DESALINATION ELSEVIER
Desalination 116 (1998) 19
Optimization of collector and basin areas for a higher yield for active solar stills Sanjeev Kumar, G.N. Tiwari* Centre for Energy Studies, lndian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Tel. +91 (11) 6861977; Fax +91 (11) 6862208; email:
[email protected] Received 12 May 1997 ; accepted 13 M a y 1998
Abstract This communication presents a thermal anab o,s of an active solar still for the optimization of collectors as well as the basin area for a higher yield for a given water depth. Expressions for the temperatures, the water and glass covers and the yield have been derived. In order to have numerical appreciation of the results, meteorological data for a summer day of Delhi climate have been used. It has been observed that the optimization is a strong function of water depth.
Keywords:Solar distillation; Purification of water; Solar energy
1. Introduction The performance of a solar distillation system is governed by the rate of evaporation from the water surface in the basin. This depends on the water and glass cover temperature difference. The rate o f evaporation can be maximized by increasing the temperature difference between the water and glass cover. This is achieved either by passive or active modes. Several researchers [1,2] have reviewed the work on solar distillation systems. There are various active methods:
*Corresponding author.
•
•
•
Nocturnal production   the feeding of hot water into the basin once in a day in the morning/evening [35] Preheated water application   the feeding of hot water into the basin at a constant flow rate either continuously or intermittently [6,7] High temperature distillation   the feeding of hot water into the basin from the collector panel [813].
However, no optimization of either collector or basin area was carried out by any one of authors. In this communication an attempt has been made to optimize the collector/basin area for a given climatic condition and other design
00119164/98/$  see front matter © 1998 Elsevier Science B.V. All fights reserved PII S 0 0 1 1  9 1 6 4 ( 9 8 ) 0 0 0 5 2  6
2
S. Kumar, G.N. Tiwari / Desalination 116 (1998) 19
parameters. Basic energy balance equations have been used for analytical solutions for water and glass cover temperatures and hourly yield. The overall thermal efficiency of an active system has also been defined. Numerical computations have been carried out for a typical day (15 June 1996) in Delhi. On the basis of numerical results, it is inferred that the optimum number of collectors for maximum yield a r e 8 m 2 for a 1 m 2 basin area for 0.15 m water depth in the basin.
4. The solar distiller unit is vapour leakage proof, etc. The energy balance for different components of number of collectors coupled with solar still are as follows: •
Glass cover:
o:/gI(t)4.+h]~(T~Tg).As:h,g(TT •
2. E n e r g y b a l a n c e s
In order to write the energy balance for different components of this system (Fig. 1), the following assumptions have been made: 1. Inclination of the glass cover is small. 2. The heat capacity of the glass cover and insulating and conductive materials of the solar still and collectors are negligible. 3. The system is perfectly insulated from the side and bottom.
(1)
Water mass:
[c%,I(t) +hw (Tb  T )]A~.
(m.Cw
(2)
• Basin liner: ~b / I(t).As = h w (TbTw).A / + h b ( T b  L ~ A s
(3)
where Sol4u" [~dltOrlJ
m., = A x d x 9
RIIQIdnkli~ltO i a"l  Gll~l ~ ,
and the expressions for various heat transfer coefficients are given in the appendix. After substituting the values for Tg and Tb from Eqs. (1) and (3) in Eq. (2) and simplifying, the result may be expressed as follows:

~ Sahne
Water

dT
Pump
+ aT
/ a
Fig. 1. Schematic view of a solar still coupled with a flat plate collector.

