13.58 Consider two large, diffuse, gray, parallel surfaces separated by a small distance. If the surface emissivi- ties are 0.8, what emissivity should a thin radiation shield have to reduce the radiation heat transfer rate between the two surfaces by a factor of 10?

13.59 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 emissivi- ties on opposite surfaces. In particular, one surface has
the emissivity ss 0.5, while the opposite surface has an emissivity of 2ss.
wall, as shown in the schematic. Assume all surfaces are diffuse-gray.

(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 ss or that of emissivity 2ss be oriented toward the plate at T1?

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