Use of waste hot water in double slope solar still through heat exchanger

Energy Convers. Mgmt Vol. 30, No. 2, pp. 81-89, 1990

0196-8904/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press pie

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USE OF WASTE HOT WATER IN DOUBLE SLOPE SOLAR STILL THROUGH HEAT EXCHANGER ASHOK KUMAR and G. N.

TIWARIt

Centre of Energy Studies, Indian Institute of Technology, Delhi, New Delhi-110 016, India

(Received 31 August 1987; received for publication 12 October 1989) Abstract--In this communication, a transient analysis of a double slope single basin solar still has been presented, incorporating the effects of inlet temperature of waste hot fluid (water, in this case), heat exchanger length, temperature dependence of internal heat transfer coefficients, water depth, flow rate of waste hot water, etc. It is observed that the internal evaporative heat transfer coefficient is a strong function of the initial water temperature of the waste hot water. Numerical calculations have been made for a typical s u m m e r day in Delhi, viz. 26 May 1978. On the basis o f the numerical results, some interesting conclusions have been drawn. Solar distillation

Solar still

Heat exchanger

NOMENCLATURE Ab = Absorber area (m 2) Cf = Specific heat of fluid of heat exchanger (J/kg °C) H s = Solar intensity (W/m 2) h = Heat transfer coefficient per unit length of heat exchanger (W/m °C) h b = Overall bottom heat transfer coefficient from absorber to ambient (W/m 2 °C) hew = Convective heat transfer coefficient from water to glass cover (W/m 2 °C) hew = Evaporative heat transfer coefficient from water to glass cover (W/m 2 °C) h~w= Radiative heat transfer coefficient from water to glass cover (W/m 2 °C) h~ -- Total heat transfer coefficient from bottom of still to ambient (W/m 2 °C) h~ = T o p heat transfer coefficient from water to glass cover (W/m 2 °C) h 2 = Total heat transfer coefficient from glass cover to ambient (W/m 2 °C) h3 = Convective heat transfer coefficient from basin liner to water (W/m 2 °C) K i = Thermal conductivity of insulation (W/m °C) L = Latent heat of vaporization of water (J/kg) L ' = Length of heat exchanger (m) L~ = Thickness of insulation (m) Me = Daily yield of still (kg/m 2 day) Mw = Heat capacity of water mass in basin (J/°C) n~ = Flow rate of fluid in heat exchanger (kg/m 2 s) me. = Instantaneous yield of still per second at nth time interval (kg/m: s) n = An integer Pg = Partial vapour pressure at glass temperature (Pa) Pw = Partial vapour pressure at water temperature (Pa) Qa = Energy transferred from glass cover to ambient (W/m 2) Qcw = Convective heat transferred from water to glass cover (W/m 2) Qew = Evaporative heat transferred from water surface to glass cover (W/m 2) Q ~ = Radiative heat transferred from water surface to glass cover (W/m 2) Qw = Total energy transferred from water surface to glass cover (W/m 2) Qu = Energy transferred from heat exchanger fluid to water mass (W/m °C) 7~ = Ambient air temperature (°C) Tb = Basin liner temperature (°C) Tf = Temperature of fluids inside heat exchanger (°C) T~ = Glass temperature (°C) To = Inlet temperature o f flowing fluids through heat exchanger (°C) T~ = Outlet temperature of heat exchanger fluid (°C) Tw = Water temperature (°C) Two = Initial temperature of water at t = 0(°C) t = Time (s) At = Time interval from 0 to t (s) t T o w h o m correspondence should be addressed at: Physics Department, University of Papua New Guinea, P.O. Box 320, Papua New Guinea. 81

82

K U M A R and TIWARI: Ub = Ut = V= X = rb = E= cr = =

DOUBLE SLOPE SOLAR STILL

Overall heat transfer coefficient from water to ambient through bottom (W/m 2 °C) Overall heat transfer coefficient from water to ambient through glass cover (W/m 2 °C) Wind velocity (m/s) Position coordinate (m) Fraction of solar energy absorbed by the basin liner Emissivity of glass Stefan-Boltzmann constant (W/m 2 K 4) Efficiency of still

