�
�
�
�
�
�
�
�
� �
�
�
�
�
�
�
⎡
⎤
1
(
) ⎥
ln R dx i dx j + ln R dy i dy j + ln R dz i dz j ⎦
(12.11)
F Ai−Aj =
⎢
⎣
2πA i
c i c j
Apply Stokes’ theorem to reduce quadric to double integrations as
⎧
⎡ b
b
1
dx j
⎨
⎩
ln (x i − x j )
2
+ a
2
1/2
F Ai−Aj
dx
⎣
= 2πbc
0
0
⎫
0
⎬
1/2
2
+ c
2
+ a
2
ln (x i − x j )
dx i
+
⎭
b
⎧
0
b
1/2
dx j
⎨
⎩
ln (x i − x j )
2
+ 0
2
dx
+
b
0
⎫ ⎤
0
⎬
ln (x i − x j )
2
+ c
2
+ 0
2
1/2
dx i ⎦
(12.12)
+
⎭
b
View Factor
251
z
a
c
b
y
dA j
A j
A i
dA i
θ j
θ i
x
FIGURE 12.9
View factor between two adjacent surfaces.
12.2.3 Method 3—Contour Integration
Use Stokes’ theorem to transform area to line integration.
Determine the view factor between two adjacent surfaces as shown in
Figure 12.9.