A surface at $85C$ is to be cooled down by attaching a heat sink having twenty$-$five $2-cm-$long, $0\mathrm{.}2-cm-$

square aluminum pin fins $(k=231(W)m^{-1}(K))$ to it $($Figure $2).$ The center$-$to$-$center distance between the

fins is of $0\mathrm{.}5$ cm $.$ The temperature of the surrounding medium is $32C,$ and the combined heat transfer

coefficient for radiation and convection is $18W{m}^{-2}K$ on all surfaces. Neglecting the heat transfer at

the tip of the fin, determine:

a$.$ The efficiency of one of the fins.

b$.$ The total rate of heat transfer from the heat sink.

c$.$ The overall effectiveness of the heat sink.

d$.$ The temperature at the mid$-$length and tip of the fin.

e$.$ Discuss the answers obtained in $d.$ Were these values expected?

Figure $2$: Schematic of the heat sink and its dimensions