Chapter 12, Problem 12.117P

In the central receiver concept of solar energy collection, a large number of heliostats (reflectors) provide a concentrated solar flux of $q_s^{"}=80,000{\text{ W/m}}^2$ to the receiver, which is positioned at the top of a tower.

The receiver wall is exposed to the solar flux at its outer surface and to atmospheric air for which $T_{\infty ,o}=300K{\text{ and h}}_o=25{\text{ W/m}}^2\cdot K$ . The outer sur- face is opaque and diffuse, with a spectral absorptivity of ${\alpha }_{\lambda }=0.9\text{ for }\lambda \text{<3 }\mu \text{m }{\alpha }_{\lambda }=0.2\text{for }\lambda >\text{3 }\mu \text{m}$ . The inner surface is exposed to a working fluid (a pressurized liquid) for which $T_{\infty ,i}=700K{\text{ and h}}_i=1000{\text{ W/m}}^2\cdot K$ . The outer surface is also exposed to surroundings for which $T_{sur}=300K$ . If the wall is fabricated from a high-temperature material for which $\text{K=15W/m}\cdot K$ ,what is the minimum thickness L needed to ensure that the outer surface temperature does not exceed $T_{s,o}=1000K$ ? What is the collection efficiency associated with this thickness?