UL mwC w
=f(t)
(4)
S. Kumar, G.N. Tiwari / Desalination 116 (1998) 19
3
Now the average water temperature is given by
U~ = AcNFRN + UIb A s + Ulg
t
dt
hlw hbv
o
Ulb  h w + hb = f(t)a [1  1 exp(aAt)aAt hlw h l g Uig  hi + hlg
(6) + To [.1 eXPaAt(aAt)
fit) =
[AcNFmv(O~)//(t)+ (~/w+~/gh/+IX/b h)l(t)As]+ULT
After knowing Tg can be optained from Eq. (1),
mwC w
: h
.,I(t)+hlwL +hlgL
tllw hw +hb
The basic interanal heat transfer coefficient can be further evaluated for known Tw and Tg for the next set of computations. Eqs. (6) and (7) can be used to evaluate the hourly yield as follows:
and h/
hlw
hlw + hlg
?hew = The coefficient hlw can be evaluated at known values of intial water and glass temperature at
hew ( T  T ) × 3600
(8)
L
where t : 0 i.e. Tl,oo = Two,
Tl,=o: Tg0 L = 2.4935x106 (19.4779×10 4 T
In order to obtain an approximate analytical solution to Eq. (4), the following assumptions have been made: • the taking interval At=t0 is small • fit) is considered a s f t ) for time interval 0t • a is constant during At.
a
9
T3)
The overall daily thermal efficiency for active solar still is defined as rhe~ x L
Now the solution to Eq. (4) is Tw = fit) [1  e x p (  a t) + T Oexp (  a t)]
+ 1.3132x 107T 2  4.7974x 1 0
(5)
1] = [~_, I(t)A + ~_, I/(t)Ac]X 3600
(9)
4
S. Kumar, G.N. Tiwari / Desalination 116 (1998) 19
4. R e s u l t s a n d d i s c u s s i o n
The following design parameters have been used for numerical computations of Eqs. (6) (9): A c = 2 m 2, A~ = 1 m 2, N = 1  5 C f = Cw = 4 1 9 0 . 0 J / k g ° C dw = 0.15m, F' = 0.7,
there are reductions in the variation of the internal heat transfer coefficients (Figs. 46) and the yield (Fig.7). Theeffect of the number of collector areas on the hourly yield is shown in Fig. 8. It is clear that the yield increses with increase of number of collectors, as expected, due to more heat transfer from the collector panel into the basin. 90
hlg = 20.7W/m 2
I
"'1
80
UL = 8W/m 2, v = 4m/s, L = 2.345x103 J/kg m
=
50 k g / h ,
[3 = 45 o
,
r
/,."..,,%.
,
,
,
50
/
E ~o
40
400
35 ~=
200
i 30
0
25 Time
0
o
10
6
I
I
r
I
I
I
1~
12
16
20
24
4
0
Time (hr) Fig. 3. Hourly variation of water and glass temperatures. Ac=2m2, N=5, d,~ = 0.15 m.
m A~ ( "~))
l
•
'
'
'
"
'
'
1 3
6
o
.... 20
" O,O.O.
"E 8
a
16
"~J,~.'~'. ~
,m"oI"
10
600
12
I
/.. .~ ,,~ . . . ~ c . ~  , ~ , .
20
Symbols
,5
8
1
55
800
4
.........
30
50
0
I
.~:~'
40
12
g
I
60
1000
"~
I
70
The hourly variation of solar intensity and ambient temperature are shown in Fig. 2. They have been used to calculate intensity on the collector surface by using the Liu and Jordan formula [14]. Figs. 37 show hourly variations of the water and glass cover temperatures, internal heat transfer coefficents and the yield for different basin areas for a given number of collectors and water depths in the basin. It was observed that the temperatures of the water decrease with an increase of basin area due to the large storage capacity o f the water mass in the basin. Therefore, 1200
I
24
(hr)
Fig. 2. Hourly variation of solar intensity and ambient temperature.
J
8
I
12
I
I
l
I
16
20
24
4
Time (hr) Fig. 4. Hourly variation of radiative heat transfer coefficient. Ac=2m2, N=5, d,, = O. 15 m.
S. Kumar, G.N. Tiwari / Desalination 116 (1998) 19 4.0,
, I/Symbols
o L)
.. , A s (m 2)
I
I
120
I
.
3.5
:
3
3.0 "
o
5
"E
I
80
as..,&,~ a,__~,~=
2.5 r,
t (£)
(me)=) / ~ o Sa (m
100
,,, 2x
5
2.0
~E
60
v
40 1.0
I
I
8
I
12
I
16 `20 Time (hr)
I
I
24
4
20
Fig. 5. Hourly variation of convective heat transfer coefficient. Ac=2 m2, N=5, d~ = 0.15 m.
I
I
I
8
12
16
I
I
20
24
,
I
4
Time (hr)
1.4
l
,
I ~
1.2 1.0
,
.~
,
, 
2
~ I me •
3 m2
o
5ra
Fig. 6. Hourly variation of evaporative heat transfer coefficient. Ac=2 m2, N=5, dw = 0.15 m.
/ h ~
/
2.0
~
/ E
i
A3
i
[
i
l
a.,, 1.5
0.6
/
f
~E ~
0.4
a
!
•
2
¢
4
* 6 o 8
,~
%,,,,
1,o
v
_
0.2
i 3/hi l)l)lll N
/
...~.~..~~'~"'~'"~,_~=
8
12
16
20
24
4
Time (hr)
Fig. 7. Hourly variation of yield. Ac=2m 2, N=5, dw = 0.15m.
The variation o f the daily yield with water depth for a given number of collectors is shown in Fig. 9. It shows the decrease of yield with water depth due to large storage capacity. Figs. 10 and 11 show the effect o f the number of collector areas and basin area on daily yield, while the overall efficiency curve is shown in Fig. 12. The increase
0.0
.
i 8
12
16 Time (hr)
i
i
,20
24
i 4
Fig. 8. Hourly variation of yield. As=l m2, Ac=2mz, dw = 0.15 m. of yield with number of collector further shows the greater transfer of thermal energy from the collector panel (Fig. 10). The optimum number of collectors for maximum yield is 8m 2 because the increase in gain becomes lower than thermal loss
6
S. Kumar, G.N. Tiwari/Desalination 116 (1998) 19 2.~ i
~
25
20
~
for N= 1 A for N = 2
15
~k
o forN=S
2O
"~
"~
1:5
10'
0
/
/ '
0.0
I
1
i
0.1
0.2
03
0.4
}
I
I
I
2
4
6
B
Number
Water depth (m)
Fig. 9. Variation of daily yield vs. water depth. As=l m 2, Ac=2 m2, N=5.
f
i
i
I
i
14 12
8
~ii/
6
Fig. 10. Variation o f daily yield vs. n u m b e r o f collectors. A~= 1 m 2, A~=2 m 2, d,~=0.15 m.
5. Symbols
16
"
of Collectors
4
0
o
I
I
I
I
]
2
3
4
__~_l
A, A,. A~, C%

