Chapter 13, Problem 13.62P

A furnace is located next to a dense array of cryogenic fluid piping. The ice-covered piping approximates a plane surface with an average temperature of $T_p=0°\text{C}$ and an emissivity of ${\epsilon }_p=0.6$ . The furnace wall has a temperature of $T_f=200°\text{C}$ and an emissivity of ${\epsilon }_f=0.9$ . To protect the refrigeration equipment and piping from excessive heat loading, reflective aluminum radiation shielding with an emissivity of ${\epsilon }_s=0.1$ is placed between the piping and the furnace wall, as shown in the schematic. Assume all surfaces are diffuse-gray.

If the temperature of the shield closest to the piping T_s,Nmust be less than 30°C, how many radiation shields, N, must be installed between the piping and the furnace wall?