A metallic rod (k = 32 W/m°C), 10 mm in diameter and 80 mm long, with an insulated end is to be used as spine. It is expossed to sourrounding with a temperature of 80°C and a heat transfer coefficient 55 W/m²°C. The temperature at the base of fin is 100°C. What is the efficiency of the pin?
Efficiency of fin =
\[\eta =\frac{tan\,h\left ( mL \right )}{mL}\]
\[L=80\times10^{-3}\,m\,=0.080\,m\]
\[m=\sqrt{\frac{hP}{KA}}=\sqrt{\frac{h\times\pi d}{K\frac{\pi d^{2}}{4}}}=\sqrt{\frac{4h}{kd}}=\sqrt{\frac{4\times 55}{32\times 0.010}}=26.22\]
\[\eta = \frac{tan\,h\left ( 26.22\times0.080 \right )}{26.22\times0.080} = 0.4625=46.25\, \%\]
