Superheated steam at 575ºC is routed from a boiler to the turbine through steel tubes (k = 35 W/(m·K)) with 300 mm inner diameter and 30 mm wall thickness. To reduce heat loss and maintain a safe-to-touch outer surface temperature a layer of calcium silicate insulation (k = 0.10 W/(m·K)) is applied. The contact resistance of the layer with the pipe is R’’=0.02 m2K/W. Degradation of the insulation is prevented by wrapping it in a very thin layer of aluminum foil with emissivity of 0.20 and contact resistance of R’’=0.03 m2K/W. The air and wall temperatures of the power plant are 27ºC. Assume that the steam has a convection coefficient of 1500 W/(m2K) and that the outer surface has a convection coefficient of 6 W/(m2K). What minimum insulation thickness is needed to ensure that the outside temperature does not exceed 50ºC? What is the corresponding heat loss per meter of tube length?