TABLE 12.1 (continued)
View Factors for 2-D Geometries
Geometry
Relation
�
�
r
Cylinder and parallel rectangle
F ij =
tan −1 s 1 − tan −1 s 2
s 1 − s 2
L
L
r
j
L
i
s 2
s 1
�
� 1/2
�
� � 2
� �
� 1/2
2 − D 2
D
D
s
Infinite plane and row of cylinders
F ij = 1 − 1 −
+
tan −1
s
s
D 2
s
D
j
i
Concentric cylinders
A 1
F 12 = 1; F 21 = A 2
A 2
A 1
F 22 = 1 − F 21 = 1 − A 2
A 1
1
Long duct with equilateral triangular
F 12 = F 13 = 2
cross-section
1
2
3
�
( ) 2
� 1/2 ( )
c
c
Long parallel plates of equal width
F 12 = F 21 = 1 +
−
a
a
1
c
2
a
248
Analytical Heat Transfer
continued
View Factors for 2-D Geometries
Geometry
Relation
�
�
r
Cylinder and parallel rectangle
F ij =
tan −1 s 1 − tan −1 s 2
s 1 − s 2
L
L
r
j
L
i
s 2
s 1
�
� 1/2
�
� � 2
� �
� 1/2
2 − D 2
D
D
s
Infinite plane and row of cylinders
F ij = 1 − 1 −
+
tan −1
s
s
D 2
s
D
j
i
Concentric cylinders
A 1
F 12 = 1; F 21 = A 2
A 2
A 1
F 22 = 1 − F 21 = 1 − A 2
A 1
1
Long duct with equilateral triangular
F 12 = F 13 = 2
cross-section
1
2
3
�
( ) 2
� 1/2 ( )
c
c
Long parallel plates of equal width
F 12 = F 21 = 1 +
−
a
a
1
c
2
a
248
Analytical Heat Transfer
continued