Table 13.1

Table 13.1 View factors for two-dimensional geometries.

Geometry	Relation
Parallel Plates with Midlines Connected by Perpendicular	$\begin{matrix} F_{i j} = \frac{{[{(W_{i} + W_{j})}^{2} + 4]}^{1 / 2} - {[{(W_{j} - W_{i})}^{2} + 4]}^{1 / 2}}{2 W_{i}} \\ W_{i} = w_{i} / L, W_{j} = w_{j} / L \end{matrix}$
Inclined Parallel Plates of Equal Width and a Common Edge	$F_{i j} = 1 - \sin (\frac{α}{2})$
Perpendicular Plates with a Common Edge	$F_{i j} = \frac{1 + (w_{j} / w_{i}) - {[1 + {(w_{j} / w_{i})}^{2}]}^{1 / 2}}{2}$
Three-Sided Enclosure	$F_{i j} = \frac{w_{i} + w_{j} - w_{k}}{2 w_{i}}$
Parallel Cylinders of Different Radii	$\begin{matrix} F_{i j} & = & \frac{1}{2 π} {π + {[C^{2} - {(R + 1)}^{2}]}^{1 / 2} \\ - {[C^{2} - {(R - 1)}^{2}]}^{1 / 2} \\ + (R - 1) \cos^{- 1} [(\frac{R}{C}) - (\frac{1}{C})] \\ - (R + 1) \cos^{- 1} [(\frac{R}{C}) + (\frac{1}{C})]} \end{matrix}$ $\begin{matrix} R & = & r_{j} / r_{i}, S = s / r_{i} \\ C & = & 1 + R + S \end{matrix}$
Cylinder and Parallel Rectangle	$F_{i j} = \frac{r}{s_{1} - s_{2}} [\tan^{- 1} \frac{s_{1}}{L} - \tan^{- 1} \frac{s_{2}}{L}]$
Infinite Plane and Row of Cylinders	$F_{i j} = 1 - {[1 - {(\frac{D}{s})}^{2}]}^{1 / 2} + (\frac{D}{s}) \tan^{- 1} [{(\frac{s^{2} - D^{2}}{D^{2}})}^{1 / 2}]$