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
aA,()(A, ()) = a1 cos () A Ac
aA,()(A, ()) = a2 A > Ac
The zenith angle () is formed by the sun's rays and the plate normal, and a1 and a2 are constants.
(a) Obtain an expression for the total, hemispherical absorptivity, aS, of the plate to solar radiation incident at () = 45°. Evaluate aS for a1 = 0.93, a2 = 0.25, and a cut-off wavelength of Ac = 2 µ,m.
(b) Obtain an expression for the total, hemispherical emissivity s of the plate. Evaluate s for a plate temperature of Tp = 60°C and the prescribed values of a1, a2, and Ac.
(c) For a solar flux of qS" = 1000 W/m2 incident at () = 45° and the prescribed values of a1, a2, Ac, 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 temperature of Tsky = 0°C. The bottom side of the leaf is irradiated from the ground which is at a temperature of Tg = 20°C. Both the top and bottom of the leaf are subjected to convective conditions characterized by h = 35 W/m2 · K, T00 = 25°C and also experience evaporation through the stomata. Assuming the evaporative flux of water vapor is 50 X 10-6 kg/m2 · s under rural atmospheric CO2 concentrations and is reduced to 5 X 10-6 kg/m2· s when ambient CO2 concentrations are doubled near an urban area, calculate the leaf temperature in the rural and urban locations.
The heat of vaporization of water is hfg = 2400 kJ/kg and assume a = s = 0.97 for radiation exchange with the sky and the ground, and aS = 0.76 for solar irradiation.