The absorber plate of a solar collector may be coated with an opaque material for which the spectral, directional absorptivity is characterized by relations of the form the zenith angle θ is formed by the sun's rays and the plate normal, and α1. and α2 are constants.

(a) Obtain an expression for the total, hemispherical absorptivity, αS, of the plate to solar radiation incident at θ = 45°. Evaluate αS for α1 = 0.93, α2 = 0.25, and a cut-off wavelength of λc = 2μm.

(b) Obtain an expression for the total, hemispherical emissivity ε of the plate. Evaluate ε for a plate temperature of Tp = 60°C and the prescribed values of α1, α2, and λc.

(c) For a solar flux of q''S = 1000 W/m2 incident at θ = 45° and the prescribed values of α1, α2, λc, and Tp, what is the net radiant heat flux, q''net to the plate?

(d) Using the prescribed conditions and the Radiation/Band Emission Factor option in the Tools section of IHT to evaluate F(0→λ), explore the effect of λc on αS, ε, and q''net for the wavelength range 0.7 < λc < 5μm.