A 2 m by 2 m flat plate solar collector for domestic hot water heating is shown

Question:

A 2 m by 2 m flat plate solar collector for domestic hot water heating is shown schematically in the sketch. Solar radiation at a rate of 750 W/m2 is incident on the glass cover which transmits 90% of the incident flux. Water flows through the tubes soldered to the backside of the absorber plate, entering with a temperature of 25?C. The Glass cover has a temperature of 27?C in the steady state and radiates heat with an emissivity of 0.92 to the sky at ??50?C. In addition, the glass cover losses heat by convection to air at 20?C flowing over its surface at 20 mph.

(a) Calculate the rate at which heat is collected by the working fluid, i.e., the water in the tubes, per unit area of the absorber plate.(b) Calculate the collector efficiency ηc defined as the ratio of useful energy transferred to the water in the tubes to the solar energy incident on the collector cover plate.(c) Calculate the outlet temperature of the water if its flow rate through the collector is 0.02 kg/s. The specific heat of the water is 4179 J/(kg K).GIVENA flat plate solar collector with air flowing over itCollector dimensions = 2 m × 2 mIncident solar flux = 750 W/m2Glass cover transmits 90% of solar fluxWater enters tubes at a temperature (Twi = 25?C)Glass cover steady state temperature (Ts) = 27?C = 300 KEmissivity of glass cover (ε) = 0.92Sky temperature (T??r) = ??50?C = 223 KAmbient air temperature (T??c) = 20?C = 293 KAir speed (U??) = 20 mi/hWater flow rate (m) = 0.02 kg/sSpecific heat of water (cp) = 4179 J/(kg K)ASSUMPTIONSSteady StateRadiative heat transfer between the absorber and the glass plate is negliagibleThe absorber plate absorbs all the incident solar radiationRadiative heat transfer from the absorber plate, through the glass to the sky, is negligibleHeat transfer through the back and sides of the collector is negligibleSolar radiation blocked by the collector frame is negligibleGlass cover and absorber temperatures are uniformThe solar energy absorbed by the glass is negligibleThe sky behaves as ablackbody