An insulation $)=(0\mathrm{.}14\frac{W}{mK}$ layer that is $0\mathrm{.}002m$ thick surrounds a wire diameter $=0\mathrm{.}0025m$ in room at $25C.$ Current is passed through the wire, resulting in the generation of heat. The boundary between the wire and insulation has a thermal contact resistance of $R^{\text{'}}=5\mathrm{.}5{10}^{-3}\frac{mK}{W}.$ The convective heat transfer coefficient at the outer surface of the insulation is $h=21\frac{W}{m^2(K)}.$ The insulation will emit a concerning odor once it has reached $40C.$

$($a$)$ What is the maximum power that can be released at steady state by the conductor to avoid production of the odor?

$($b$)$ What is the temperature at the outer surface of the wire at the power you found in $($a$)?$