GATE 2022 CH – Question 54
A cylindrical fin of diameter 24 mm is attached horizontally to a vertical planar wall. The heat transfer rate from the fin to the surrounding air is 60% of the heat transfer rate if the entire fin were at the wall temperature. If the fin effectiveness is 10, its length is ___________ mm (rounded off to the nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 100
Explanation
The first statement says that the fin efficiency is $\eta = 0.6$. The effectiveness is the heat transfer divided by that of the base area without the fin: $\varepsilon = \eta\frac{A_{fin}}{A_c} = \eta\frac{\pi DL}{\pi D^2/4} = \frac{4\eta L}{D}$. So $10 = \frac{4 \times 0.6 \times L}{24}$ and $L = 100$ mm.