14-63 14-72 The absorber plate and the glass cover of a flat-plate solar collector are maintained at specified temperatures. The rate of heat loss from the absorber plate by natural convection is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Heat loss by radiation is negligible. 4 The air pressure in the enclusure is 1 atm. Absorber Properties The properties of air at 1 atm and the average temperature of Plate (T1+T2)/2 = (80+40)/2 = 60qC are (Table A-22) 80qC k 0.02808 W/m.qC Solar Q 1.896 u 10 5 m 2 /s radiation Pr 0.7202 1 1 1.5 m E 0.003003 K -1 (60 273)K Tf L = 2.5 Analysis For T 0q , we have horizontal Glass Insulation rectangular enclosure. The characteristic length T Cover, in this case is the distance between the two 40qC glasses Lc = L = 0.025 m Then, Ra gE (T1 T2 ) L3 Q2 Pr (9.81 m/s 2 )(0.003003 K -1 )(80 40 K )(0.025 m) 3 (1.896 u 10 5 m 2 /s) 2 ª Ra 1 / 3 º ª 1708 º Nu 1 1.44 «1 « 1» » Ra ¼ ¬ »¼ ¬« 18 3.689 u10 4 (0.7202) ª (3.689 u 10 4 )1 / 3 º 1708 º ª 1 1.44 «1 1» « » 18 ¬ 3.689 u 10 4 ¼ »¼ «¬ 3.223 Then As (1.5 m)(3 m) T1 T2 L 30q , we obtain Q For T H uW kNuAs 4.5 m 2 (0.02808 W/m.qC)(3.223)(4.5 m 2 ) (80 40)qC 0.025 m 1708 º ª 1708(sin 1.8T )1.6 º ª (Ra cos T )1 / 3 º ª 1» Nu 1 1.44«1 »« » «1 Ra cos T 18 ¬ Ra cos T ¼ ¬« »¼ ¼» ¬« ª º 1708 1 1.44 «1 » 4 «¬ (3.689 u 10 ) cos(30) »¼ 652 W > @ 1/ 3 º ª 1708>sin(1.8 u 30)@1.6 º ª (3.689 u 10 4 ) cos(30) « » 1 «1 » 4 18 » «¬ (3.689 u 10 ) cos(30) »¼ «¬ ¼ 3.074 T1 T2 (80 40)qC (0.02808 W/m.qC)(3.074)(4.5 m 2 ) 621 W 0.025 m L For T 90q , we have vertical rectangular enclosure. The Nusselt number for this geometry and orientation can be determined from (Ra = 3.689u104 - same as that for horizontal case) Q Nu kNuAs §H· 0.42 Ra 1 / 4 Pr 0.012 ¨ ¸ ©L¹ 0.3 § 2m · 0.42(3.689 u 10 4 )1 / 4 (0.7202) 0.012 ¨ ¸ © 0.025 m ¹ 0.3 1.557 T1 T2 (80 40)qC 315 W (0.02808 W/m.qC)(1.557)(4.5 m 2 ) 0.025 m L Discussion Caution is advised for the vertical case since the condition H/L < 40 is not satisfied. Q kNuAs 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.