14-100 14-100 A flat-plate solar collector tilted 40qC from the horizontal is exposed to the calm ambient air. The total rate of heat loss from the collector, the collector efficiency, and the temperature rise of water in the collector are to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. 4 There is no heat loss from the back surface of the absorber plate. Properties The properties of air at 1 atm and the film temperature of (Ts+Tf)/2 = (40+20)/2 = 30qC are (Table A-22) k 0.02588 W/m.qC Absorber 2 5 Plate Q 1.608 u 10 m /s Solar radiation Pr 0.7282 650 W/m2 1 1 Outdoors, E 0.0033 K -1 Tf = 20qC (30 273)K Tf Tsky = -40qC Analysis (a) The characteristic length in 1.5 m this case is determined from Lc As p (1.5 m)(2 m) 2(1.5 m + 2 m) G = 3 cm 0.429 m 2 Glass Cover, 40qC Then, Ra gE (Tf Ts ) L3c Q2 (1.608 u10 Nu 0.15 Ra h k Nu Ls As and Q conv 5 2 m /s) 0.15(1.103 u 10 ) 8 1/ 3 2 (0.7282) 1.103 u10 8 71.94 0.02588 W/m.qC (71.94) 0.429 m (1.5 m)(2 m) Insulation Pr (9.81 m/s 2 )(cos 40q)(0.0033 K -1 )(40 20 K )(0.429 m) 3 1/ 3 T =40q 4.340 W/m 2 .qC 3 m2 hAs (Ts Tf ) (4.340 W/m 2 .qC)(3 m 2 )(40 20)qC 260.4 W Heat transfer rate by radiation is Q rad HAs V (Tsurr 4 Ts 4 ) (0.9)(3 m 2 )(5.67 u 10 8 W/m 2 .K 4 )[(40 273 K ) 4 (40 273 K ) 4 ] 1018 W and Q total 260.4 1018 1278 W (b) The solar energy incident on the collector is Q incident DqAs (0.88)(650 W/m 2 )(3 m 2 ) 1716 W Then the collector efficiency becomes Q incident Q lost 1716 1278 efficiency 1716 Q incident 0.255 25.5% (c) The temperature rise of the water as it passes through the collector is Q (1716 1278) W Q m c p 'T o 'T 6.3qC m c p (1 / 60 kg/s)(4180 J/kg.qC) 14-101 ….. 14-103 Design and Essay Problems KJ PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.

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# 14-100 total rate of heat loss from the collector, the collector...