A $1\mathrm{.}0$mm$-$diameter wire is maintained at a temperature of $400\backslash$deg C and

exposed to a convection environment at $40\backslash$deg C with h $=120$ W$/$m$2$

$.\backslash$deg C$.$

Calculate the thermal conductivity which will just cause an insulation

thickness of $0\mathrm{.}2$mm to produce a critical radius. If the surface temperature

is $40\backslash$deg C and the convection layer ignored, how much of this insulation must

be added to reduce the heat transfer by $75\%$ from that which would be

experienced by the bare wire?