INTRODUCTION Various designs of solar stills have been described by Malik et al. [1] and Tiwari [2], and it was concluded that only the double slope conventional solar still is economical for a large scale installation for the supply of drinking water. In order to increase further the daily yield per m 2, the use of flat plate collectors and waste hot water available from chemical industries and thermal power plant, etc. in a single basin solar still have been studied by Rai and Tiwari [3], Tiwari and Dhiman [4]. Sodha et al. [5] and Madhuri and Tiwari [6]. Recently Tiwari et al. [7] have studied the use of intermittent flow of waste hot water during off-sunshine hours in a single basin solar still by incorporating the effect of water flow over the glass cover. According to their findings, one needs a larger length of solar still for higher yield which requires large ground area. To avoid the constraint of large ground area, one can solve this problem by using a heat exchanger in the basin of the still without disturbing the water mass of the basin. In this communication, a transient analysis of the proposed system has been presented. The effects of various parameters, viz. flow rate, heat exchanger length, inlet temperature of fluid, water depth, temperature dependence of internal heat transfer coefficients etc., have been incorporated in the analysis. In order to appreciate the numerical results of the proposed system, numerical computations have been carried out for a typical summer day in Delhi, viz. 26 May 1978. On the basis of numerical results, the following conclusions have been drawn: (i)

The evaporative heat transfer coefficient is a strong function of water temperature, even for the higher water depth in the proposed system, (ii) Daily yield increases with increases in flow rate, initial temperature of waste hot fluid and heat exchanger length, (iii) Daily yield increases with increase in water depth for higher water temperature, and (iv) Yield decreases during sunshine hours for lower inlet fluid temperature, as expected. Hence, in this case, waste hot fluid should be used only during off-sunshine/low intensity hours. ANALYSIS Solar radiation falling on the glass cover is transmitted through it and the water and is then absorbed by the basin liner. This results in heating the water mass by convection and, thus, in evaporation. Hot water or another fluid flowing through the heat exchanger also transfers energy to the water mass [Fig. l(a)]. The following assumptions have been made in writing the energy balance equations: (i) (ii) (iii) (iv)

Absorptivity and heat capacity of the glass cover are negligible, The inclination of the glass cover is very small, There is no vapour leakage in the still, and there is total condensation of evaporated water, The temperature gradient along the glass cover thickness and water depth is negligible.

The energy balance for the different components may be written as follows Glass cover

Qw = Qa or

h,(Tw- 7"~)= h ~ ( ~ - 7"~)

(1)

K U M A R and TIWARI:

83

D O U B L E SLOPE SOLAR STILL

(al

SOLAR RADIATION

.ASS COVER RAINAGE EAT EXCHANGER

II To

,o>To

~LINE WATER ASlN LINER ISULATION

rg 4

Li

hi

~- Tf

-dTf

(b) LI

To

='

Tf

~ ~

X:O Fig.

/

~I dx II~

--~.-

To

X_-Lt

1.(a) Schematic representation of double slope single basin solar still with heat exchanger; (b) cross-sectional representation of heat exchanger.

where Qw = Qew + Qcw + Qr~ = hl(Tw - Tg)

(2a)

hi = hew + he. + h~w h~w = 0.884

I

T.-

(Pw - Pg)(Tw + 273) 1/3 Tg+ 268.9 x 103--Pww _j

1

(2b)

Pw - Pg hew = 0.016 x hew x - -

(2c)

h~w = E . o [ ( T ~ + 273) 2 + (Tg + 273)2][(Tw + 273) + (Tg + 273)]

(2d)

and h2 = 5.8 + 3 V. Basin liner % H s ' A b = hs(Tb - Tw)Ab + hb(Tb -- T . ) A b

(3)

where

hb-- [ L i

1 -]

Water mass

dTw Q. + h3(Tb - Tw)Ab = Mw ~ - + hjTw - Tg)Ab where Qu = mCr(To - T~).

(4)

84

K U M A R and TIWARI:

D O U B L E SLOPE SOLAR STILL

In order to evaluate Qu in terms of the required parameters, we consider the elemental length dx of the heat exchanger Fig. (lb), as mCf ~ - ~ . d x = - h " d x ( T r - Tw).

The above equation with the intial condition Tr[x=O= To gives Tf = To - (To - Tw)[1 - e x p ( - h x / r h C r ) ] . The water temperature at the outlet of the heat exchanger is T~ = Tr[ x=L, = T o - ( T o - Tw)[1 - e x p ( - h L ' / r h C f ) ] or

To - T~ = (To - Tw)[1 -- exp( -- hL'/rhCf)] which yields Qu = rhCr[1 - exp( - hL'/rhCO](To - Tw).

