Chapter 13, Problem 13.64P

A diffuse, gray radiation shield of 60−mm diameter and emissivities of ${\epsilon }_{2,i}=0.01$ and ${\epsilon }_{2,o}=0.1$ 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 con vection with air at 27°C and a convection heat transfer coefficient of $10{\text{W/m}}^{\text{2}}\cdot \text{K}$ .

Determine the operating temperature for the inner tube if the shield temperature is maintained at 42°C.