitted by the small particulates
generated during combustion processes. It means that we can assume a luminous
flame including soot particles as a gray gas. Therefore, it is convenient to approxi-
mate the variable absorptivity of combusting or burned gases, even containing soot
particles, with the weighted sum of gray gases. Johnson and Beér
12
have proposed
Search WWH ::
Custom Search