E A1−A4 = F A1−A4
' -v '
diffuse
+ ρ
s
3 F A1(3)−A4
'
-v
'
specular reflection
E A2−A4 = F A2−A4 + ρ
s
3 F A2(3)−A4
(13.22)
(13.23)
( )
� ( )
270
Analytical Heat Transfer
13.3 Radiation Exchange between Nongray Diffuse
Isothermal Surfaces
The following (a) integral model or (b) band model can be used to determine radiation exchange among isothermal diffuse nongray surfaces [4,5] as
sketched in Figure 13.10.
a. Integral model
∞
q
q
=
dλ
(13.20)
A i
A i
0
b. Band model
( )
N ( )
q
q
=
Δλ k
(13.21)
A i
A i
k=1
13.4 Radiation Interchange among Diffuse and Nondiffuse
(Specular) Surfaces [4,5]
Exchange factor by using the image method, as shown in Figure 13.11,
Reciprocity Rules A i E Ai−Aj = A j E Aj−Ai
Metal
ε λ
Δλ 1
Δλ 2
Δλ 3
ε λ
Nonmetal
λ
λ
FIGURE 13.10
Radiation exchange among diffuse, isothermal, nongray surfaces.
' -v '
diffuse
+ ρ
s
3 F A1(3)−A4
'
-v
'
specular reflection
E A2−A4 = F A2−A4 + ρ
s
3 F A2(3)−A4
(13.22)
(13.23)
( )
� ( )
270
Analytical Heat Transfer
13.3 Radiation Exchange between Nongray Diffuse
Isothermal Surfaces
The following (a) integral model or (b) band model can be used to determine radiation exchange among isothermal diffuse nongray surfaces [4,5] as
sketched in Figure 13.10.
a. Integral model
∞
q
q
=
dλ
(13.20)
A i
A i
0
b. Band model
( )
N ( )
q
q
=
Δλ k
(13.21)
A i
A i
k=1
13.4 Radiation Interchange among Diffuse and Nondiffuse
(Specular) Surfaces [4,5]
Exchange factor by using the image method, as shown in Figure 13.11,
Reciprocity Rules A i E Ai−Aj = A j E Aj−Ai
Metal
ε λ
Δλ 1
Δλ 2
Δλ 3
ε λ
Nonmetal
λ
λ
FIGURE 13.10
Radiation exchange among diffuse, isothermal, nongray surfaces.