�
�
and
J i = ε i E bi + (1 − ε i )G i
(14.23)
Therefore,
E bi − J i
q i =
(14.24)
(1 − ε i )/(A i ε i )
Performing energy balance between surface i and the rest of surfaces j
through radiation gases,
q i = A i ( J i − G i )
= A i J i −
F ij J j (1 − α ij,g ) − E bg ε i,g + A i ε i,g J i − A i ε i,g J i
= A i ε i,g ( J i − E bg ) +
A i F ij (1 − α ij,g )( J i − J j )
(14.25)
where
A i G i =
A j F ji J j (1 − α g ) + A i ε i,g E bg
=
A i F ij J j (1 − α g ) + A i ε i,g E bg
(14.26)
And from the following relationships:
A i (J i − ε i,g J i ) = A i J i (1 − ε i,g )
= A i J i (1 − α i,g )
=
A i F ij (1 − α i,g )J i
Therefore,
N
J i − E bg
J i − J j
q i = �
� +
�
�
(14.27)
1
1
j=1
A i ε i,g
A i F ij (1 − α ij,g )
' -v '
'
-v
'
resistance due to
resistance due to view factor
gas emissivity
and gas absorptivity
If gas has no radiation properties, that is, ε g = α g = 0, τ g = 1, then the above
equation returns to the one we have seen before as
N J i − J j
q i =
1/A i F ij
j=1
283
Radiation Transfer through Gases