A $2-$mm$-$diameter electrical wire is insulated by a

$2-$mm$-$thick rubberized sheath $(k=0\mathrm{.}13\frac{W}{m}*K),$ and

the wire$/$sheath interface is characterized by a thermal

contact resistance of $R_{t,c}^{\text{'}\text{'}}=3{10}^{-4}{m}^2*\frac{K}{W}.$ The con$-$

vection heat transfer coefficient at the outer surface of

the sheath is $10\frac{W}{m^2}*K,$ and the temperature of

the ambient air is $20C.$ If the temperature of the insula$-$

tion may not exceed $50C,$ what is the maximum allow$-$

able electrical power that may be dissipated per unit

length of the conductor? What is the critical radius of

the insulation?