A rectangular flat water tank is placed on the roof of a house with its lower portion perfectly insulated. A sheet of glass whose transmission characteristics are tabulated below is placed 1 cm above the water surface. Assuming that the average incident solar radiation is 630 W/m2, calculate the equilibrium water temperature for a water depth of 12 cm if the heat transfer coefficient at the top of the glass is 8.5 W/(m2 K) and the surrounding air temperature of 20?C. Disregard intereflections.τλ of glass = 0 for wavelength from 0 to0.35 μm= 0.92 for wavelength from 0.35 to 2.7 μm= 0 for wavelength larger than 2.7 μmρλ of glass = 0.08 for all wavelengthsGIVENA glass covered water tank on the roof of a houseLower portion of tank is perfectly insulatedDistance between glass cover and water surface (δ) = 1 cm = 0.01 mAverage incident solar radiation (Is) = 630 W/m2Water depth = 12 cm = 0.12 mHeat transfer coefficient on the top of the glass (hco) = 8.5W/(m2 K)Surrounding air temperature (T??) = 20?C = 293 KTransmissivity of glass (λ λ) = 0 for 0 = 0.92 for 0.35 = 0 for λ > 2.7mmReflectivity of Glass (ρ λ) = 0.08ASSUMPTIONSThe effect of inter-reflections is negligibleThe water temperature is uniform (internal resistance of the water is negligible)Steady state conditionsIs value given is normal to the glass surfaceThe water absorbs all the radiation reaching itWater behaves as a blackbodyThe conductive thermal resistance of the glass is negligibleThe sky behaves as a blackbody enclosure at Tsky = 0 KThe sun is blackbody at 6000 K (see Table 9.2)The shape factor between the surface and the glass can be taken to be unityThe air properties are the same as dry air propertiesThe glass acts as a black surface for the reradiatedenergy

T= 20C = 293 K I = 630 W/m? 1 cm Glass Insulation Water