Chapter 13, Problem 13.10P

The reciprocity relation, the summation rule, and Equations 13.5 to 13.7 can be used to develop view factor relations that allow for applications of Figure 13.4 and/or 13.6 to more complex configurations.
Consider the view factor F₁₄for surfaces 1 and 4 of the following geometry. These surfaces are perpendicular but do not share a common edge.

(a) Obtain the following expression for the view factor F14:

$F_{14}=\frac{1}{A_1}\left[\left(A_1+A_2\right)F_{\left(1,2\right)\left(3,4\right)}+A_2{F}_{23}-\left(A_1+A_2\right)F_{\left(1,2\right)3}-A_2{F}_{2\left(3,4\right)}\right]$

(b) It $L_1=L_2=L_4=\left(W/2\right)$ and $L_3=W$ , what is the value of F₁₄?