Question

A cylindrical pin fin of diameter 0.6 cm and length of 3 cm with negligible heat loss from the tip has an efficiency of 0.7. The effectiveness of this fin is _______.

• A. 12
• B. 14
• C. 20
• D. 15

Answer 1

The correct option is B 14

$\begin{array}{cc}L& =3cm\\ d& =0.6cm\\ \eta & =0.7\\ \text{We know,}& \\ \eta & =\frac{\tan hmL}{mL}\left(\text{for insulated fin tip}\right)\\ 0.7& =\frac{\tan hmL}{mL}\\ \tan h\left(mL\right)& =0.7mL\\ & \text{effectiveness of insulated fin tip:}\\ \epsilon & =\sqrt{\frac{Pk}{h{A}_c}}\times \tan hmL\\ & =\sqrt{\frac{PK}{h{A}_c}}\times 0.7mL\\ & =\sqrt{\frac{Pk}{h{A}_c}}\times 0.7\sqrt{\frac{Ph}{k{A}_c}}\times L\\ & =\frac{P}{A_c}\times L\times 0.7=0.7\times \frac{PL}{A_c}\\ & =0.7\times \frac{\pi \times d\times L}{\frac{\pi }{4}\times d^2}=0.7\times \frac{4L}{d}\\ & =0.7\times 4\times \frac{3}{0.6}\\ \epsilon & =14\end{array}$