A $1\mathrm{.}0-$mm$-$diameter wire is maintained at a temperature of $400C$ and exposed to a convection environment at $40C$ with $h=120\frac{W}{m^2}C.$ Calculate the thermal conductivity that will just cause an insulation thickness of $0\mathrm{.}2$ mm to produce a "critical radius." How much of this insulation must be added to reduce the heat transfer by $75$ percent from that which would be experienced by the bare wire?A $1\mathrm{.}0-$mm$-$diameter wire is maintained at a temperature of $400C$ and exposed to a convection environment at $40C$ with $h=120\frac{W}{m^2}C.$ Calculate the thermal conductivity that will just cause an insulation thickness of $0\mathrm{.}2$ mm to produce a "critical radius." How much of this insulation must be added to reduce the heat transfer by $75$ percent from that which would be experienced by the bare wire?