Question

One end of the long rod 35 mm in diameter, is inserted into a furnace with the other end projecting in the outside air having heat transfer coefficient of $65W/m^2{}^{\circ }C$ and temperature ${25}^{\circ }C$ and thermal conductivity of the fin material is $512.W/m{}^{\circ }C,$ the effectiveness of the fin was found that 9.5. If the heat transfer coefficient of the air to which the fin is exposed is reduced to $25W/m^2{}^{\circ }C,$ then the effectiveness of the fin is

• A. 15.32
• B. 234
• C. 24.7
• D. 13.6

Answer 1

The correct option is A 15.32

$\begin{array}{cc}{h}_1& =65W/m^2-K\\ k=51.2W/m-K& \\ {\epsilon }_1& =9.5\\ h_2& =25W/m^2-K\\ \text{Effectiveness of the fin}\left(\epsilon \right)& =\sqrt{\frac{pk}{hA}}\\ & \text{(considering the rod of infinite length)}\\ \epsilon \propto \sqrt{\frac{1}{h}}& \text{(everything is constant except 'h')}\\ \frac{{\epsilon }_1}{{\epsilon }_2}& =\sqrt{\frac{h_2}{h_1}}\\ \frac{9.5}{{\epsilon }_2}& =\sqrt{\frac{25}{65}}\\ {\epsilon }_2& =15.32\end{array}$