View Factor
253
x
y
z
A 2 (x 2 , y 2 , c)
A 1 (x 1 , y 1 , 0)
a
b
b
c
c
FIGURE 12.10
View factor between two opposite surfaces.
Example 12.5
Determine view factors F 1−2 and F 2−1 for the following geometries shown in
Figure 12.11.
For geometries (a) and (b),
F 1−1 + F 1−2 + F 1−3 = 1
F 1−1 = 0
∴ F 1−2 = 1 − F 1−3 (can be obtained from Table 12.2)
A 1 F 1−2 = A 2 F 2−1
A 1
∴ F 2−1 =
F 1−2
A 2
12.2.4 Method 4—Algebraic Method
Determine the unknown view factor between surface areas A 1 and A 2 , as
shown in Figure 12.12, from the known value of view factors.
A 1 F 1−2 = A 1 F 1−j − A 1 F 1−4
= A j (F j−i − F j−3 ) − A 4 (F 4−i − F 4−3 )
(12.14)
where F j−i , F j−3 , F 4−i , and F 4−3 , are available from formulas or charts.
Example 12.6
Determine view factors F 1−4 and F 4−1 from Figures 12.13a and b:
A 1 F 1−4 = A 2 F 2−3
A i F i−j = A 1 F 1−j + A 2 F 2−j
= A 1 F 1−3 + A 1 F 1−4 + A 2 F 2−3 + A 2 F 2−4
= A 1 F 1−3 + 2A 1 F 1−4 + A 2 F 2−4
253
x
y
z
A 2 (x 2 , y 2 , c)
A 1 (x 1 , y 1 , 0)
a
b
b
c
c
FIGURE 12.10
View factor between two opposite surfaces.
Example 12.5
Determine view factors F 1−2 and F 2−1 for the following geometries shown in
Figure 12.11.
For geometries (a) and (b),
F 1−1 + F 1−2 + F 1−3 = 1
F 1−1 = 0
∴ F 1−2 = 1 − F 1−3 (can be obtained from Table 12.2)
A 1 F 1−2 = A 2 F 2−1
A 1
∴ F 2−1 =
F 1−2
A 2
12.2.4 Method 4—Algebraic Method
Determine the unknown view factor between surface areas A 1 and A 2 , as
shown in Figure 12.12, from the known value of view factors.
A 1 F 1−2 = A 1 F 1−j − A 1 F 1−4
= A j (F j−i − F j−3 ) − A 4 (F 4−i − F 4−3 )
(12.14)
where F j−i , F j−3 , F 4−i , and F 4−3 , are available from formulas or charts.
Example 12.6
Determine view factors F 1−4 and F 4−1 from Figures 12.13a and b:
A 1 F 1−4 = A 2 F 2−3
A i F i−j = A 1 F 1−j + A 2 F 2−j
= A 1 F 1−3 + A 1 F 1−4 + A 2 F 2−3 + A 2 F 2−4
= A 1 F 1−3 + 2A 1 F 1−4 + A 2 F 2−4