$3\mathrm{.}63$ An uncoated, solid cable of length $L=1m$ and diam$-$

eter $D=35mm$ is exposed to convection conditions

characterized by $h=55\frac{W}{m^2}*K$ and $T_{}=24C.$

Determine the maximum electric current that can be

carried by the cable if it is pure copper, pure aluminum,

or pure tin. Calculate the corresponding minimum wire

temperatures. The electrical resistivity is ${}_e=10{10}^{-8}$

$*m$ for copper and aluminum at their melting points,

while the electrical resistivity of tin is ${}_e=20{10}^{-8}$

$*m$ at its melting point.