Answer Happy

Superheated steam at 600°C is routed from a boiler to the turbine of an electric power plant through steel tubes (k = 30 W/m K) of 300-mm inner diameter and 25-mm wall thickness. To reduce heat loss to the surroundings and to maintain a safe-to-touch outer surface temperature, a layer of calcium silicate insulation (k = 0.10 W/m K) is applied to the tubes, while degradation of the insulation is reduced by wrapping it in a thin sheet of aluminum having an emissivity of ε = 0.25. The air and wall temperatures of the power plant are 28°C. (a) Assuming that the inner surface temperature of a steel tube corresponds to that of the steam and the convection coefficient outside the aluminum sheet is 8 W/m². K, what is the minimum insulation thickness needed to ensure that the temperature of the aluminum does not exceed 60°C? What is the corresponding rate of heat loss per meter of tube length?