Cf

dw F~ F' hb

hlg

ht~

h~

.w
% ~m~)
W/m2°C
Fig. 11. Variation of daily yield vs. still area. A~=2m2, N=5, d~=0.15 m.
(Fig. 12a). The daily yield and overall thermal efficiency decrease with an increase o f basin area due to the large thermal storage capacity for a given depth o f water (Figs. 11 and 12b).
Area o f the solar collector, m 2 Basin liner area o f the solar still, lla 2 Side area o f the solar still, m 2 Specific heat o f water in the solar still, J/kg. °C Specific heat o f fluid through the collector, J/kg. °C Depth o f the water mass, m Collector heat removal factor Collector efficiency factor Overall heat transfer coefficient from the basin liner to an ambient air through bottom and side insulation, Convective heat transfer coefficient from the glass cover to an ambient air, w/m2°C Total heat transfer coefficient from the water surface to the glass cover, W/m2°C
Convective heat transfer coefficient from the basin liner to the water, W/m 2° C
S K u m a r , G.N. T i w a r i / D e s a l i n a t i o n 1 1 6 (1998) 1  9 0.20
0.16
0.12
l(t)

r(t)

K

L

m w
0.08
I 2
0
L 4 Number
i 6
rh d

ff'l t,w

Pg

Pw

i 8
of Collectors
Fig. 12a. Variation of number of collectors vs. efficiency. As=l m2, A~=2rn2, d,,=0.15 m.
0.20
0.16
Q uN

T

ra

rio

Tg

t

U'L

UL

0.12
0.08
\ 0.04
0.00 0
i
i
i
i
i
I
2
3
4
5
% (m') Fig. 12b. Variation of still area vs. efficient. A~=2m2, N=5, dw=0.15 m.
h~
hew
hrw



