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Effect of condensing cover material on yield of an active solar still: an experimental validation
Desalination 227 (2008) 178–189
Effect of condensing cover material on yield of an active solar still: an experimental validation Vimal Dimria, Bikash Sarkara, Usha Singhb, G.N. Tiwaria* a
Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Tel. +91 (11) 2659-1258/6464; Fax: +91 (11) 2658-1121; email: [email protected] b Department of Physics, University of Rajasthan, Rajasthan, India Received 27 April 2006; Accepted 21 June 2007
Abstract An attempt has been made to evaluate inner and outer glass temperature and its effects on yield. Numerical computations have been performed for a typical day in the month of December, 2005, for the climatic condition of New Delhi (latitude: 28E35N N; longitude: 77E12N E and an altitude of 216 m above mean sea level). Higher yield was observed for an active solar distillation system as compared to the passive mode due to higher operating temperature differences between water and inner glass cover. The parametric study has also been performed to find out the effects of various parameters, namely thickness of condensing cover, collector absorbing surface, wind velocity and water depth of the still. It is observed that there is significant effect on daily yield due to change in the values of collector absorbing surface, wind velocity and water depth. For all the cases, the correlation of coefficients (r) between predicted and experimental values have been verified and they showed fair agreement with 0.90 < r < 0.99 and root mean square percent deviation 3.22% < e < 22.64%. Effect of condensing cover materials, namely copper and polyvinyl chloride (PVC), on daily yield have also been investigated and compared. Keywords: Solar distillation; Active system; Heat transfer coefficient; Parametric studies
1. Introduction Solar distillation is a process to distill brackish/saline water by utilizing solar energy. In general, solar distillation process is carried out in two modes e.g., passive and active. Malik et al. *Corresponding author.
[1] reported on passive solar stills until 1982. Soliman [2] studied the performance of basin type solar stills integrated with a flat plate collector. Kiatsiriroat et al. [3] analyzed the performance of multiple effect vertical solar stills with a flat plate solar collector. Zaki et al. [4] studied an active system of conventional single slope solar still integrated with a flat plate collector under the
0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.06.024
V. Dimri et al. / Desalination 227 (2008) 178–189
thermosyphon mode of operation and found that the maximum increase in the yield was up to 33% when the water in the still was preheated in the collector. Tiwari [5] reviewed the work on passive as well as active solar stills. Tripathi and Tiwari [6] carried out an experiment with the effect of water depth on internal heat and mass transfer for active system. Tiwari et al. [7] worked out computer modeling of passive/active solar stills by using inner glass temperature for limited period. However, they have not considered this effect in thermal modeling. Further, Tiwari et al. [8] reviewed the present status of solar distillation systems for both passive and active modes. In this field a large group of authors reported that the passive solar distillation system is a slow process for purification of brackish water. The yield of this still is about 2 L/day per m2 of still area, which is much less and may not be economically useful. Effect of shape and size by using plastic condensing cover for passive solar still has also been carried out by various scientists [9–15]. They concluded that the daily yield is decreased due to reduction in top loss and large surface tension between condensed water and condensing cover for a same design. However, there is a method to increase the yield by integration of solar collector into the basin. This is generally referred to as active solar stills. These may be flat plat collector, solar concentrator or evacuated collector. These collectors may produce temperatures within the range of 80–120EC depending upon the type of solar collector. However, the range of temperature within solar stills is reduced to about 80EC due to high heat capacity of water mass within the basin. Hence there is a practical application of such active systems to extract the essence of medicinal plants placed under the solar still at about 80EC. The systems used for extraction of the essence of medicinal plants have become economical. Among these, the flat plate collector is becoming more popular due to its easy operation, low
179
cost and easy maintenance. In this system, additional thermal energy is fed into the basin from a collector panel [3,4,6]. Therefore the objectives of the present studies are: C to investigate the effects of inner and outer glass temperature on yield; C to study the effects on various parameters on yield, viz., thickness of glass cover, collector absorbing surface, wind velocity and water depth. C to study the effects of different condensing cover materials.
2. Materials and methods 2.1. Experimental set-up The experiment was carried out at the solar Energy Park at IIT Delhi (latitude: 28E35NN; longitude: 77E12NE and an altitude of 216 m above mean sea level) [6]. The cross sectional view of an active solar still is shown in Fig. 1. The bottom surface of the still was painted black for higher absorptivity and a glass cover of 0.003 m thickness covers the still. The area of the still was taken to be 1 m2. The still was coupled by using well insulated pipes to two flat plate collectors of effective area 4 m2. The depth of water in the basin has been kept equal to 0.05 m. 2.2. Instrumentation and observations Parameters such as water, inner glass, outer glass and ambient temperatures, total and diffuse radiations on the glass cover and collector and the yield were measured hourly. Water and glass temperatures were recorded with the help of calibrated copper-constantan thermocouples and a digital temperature indicator having the least count of 0.1EC. The ambient temperature and the yield were recorded with the help of calibrated mercury thermometer having a least count of 0.1EC and with a measuring cylinder of least count 10 ml, respectively. The solar intensity was
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Fig. 1. Cross sectional view of an active solar still coupled with a flat plate collector.
measured with the help of calibrated solarimeter of least count 2 mW/cm2. During the active distillation process, the hot water from the collector was pumped into the basin of the still to increase the temperature difference between the glass and water surface. The pump was operated only for the sunshine hours (9 am to 4 pm) to avoid the heat losses caused by reverse flow during off-sunshine hours. Table 1 shows the experimental observations for particular days for hourly variation of solar intensity, water, glass and ambient temperature and yield for 0.05 m depth. Experiments were conducted from 9 am to 8 am (i.e., 24 h) and validation was done for a clear typical day — December 7, 2005 — for 0.05 m water depth. A computer program in MATLAB was made to calculate various heat transfer coefficients, the values of which were then used to calculate the theoretical values of water, inner, outer glass temperature and the yield, by providing the initial values of water and glass temperature and the effective solar intensity values.
