Gray gases T g

CO 2 + H 2 O

Black six-surface
T s A s
ε s = α s = 1
surface is a blackbody at a uniform temperature as shown in Figure 14.9. Net
heat transfer rate = hot gas emission and absorbed by the black surface-black
surface emission and absorbed by gases [1].
q net = (ε g A s σT
4
g ) · α s − (ε s A s σT
4
s ) · α g = A s σ(ε g T
4
g − α g T
4
s )
(14.33)
'
-v
'
'
-v
'
emission
from the gas
emission
from the surface
For gray gas,
ε g = α g (Otherwise, ε g = α g )
and for nongray gas
ε g = ε c + ε w − Δε
α g = α c + α w − Δα
Δα = Δε
For water vapor,
α w = C w
� T g
T s
� 0.45
· ε w
�
T s , P w L
T s
T g
�
(14.34)
For carbon dioxide,
α c = C c
� T g
T s
� 0.65
· ε c
�
T s , P c L
T s
T g
�
(14.35)
287
Radiation Transfer through Gases
FIGURE 14.9
Radiation between hot gases and single black enclosure.
Note that the problem will be more complicated if we consider radiation
exchange between nongray gases and a single gray enclosure, or radiation
exchange between nongray gases and an N-surfaces enclosure, where N =
1, 2, 3, . . . , N.