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
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