Question

A rectangular fin width 8 mm, thickness 4 mm and length 30 mm, is provided on an I.C. engine for maximizing heat transfer from surface. The ratio of effectiveness of fin to efficiency of the fin is

• A. 22.5
• B. 0.044
• C. 1.25
• D. 25.6

Answer 1

The correct option is A 22.5

$\begin{array}{cc}{\epsilon }_{fin}& \frac{Q_{withfin}}{Q_{withoutfin}}\\ {\eta }_{fin}& =\frac{Q_{withfin}}{Q_{max}}\\ \frac{{\epsilon }_{fin}}{{\eta }_{fin}}& =\frac{Q_{max}}{Q_{withoutfin}}\\ & =\frac{h\left(PL\right){\theta }_{\circ }}{hA{\theta }_{\circ }}\text{(Assumption tip is insulated)}\\ & =\frac{PL}{A}=\frac{2(W\times t)\times L}{W\times t}\\ & =\frac{2(8\times 4)\times {10}^{-3}\times 30\times {10}^{-3}}{8\times {10}^{-3}\times 4\times {10}^{-3}}=22.5\end{array}$