(Solved): 4. (Total of 15 points) A solar collector consists of a plate coated with black nickel, which can ...

4. (Total of 15 points) A solar collector consists of a plate coated with black nickel, which can be approximated as diffuse. The spectral, hemispherical emissivity of the collector is: EX 0.70, i<1.81 um 0.35, i>1.81 um The collector is irradiated by the sun with a strength of qot = 1300 Wm? On its top, the surface loses heat by radiation and free convection (heat transfer coefficient hi = 5 WmK*, both to an atmosphere at 20°C (i.e., 1.0,1 = Tsur = 20°C). The bottom surface delivers heat to a collector fluid having a heat transfer coefficient h2 = 100 Wm-K and a temperature 60,2 = 18°C. Since the solar collector is thin and has a large thermal conductivity, it is safe to assume that the collector is at a single and uniform temperature T at steady state. (a) (5 points) Calculate the total solar irradiation absorbed by the collector. (6) (3 points) Calculate the total, hemispherical emissivity of the solar collector by assuming that To will never be greater than 50°C. (e) (2 points) If you wanted to minimize radiative losses, should you increase or decrease the spectral emissivity at i > 1.81 um? Justify your answer. (d) (5 points) Derive an equation that allows calculation of the steady-state, equilibrium temperature of the collector Ic. Please note that: (1) you don't need to solve the equation, and (ii) you can assume that I will never be greater than 50°C.