Discussion
Which one of the following configurations has the highest fin effectiveness?
Answer: A
The key's answer is thin, closely spaced fins.
Fin effectiveness compares the heat transferred with the fin to the heat transferred from the bare base area it occupies. For a long fin:
\[ \varepsilon = \sqrt{\frac{kP}{hA_{c}}} \]
A thin fin has a large perimeter P for a small cross-section Ac, so each fin is more effective. Spacing them closely puts more fins, and so more surface, on a given base area.
Thick fins have a smaller P/Ac ratio and so lower effectiveness, and wide spacing wastes base area. Very close spacing can starve the gaps of air flow in practice, but the standard answer to this question takes thin and closely spaced as best.
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