A 1.0-mm-diameter wire is maintained at a temperature of 400C and exposed to a convection environment at

A 1.0-mm-diameter wire is maintained at a temperature of 400ºC and exposed to a convection environment at 40ºC with h = 120 W/m2 ∙ ºC. Calculate the thermal conductivity that will just cause an insulation thickness of 0.2 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?