10 m long pipe is being used to deliver steam through a processing plant. The inner radius of the pipe is r, = 6 cm and the thickness of the pipe is 2 cm. Thermal conductivity k = 8 W/m K and the average temperature steam flowing through the pipe is 160°C, the average convection heat transfer coefficient on the inner surface is given to be h = 20 W/m2 K. If the average temperature on the outer surfaces of the pipe is T, = 70°C, (a) express the differential equation and the boundary conditions for steady operating conditions, (b) determine a relation for the variation of temperature in the pipe, and (c) evaluate the rate of heat loss (heat of conduction) from the steam through the pipe.
10 m long pipe is being used to deliver steam through a processing plant. The inner radius of the pipe is r1 = 6 cm and the thickness of the pipe is 2 cm. Thermal conductivity k = 8 W/m⋅K and the average temperature steam flowing through the pipe is 160°C, the average convection heat transfer coefficient on the inner surface is given to be h = 20 W/m2⋅K. If the average temperature on the outer surfaces of the pipe is T2 = 70°C, (a) express the differential equation and the boundary conditions for steady operating conditions, (b) determine a relation for the variation of temperature in the pipe, and (c) evaluate the rate of heat loss (heat of conduction) from the steam through the pipe.
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