� �
�
�
�
From Equation 12.3,
1
cos θ i cos θ j
πR 2
F ij
dA i dA j
= A i
A i A j
cos θ i cos θ j dA j
πR 2
=
A j
A i
= θ, R 2
where A i =
with θ i = θ j
dA i ,
2 + L 2 , cos θ = L/R, and dA j = 2πr dr ,
= r
2 θ
cos
F ij
dA j
=
πR 2
A j
D 2
/
�
r dr
D 2
=
(r 2 + L 2 ) 2
D 2 + 4L 2
= 2L 2
0
View Factor
243
12.2 Evaluation of the View Factor
View factor is a function of geometry only. The following shows several wellknown methods to obtain the view factor for common geometry for radiation
heat transfer applications [3].
Elongated surfaces—use Hottel’s String method for 2-D geometry.
Direct integration—need to perform double-area integration (difficulty).
Contour integration—use Stoke’s theorem to transform area-to-line
integration.
Algebraic method—determine the unknown view factor from the
known value.
12.2.1 Method 1—Hottel’s Crossed-String Method for 2-D Geometry
Hottel proposed the following view factor between surface i and surface j for
2-D geometry (with surfaces elongated in the direction normal to the paper
as shown in Figure 12.5.
Find
(1)
L 1 + L 2 − L ac
F 1−2 =
(12.7)
2L 1