Convective heat transfer coefficient from the water surface to the glass cover, W/m 2oC Evaporative heat transfer coefficient from the water surface to the glass coverm W/m 2° C Radiative heat transfer coefficient from the water surface to the glass cover, W/m 2oC
7
Total radiation available in the plane of glass cover of the solar still, W/m 2 Total radiation available in the plane of absorber of the collector, W / m 2 Thermal conductivity, W/m°C Latent heat of vapourization, J/kg Mass of water in basin, kg Floud flow rate through the collector, kg/h. Instantaneous yield of still per unit area, kg/m 2 Partial vapour pressure at glass temperature, N/m 2 Partial vapour pressure at water temperature, N/m 2 Rate of useful energy from N collectors connected in series, W Temperature, °C Ambient air temperature, ° C Inlet temperture of fluid to collector, °C Outlet temperature of fluid to collector, °C Average water temperature, ° C Average glass temperature, °C Time, s Heat loss coefficient for collector, W/m2°C Overall heat transfer coefficient, W/m2°C Wind velocity, m/s
Greek
0~b ,

~W'
m
0~g,
rl

Absorptivity Fraction of solar flux absorbed by basin liner Fraction of solar flux absorbed by water mass Fraction solar flux absorbed by glass cover Fraction of energy transfered to water in the basin Efficiency of still
the the the the
8 At
S. Kumar, G.N. Tiwari/Desalination 116 (1998) 19 B
o
Temperature difference, °C Stefan Boltzman constant, 5.67× 10 8, W/m 2° K
Subscripts w g b N

Appendix In Eqs. (1), (2) and (3), different heat transfer coefficients are as follows:
hlg = Water Glass cover Basin liner N u m b e r o f collectors
5.7 + 3.8 v [14]
hlw=h~+hr~+hew hc~ = 0.884
[TwTg+ (P,,Pg) (Tw +273)/
(268.9 x 103P~)] v3
References [I]
[2] [3]
[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
M.A.S. Malik, G.N. Tiwari, A. Kumar and M.S. Sodha, Solar Distillation, Pregamon Press, U.K., 1982. G.N. Tiwari, in: Solar Energy and Energy Conservation, Wiley Eastern, New Delhi, 1992. W.A. Grune, R.A. Collines, R.B. Hughes and T.L. Thompson, DSW Report No. 60 PB 1811 44, 1962, p.l15. M.A.S. Malik and V.V. Tran, SolarEnergy, 14 (1973) 371. S.O. Onyegegbu, Appl. Energy, 24 (1986) 29. E. Sartori, in: Advances in Solar Energy Technology, Vol. 2, Pergamon Press, New York, 1982, p.27. G.N. Tiwari, H.P. Garg and [initial?] Madhuri, Energy Convers. Mgmt, 25 (1985) 315. H.S. Soliman, MOSul, Iraq, 1976, p.43. S.N. Rai, and G.N. Tiwari, National Solar Energy Convection of India, 1982, p. 7009. G.M. Zaki, T.EI. Dali and H. E! Shafieng, First Arab Int. Solar Energy Conf., Kuwait, 1983, pp. 331335. A.A. Madani and G.M. Zaki, Desalination, 73 (1989) 67. S.A. Lawrence and G.N. Tiwari, Energy Conserv. Mgmt., 30 (1990) 205. J. Fernandez and N. Chargoy, Solar Energy, 44(4) (1990) 215. J. Duffle and W.A. Backman, Solar Engineering Thermal Process, Wiley, New York, 1991.
h,~ = cefr.o [(Tw+ 273) 4 h~.w= 16.273×10 3
(Tg+ 273) 4]/(T,, Tg)
ho~ × (P~, Pg)/(Tw Tg)
where the expressions for saturated vapour pressure as a function o f temperature (°C) are as follows [13]: P~ = exp [25.317  5 1 4 4 / (Tw +273.15)]
Pg =
exp [25.317  5 1 4 4 / (Tg+273.15)]
The useful energy o f N collectors is:
where
L
re.
+ Tfiexp
Then
(NA cUL. F/) mcf
j
S. Kumar, G.N. Tiwari / Desalination 116 (1998) 19 (~crN = AcNFmv[(~z)I'(t)  UL(T~ T)]
F~v=FR [1 (1 Kx)]
NKK where
(NAcULF' ?hCf 1  exp. 7 FRN AcNUL mcf
where
A F.U rhc/ In the above equation, T~ = Tw. Then,
But the N collector connected in series:
QUN ~ AcNFr~v[(°~) I'(t) UL ( T T~)]
9