An electrical conductor of $1\mathrm{.}5$mm in diameter at a temperature $70$C is cooled by a system of air whose temperature is $15$ deg $*$ C The heat transfer coefficient from the conductor surface to air $16$ W $/($m $^2),^$ C Determine the surface temperature of the conductor if the latter is converted with rubber of $2$mm thickness $($K$=0\mathrm{.}15$W $/$ m $.^$ C$)$ leaving the intensity of the current carried by the conductor unchanged. The heat transfer coefficient from the rubber surface to pi$=8\mathrm{.}2$W $/($m deg$).^$ C$.$ b$)$ Also determine the thickness of the rubber insulating making it possible for to carry a current of maximum intensity with the temperature of the conductor remaining unchanged as $70$ deg $*$ C