Heat transfer by radiation occurs between two large parallel plates, which are maintained at temperatures T₁ and T₂, with T₁ > T₂. 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 ε_s < 0.5, while the opposite surface has an emissivity of 2ε_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 ε_s, or that of emissivity 2ε_s be oriented toward the plate at T₁?

(b) What orientation will result in the larger value of the shield temperature T_s?