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Problem $09\mathrm{.}087$E $-$ A Vertical Hot Surface Attached by a Heat Sink with Equally Spaced Fins of Rectangular Profile

A $6\mathrm{.}04-$in$-$wide and $10-$in$-$high vertical hot surface in $78F$ air is to be cooled by a heat sink with equally spaced fins of rectangular profile. The fins are $0\mathrm{.}08$ in thick and $10$ in long in the vertical direction and have a height of $1\mathrm{.}2$ in from the base. Consider base temperature to be $180F.$

Given: The properties of air at $1$ atm and the film temperature at $129F.$

$k=0\mathrm{.}01597Bt\frac{u}{h}*ft*F$

$v=0\mathrm{.}1975{10}^{-3}f\frac{t^2}{s},$

$Pr=0\mathrm{.}7217,$

$g=32\mathrm{.}2f\frac{t}{s^2}$

Problem $09\mathrm{.}087$E$.$a $-$ Optimum Fin Spacing of the Heat Sink

Determine the optimum fin spacing of the heat sink.

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