A steady$-$state, finite$-$difference analysis has been performed on a cylindrical fin with a diameter of $D=12mm$ and a thermal

conductivity of $15\frac{W}{m}*K.$ The convection process is characterized by a fluid temperature of $T_{}=25C$ and a heat transfer coefficient

of $h=25\frac{W}{m^2}*$ K$.$ Assume $T_0=100\mathrm{.}0C,T_1=93\mathrm{.}4C,$ and $T_2=89\mathrm{.}5C$

$($a$)$ The temperatures for the first three nodes, separated by a spatial increment of $x=10mm,$ are given in the sketch. Determine the

fin heat rate.

$($b$)$ Determine the temperature at node $3,T_3.$

$($a$)q_f=$

$($b$)T_3=$