A diffuse, gray radiation shield of 60-mm diameter and emissivities of ?_{2, i} = 0.01 and ?_{2, o} = 0.1 on the inner and outer surfaces, respectively, is concentric with a long tube transporting a hot process fluid. The tube surface is black with a diameter of 20 mm. The region interior to the shield is evacuated. The exterior surface of the shield is exposed to a large room whose walls are at 17?C and experiences convection with air at 27?C and a convection heat transfer coefficient of l0 W/m^2?? K. Determine the operating temperature for the inner tube if the shield temperature is maintained at 42?C.

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Shield, D, = 60 mm Heated tube. D, = 20 mm Evacuated