Chapter 13, Problem 13.59P

Heat transfer by radiation occurs between two large parallel plates, which are maintained at temperatures T₁and T₂, with $T_1>T_2$ . To reduce the rate of heat transfer between the plates, it is proposed that they be separated by a thin shield that has different emissivities on opposite surfaces. In particular, one surface has the emissivity ${\epsilon }_s<0.5$ , while the opposite surface has an emissivity of $2{\epsilon }_s$ .
(a) How should the shield be oriented to provide the larger reduction in heat transfer between the plates? That is, should the surface of emissivity ${\epsilon }_s$ or that of emissivity $2{\epsilon }_s$ be oriented toward the plate at T₁?
(b) What orientation will result in the larger value of the shield temperature T_s?