$296$ Consider a solid stainless steel wire with a thermal

conductivity of $14$ W$/$m$$K$.$ The wire has a diameter of $1$ mm$,$

a resistivity of $4531028$m$,$ and carries a current of $120$ A$.$

$($a$)$ Determine the rate of heat generated within the wire $($W$/$m$3$

$)$

and $($b$)$ calculate the maximum temperature rise in the wire.