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Similarly, the differential view factor between area i and differential area j is
J i (cos θ i cos θ j /πR 2 ) dA i dA j
dA j cos θ i cos θ j
dF Ai−dAj =
=
dA i
J i A i
A i
πR 2
A i
And the view factor between differential area j and area i is
J j (cos θ i cos θ j /πR 2 ) dA i dA j
cos θ i cos θ j
F dAj−Ai =
=
dA i
J j dA j
πR 2
A i
From reciprocity rules for diffuse and isothermal surfaces,
A i F A i −A j = A j F A j −A i
dA i dF dA i −dA j = dA j dF dA j −dA i
A i dF Ai−dAj = dA j F dAj−Ai
dA i dF dA i −A j = A j dF A j −dA i
Example 12.1
Determine the view factor between two parallel discs as shown in Figure 12.4.
Assume that A i « A j , the distance between two surfaces is L, and the larger disc
has a diameter D.
242
Analytical Heat Transfer
dA j
A j
θ j
L
R
θ i
A i
FIGURE 12.4
View factor between two parallel disks.