A $5-$meter$-$long electric wire with a diameter of $3$ mm is insulated with a $2-$mm$-$thick plastic layer having a thermal conductivity of $k=0\mathrm{.}15(\frac{W}{m}-K).$ The wire carries a current of $10,$A with a voltage drop of $8,V$ and is exposed to ambient air at $T={30}^{\text{'}}C$ with a heat transfer coefficient of $h=12,\frac{W}{m}2.K.$

Calculate the temperature at the interface between the wire and insulation.

Determine the critical radius of insulation.