Discussion
View factor of a large cylinder of 10 cm in radius and 60 cm in length from a coaxial smaller cylinder of 5 cm radius and the same length is 0.34. View factor of the larger cylinder of itself (concave inner surface) is 0.25. The view factor of the larger cylinder with respect to either annular end is
Answer: B
The view factor from the large cylinder to either annular end is 0.29.
Call the small cylinder 1 and the large cylinder's inner surface 2. The given 0.34 is \(F_{12}\), from the small cylinder to the large one. Reciprocity converts it, using the area ratio \(A_{1}/A_{2} = r_{1}/r_{2} = 5/10\) for equal lengths:
\[ \begin{aligned} F_{21} &= \frac{A_{1}}{A_{2}}F_{12} = 0.5 \times 0.34 = 0.17 \\ F_{21} + F_{22} + 2F_{2,\text{end}} &= 1 \\ 2F_{2,\text{end}} &= 1 - 0.17 - 0.25 = 0.58 \\ F_{2,\text{end}} &= 0.29 \end{aligned} \]
The summation rule over the enclosure, with two identical annular ends, gives the answer. 0.17 is \(F_{21}\) itself, and using 0.34 directly without reciprocity gives \((1 - 0.34 - 0.25)/2 \approx 0.21\), not offered. 0.33 and 0.42 match no consistent working.
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