## Related questions with answers

A pin fin of uniform, cross-sectional area is fabricated of an aluminum alloy $(k=160 \mathrm{W} / \mathrm{m} \cdot \mathrm{K})$. The fin diameter is D=4 mm, and the fin is exposed to convective conditions characterized by $h=220 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. It is reported that the fin efficiency is $\eta_{f}=0.65$. Determine the fin length L and the fin effectiveness $\varepsilon_{f}$. Account for tip convection.

Solution

VerifiedGiven:$D= 4\mathrm{mm}, k= 160\mathrm{W/m\cdot K}, h= 220\mathrm{W/m^{2}\cdot K}, \eta_{f}= 0.65$

Calculate the parameter $m$ as follows:

$\begin{align*} m&= \sqrt{\dfrac{hP}{kA}}\\ &= \sqrt{\dfrac{h\times\pi D}{k\times \pi D^{2}/4}}\\ &= \sqrt{\dfrac{4h}{kD}}\\ &= \sqrt{\dfrac{4\times220}{160\times0.004}}\\ m&= 37.08\\ \end{align*}$

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