Heat problem Steam at an unknown temperature flows through a steel pipe whose th

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Heat problem

Steam at an unknown temperature flows through a steel pipe whose thermal conductivity is 35W/( m. degree C). The pipe outside and inside diameters are 0.36m and 0.3m, respectively. A layer of insulation whose thickness is 0.2m and thermal conductivity is 0.15W/( m. degree C) is wrapped around the outside of the pipe. Then a thin sheet of aluminum whose emissivity is 0.3 is wrapped around the insulation. The pipe is located in a room whose ambient air temperature is 25 degree C and whose walls are also at 25 degree C. The film coefficient of heat transfer between the aluminum and the ambient air is 7 W/(m2. degree C). The temperature of the inside surface of the pipe is assumed equal to the steam temperature (i.e. negligible thermal resistance of the inside fluid). What is the maximum temperature of the steam if the surface temperature of the aluminum sheet is not to exceed 55 degree C? what is the heat transfer rate from the aluminum sheet to the ambient?

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