Environmental Engineering Reference
In-Depth Information
Wavelength
λ,
µ
m
10
5
4
3
2
1.0
0.8
0.6
0.4
0.2
0
1000
2000
3000
4000
5000
Wavenumber
η
,
cm
-1
FIGURE 3.11
Absorptivity of a mixed gas at 833 K, 10 atmosphere.
an expression similar to Equation 3.22 taking account of the effect of continuous
emission of soot cloud. This is illustrated in
Figure 3.12
using three terms repre-
senting emissivity bands and the corresponding weighting factor
a
g,n
can be found
in the literature; for example, see reference 13.
3.3.1.3 Nongray Models
As shown in
Figure 3.11
,
radiative heat energy of a gas molecule is transferred
through the bands corresponding to respective vibrational energy levels. However,
careful observation of these bands reveals that they consist of a series of line spectra
precise prediction of exact radiative heat transfer cannot be expected unless we
calculate the net balance of radiation energy in each wavelength (or wave number),
since real radiative heat transfer of gaseous media is carried out through these line
spectra. A number of models have been proposed intending to estimate the integrated
absorption coefficient taking account of distribution of the line spectrum. The nar-
rowband models, such as the Elsasser model
15
and the statistical model,
16
are in this
category. However, it is still difficult to determine their line intensity and overlapping
due to broadening, because there are a number of line spectra in a limited wavelength
range. Therefore, the accuracy of the obtained results is not always high enough,
despite a complex calculation that is necessary in actual execution of numerical
simulations. Consequently, practical simulation of heat transfer in furnaces using
the narrowband model seems doubtful.
In practical cases, heat transfer engineers are usually interested in estimating
radiative heat flux integrated over the spectrum. Thus, it is desirable to have models
that can readily predict the total absorption or emission through each band appearing
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