(5)

After substituting the value of Qo from equation (5), equation (4) assumes the form rhCr[1 - exp(-hL'/rhCr)](To - Tw) + h3(Tb - Tw)Ab = Mw dTw dt + h,(Tw - Tg)Ab

(6)

With the help of equations (l) and (3), equation (6) can be rewritten as

dTw

- - + aoTw = f ( t ) dt

(7)

where f(t) =

ho%Ab'Hs + U'AbTa + F(t)To

Mw U.A b + F(t)

a0=

Mw

U = Ut + Ub h I ,h 2 e t - - -

hi +h2 h 3•h b

Ub = h3 + hb

h3

ho = h3 + hb and F ( t ) = rhCf[1 - e x p ( - hL '/rhCO].

Integrating equation (7) over the limit 0 ~ t and after arranging, one gets, Tw = f ( t ) [1 - e x p ( - aot)] + Twoe x p ( - a 0 t ) a0

where

f(t)

= h°ZbAb"/Ts +

UAbT. + F(t)To Mw

(8)

KUMAR and TIWARI:

DOUBLE SLOPE SOLAR STILL

85

/-7s and Ta are the average values of Hs and Ta, respectively, for the time interval 0 ~ t . The glass temperature can be otbained from equation (1) as Tg =

hi Tw+ h2" T~ hi + h2

(9)

The hourly distillate per unit area is expressed by . mel

Tg)At

h,,(T,-

=

L

QewAt

(kg/m2h).

(10)

L

The obtained Tw and Tg can be used to evaluate hew, hew and h~ for calculation of the next set of time intervals by using the/7~ and 7'a for the same time interval with Mw = (Mw - the) (Tiwari and

Madhuri [8]). The daily yield of the still is given by 24

(11) n=l

The efficiency of the system is expressed as

MeL rl = AbZHs" A t NUMERICAL

RESULTS

x 100.

(12)

AND DISCUSSION

I n o r d e r to a p p r e c i a t e the n u m e r i c a l results, t h e f o l l o w i n g s y s t e m p a r a m e t e r s h a v e b e e n used.

System parameters Zb = 0.75, a = 5.669 X 10 -8 W / m 2 K 4, Mw = 419,000 J / ° C , Cf = 4190 J / k g ° C ( c o n s i d e r i n g w a t e r as fluid), Ab = 1 m 2, L = 2372.52 k J / k g °C, V = 5 m / s , h = 3.37 W / m °C, h2 = 20.8 W / m 2 °C, Table 1. Steam table for saturation vapour pressure

ECM 30/2--B

Temperature (°C)

P(N/m ~)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

610.8 656.6 705.5 757.55 812.0 871.8 934.5 1001.2 1072.0 1147.2 1227.0 1311.6 1401.4 ! 496.5 1597.3 1703.9 1816.8 1936.2 2062.0 2190.0 2337.0 2485.0 2642.0 2808.0 2982.0 3166.0 3360.0 3564.0 3778.0 4004.0 4241.0

Temperature (°C)

P(N/m 2)

Temperature (°C)

P(N/m 2)

31.0 32.0 33.0 34.0 35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0 50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0 60.0

4491 4743 5029 5318 5622 5940 6274 6624 6991 7375 7777 8198 8639 9100 9583 10,086 10,612 1I, 162 11,736 12,335 12,961 13,613 14,340 15,002 15,641 16,511 17,313 18,147 19,016 19,920

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

20,860 21,840 22,860 23,710 25,010 26,150 27,330 28,560 29,840 31,160 32,530 33,960 35,420 36,960 38,550 40,190 41,890 43,650 45,470 47,360 49,310 49,310 53,420 55,570 57,800 60,110 62.490 64,950 67,490 70,110

86

K U M A R and TIWARI:

DOUBLE SLOPE SOLAR STILL

1000 /

~

26 MAY 1978

?

N

60 po

E 750

=< >-

I-

,,o

500

I1: IZ

0

t

10

6

t

14 18 22 TIME OF THE DAY ( h )

2

Fig. 2. Hourly variation of solar intensity and ambient air temperature. h 3 = 135 W/m 2 °C,

hb = 0.77 W/m 2 °C,

L ' = 5-10 m,

rh = 0.0025-0.05 kg/m 2 s,

T~o = 33.5°C,

To = 50-80°C. Steam table Table 1 furnishes the required saturation vapour pressure for the corresponding temperatures [9]. Climate parameters The hourly variation of solar intensity and ambient air temperature, corresponding to 26 May 1978, has been shown in Fig. 2 which has been used for numerical computations.

=0.0025 k g / m Z s I

Without heat exchanger

II

To = 50 °C

1]! TO = 80 'C

so

~0 u

J~

~ 2O

,,,

TO

I

I

I

I

I

i

8

12

16

20

24

4

TIME OF THE DAY (h)

Fig. 3. Hourly variation of evaporative heat transfer coetficient (hew) with and without heat exchanger for different inlet temperature of the fluid.

