A $2-$mm$-$diameter and $10-$m$-$long electric wire is tightly wrapped with a $1-$mm$-$thick plastic cover whose thermal conductivity is $k=0\mathrm{.}15\frac{W}{m}*C.$ Measurements indicate that heat is generated in the wire at a rate of $80$ W $.$ If the insulated wire is exposed to air at $T_{}=30C$ with a heat transfer coefficient of $h=24\frac{W}{m^2}C,$ determine the temperature at the interface of the wire and the plastic cover in steady operation. Also determine if doubling the thickness of the plastic cover will increase or decrease this interface temperature.