EXERCISE: Optimum emissivity for hot-weather house

Incident solar radiation and thermal emission from a house and its
surroundings differ have significantly different spectra. This can be
exploited to minimise heating by incoming solar radiation and maximising
radiative cooling.

Assuming that the surface of the house will have a reflectivity of between
0.1 and 0.9 at any particular wavelength, what is an ideal emissivity, as
a function of wavelength, to minimise the daytime temperature increase,
assuming that radiative equilibrium is reached?

Reasonable assumptions are OK, but should be stated.

Supplementary questions:

(a) Neglecting convection and conduction, what would the equilibrium
temperature be?

(b) How much difference would it make if the reflectivity could vary from
0.05 to 0.95? From 0.01 to 0.99?

(c) Estimate the effectiveness of a canopy or fly over the house. What
should the emissivities of the upper and lower surfaces of the canopy be?

--
Timo
.

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