K U M A R and TIWARI:

DOUBLE SLOPE SOLAR STILL

80-I II E

87

--0.0025 k g / m 2 s Without heat exchanger TO = 50 'C To = 8 0 ' C

70

60 LIJ

(Z LIJ CL bJ p-

50

1,0

30

m

i

I

I

I

8

12

16

20

I 2~

4

TIME OF THE DAY (h)

Fig. 4. Hourly variation of water and glass temperature with and without heat exchanger for different inlet temperature of the fluid.

Figure 3 shows the hourly variation of evaporative heat transfer coefficient (hew) without and with heat exchanger for different inlet temperature To, of the heat exchanger fluid. From the figure, it is clear that the evaporative heat transfer coefficient depends strongly on temperature. Curve I represents the case when there is no flow of any fluid through the heat exchanger or, in other words, with no heat exchanger. Curves II and III correspond to To = 50 and 80°C, respectively. The variation in he,, is much more when To is higher than the water temperature in the still. It is also observed that there is no significant variation in h~, and hrw for a complete cycle. Figure 4 represents the hourly variation of basin water and glass temperature with and without heat exchanger for different inlet fluid temperatures of the heat exchanger. It is clear that both Tw and Tg increase with an increase in To. The lowering of Tw and T~ for curve I compared to II after peak sunshine hours is due to the fact that, during this period, the temperature of the basin water T,, becomes greater than To, resulting in transfer of heat from the basin water to the heat exchanger fluid. This lowers the water temperature and, consequently, the glass temperature also decreases. Due to this fact, it is advisable to use the waste hot water with either higher temperature or during off-sunshine hours. The hourly variation of yield with and without heat exchanger for different To is shown in Fig. 5. The decrease in the yield of the still after peak sunshine hours is due to the decrease in ho,,, T,, and Tg, and for greater values of To, the yield increases sharply.

88

KUMAR and TIWARI:

DOUBLE SLOPE SOLAR STILL

r~ =0.0025 k g / m Z s 180

I

Without heat exchanger

H

TO = 50 'C III To = 8 0 ' C

150

120

% x

•~

90

60

30

I

I

,I

I

I

I

8

12

1G

20

24

z,

TIME OF THE DAY {h)

Fig. 5. Hourly variation of the still yield with and without heat exchanger for different inlet temperature of the fluid.

30

¸ D

~I = 0 . 0 0 2 5 kg/m2s

2sl-

20[

D

>Z

u_ 15 U..

m

tJ. W

10

B

....

I

I

I

I

S0

GO

70

80

INLET FLUID TEMPERATURE To ( % )

Fig. 6. Variation of system efficiency with inlet temperature of the heat exchanger fluid for fixed flow rate.

KUMAR and TIWARI:

DOUBLE SLOPE SOLAR STILL

89

20To = SO oC

>-

~u

15-

t, b. LU

J

10!I

I

I

I

25

175

325

475

i

¢n x l 0 4 (kg/m $) Fig, 7. Variation of system efficiency with flow rate for fixed inlet temperature of the heat exchanger fluid.

Figure 6 shows the variation of system efficiency with inlet fluid temperature at a constant flow rate of 0.0025 kg/m 2 s. It is observed that the efficiency of the system increases with inlet temperature of the working fluid. The variation of system efficiency with flow rate at constant inlet temperature is depicted in Fig. 7. From this figure, it is clear that r/increases with rh. It is due to the fact that, at higher flow rate, more heat is transferred to the basin water. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

M. A. S. Malik, G. N. Tiwari, A. Kumar and M. S. Sodha, Solar Distillation. Pergamon Press, Oxford (1982). G. N. Tiwari, Advanced Solar Distillation System. Kamala Kuteer, Andhra Pradesh, India (1985). S. N. Rai and G. N. Tiwari, Energy Convers. Mgmt 23, 145 (1983). G. N. Tiwari and N. K. Dhiman, Desalination (1985), M. S. Sodha, A. Kumar and G. N. Tiwari, Desalination 37, 325 (1981). Madhuri and G. N. Tiwari, Desalination 42, 345 (1985). G. N. Tiwari, H. P. Garg and Madhuri, Energy Convers. Mgmt 25, 315 (1985). G. N. Tiwari and Madhuri, Desalination 61, 67 (1987). G. N. Tiwari, Singh, Usha and J. K. Nayak, Applied Solar Thermal Energy Devices. Kamala Kuteer, Andhra Pradesh, India (1985).