A pin fin $($k $=250$ W$/$mK$)$ is attached to a wall. The fin$$s diameter is $1\mathrm{.}5$ cm and it is $10$ cm

long. The hot wall is at $200$ oC$.$ The surrounding air is at $15$ oC and the convective coefficient

is $9$ W$/$m$2$K$.($a$)$ Determine the rate of heat transfer from the fin to the surrounding air. $($b$)$

Compare the result of part $($a$)$ with the result from the very$-$long$-$fin approximation. $($c$)$

Compare the result of part $($a$)$ with the insulated fin tip approximation. $($d$)$ Determine the

efficiency of the fin. $($e$)$ Determine the effectiveness of the fin.