Problem $1.(40$ pts $)$ A $1*m$ long cylindrical fuel rod is sheathed in a cylindrical metal sleave. The

metal slecre has a thermal conductivity, $k.$ The outer siceve surface has an enissivity, $C,$ and

outer surface temperature, $T_2$ at $r_2.$ Convection and radiation occur at the outer sleve serfice.

Contact resistance is negligible. Determine

$($a$)$ The volumetric heat generation of the fuel rod of $($in $\frac{W}{m}).$

$($b$)$ The inner surface temperature of the metal steeve, $T_1$ at $n.$

$($Note: the Stefan$-$Boltumann constant is $a=5\mathrm{.}67{10}^8\frac{W}{m^2}-K^{+}$