$4\mathrm{.}68$ A straight fin has a triangular profile given by the

function $y=0\mathrm{.}2(L-x)$ and is very long in the di$-$

rection normal to the page. Both top and bottom sur$-$

faces experience convection with $T_{}=15C$ and

$h=100\frac{W}{m^2}*K.$ The base of the fin is maintained

at $T_b=115C$ and the fin material has a thermal

conductivity of $25\frac{W}{m}*K.$ Assuming one$-$dimen$-$

sional heat transfer and using a finite$-$difference

method with a space increment of $10$ mm $,$ determine

the fin heat rate and efficiency.