Current Attempt in Progress

A $40-$mm long, $2\mathrm{.}8-$ mm diameter pin fin is fabricated of an aluminum alloy $(k=140\frac{W}{m}*K).$

$($a$)$ Determine the fin heat transfer rate, in W $,$ for $T_b=50C,T_{}=25C,h=1000\frac{W}{m^2}*K,$ and an adiabatic tip condition.

$($b$)$ Determine the thickness, in mm $,$ of a uniformly applied coating of paint that will maximize the fin heat transfer rate. Determine the painted fin heat transfer rate, in W $.$ The thermal conductivity of the paint is $k=2\mathrm{.}5\frac{W}{m}*K.$ Neglect any thermal contact resistance between the aluminum fin and the paint.

Part A

Your answer is correct.

Determine the fin heat transfer rate, in W $,$ for $T_b=50C,T_{}=25C,h=1000\frac{W}{m^2}*K,$ and an adiabatic tip condition.

$q_f=$ W

Attempts: $2$ of $6$ used