GATE 2021 CH – Question 53
A straight fin of uniform circular cross section and adiabatic tip has an aspect ratio (length/diameter) of 4. If the Biot number (based on radius of the fin as the characteristic length) is 0.04, the fin efficiency is _____ % (round off to nearest integer).
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Correct answer: 43
Explanation
For a uniform fin with an insulated tip, $\eta_f=\tanh(mL)/(mL)$ and $m^2=hP/(kA_c)$. For a circular fin of radius r, $P/A_c=2/r$.
Since $Bi=hr/k=0.04$, $m^2=2Bi/r^2$. The aspect ratio gives $L/(2r)=4$, so $L/r=8$ and $mL=8\sqrt{2(0.04)}=2.26274$.
Therefore $\eta_f=\tanh(2.26274)/2.26274=0.43247$, or **43%** to the nearest integer. The radius-based Biot number must not be treated as diameter-based.