3. Thermal modeling The energy balance equations in terms of various heat transfer coefficient of an active solar still [16] are as follows: C Inner and outer glass cover:
α′g I effs + h 1w (Tw − Tgi ) = Kg Lg
(T
gi
Kg Lg
(T
gi
− Tgo )
− Tgo ) = h1g (Tgo − Ta )
(1a)
(1b)
Simplifying Eqs. (1a) and (1b), one gets
α′g I effs + h 1w Tw + Tgi =
and
h 1w +
Kg Lg
Kg Lg
Tgo (2a)
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V. Dimri et al. / Desalination 227 (2008) 178–189 Table 1 Hourly variation of solar intensity, water, glass, ambient temperature and yield for 0.05 m water depth in the basin Time (h)
Ieffs (W/m2)
Ieffc (W/m2)
Tw (EC)
Tgi (EC)
Tgo (EC)
Ta (EC)
m ˙ ew (kg/m2 h)
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8
369.55 570.47 680.96 747.05 660.00 433.34 318.00 94.04 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
533.0 779.0 895.0 967.0 862.0 589.0 438.0 170.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19.1 40.6 50.0 56.0 67.9 62.6 60.5 49.4 42.6 37.4 32.5 29.5 26.3 24.1 22.4 20.8 19.4 18.4 17.5 16.8 16.1 15.6 15.2 15.1
23.0 32.6 40.8 48.3 57.7 56.9 50.8 41.6 32.9 27.7 23.6 21.3 19.4 18.1 16.9 15.6 14.7 14.0 13.4 13.1 12.8 12.6 12.5 14.9
14.0 18.0 22.0 23.0 24.0 25.0 25.0 26.0 26.0 26.0 26.0 26.0 24.0 20.0 15.0 11.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.0
14.0 18.0 22.0 23.0 24.0 25.0 25.0 26.0 26.0 26.0 26.0 26.0 24.0 20.0 15.0 11.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.0
0.000 0.068 0.281 0.495 0.590 0.570 0.450 0.340 0.180 0.120 0.090 0.060 0.053 0.047 0.030 0.027 0.021 0.018 0.016 0.014 0.013 0.011 0.011 0.011
Tgo =
α′g I effs h k + U woTw + h 1g Ta h 1g + U wo
C Water mass: (2b)
+α′ (1- α′ ) I + h ( T − T ) Q u w g effs w b w = ( M C )w
C Basin liner:
α′b (1- α′g ) (1- α′w ) I effs = hw ( Tb − Tw ) + hb ( Tb − Ta )
α′− b I effs + hwTw + hbTa hw + hb
(4)
where (3a)
After simplifying the above equation, one gets
Tb =
d Tw + h1w ( Tw − Tgo ) dt
(3b)
= A F ⎡( ατ ) ⎤ I − U ( T − T ) Q u c R ⎣ LC w a c⎦ c
(5)
Substituting the values of Tgi and Tb from Eqs. (2) and (3b) in Eq. (4) and after simplifying, we get
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d Tw + aTw = f ( t ) dT
(6)
UAeff
( MC )w
Ut =
f (t ) =
;
h1w h1g
( IA)eff
;
hw hb ; hw + hw
= NAc FR ( ατ )effc I effc + ( ατ )effs I effs
h1w U wo =
( IA)eff + (UA)eff Ta ( MC )w
; Ub =
h1g + U wo
Kg
h1w +
(UA)eff
Lg Kg
qew = hew (Tw − Tg )
(8)
and the hourly output is given by
h ew (T w - T g ) × 3600 kg/ m 2h ) ( L
24
ew = ∑ m ew M 4. Statistical analyses
U LS = U b + U t
Kg h1w +
Kg
;
hw =
Kw n C ( Gr Pr ) L
Lg
α′− b = (1 − α′g ) (1 − α′w )
= α′b
(10)
i =1
= U LS + NAC FRU LC
Lg
(9)
The daily yield is given by
Lg
−1
( ατ )eff
where Tw0 is the temperature of basin water at t = 0 and f (t ) is the average value of f(t) for the time interval between 0 and t. Inner, outer glass and basin temperatures in terms of water temperature can be calculated using Eqs. (2a), (2b) and (3b), respectively. Now the rate of evaporation is given by:
ew = m
⎡L 1 ⎤ hb = ⎢ 1 + ⎥ ; ⎣⎢ K1 h1g ⎥⎦
hk =
f (t ) ⎡1 − exp ( −a Δt )⎤⎦ + Tw 0 exp ( -a Δt ) a ⎣
(7)
where
a=
Tw =
hw h1w hk + α′w + α′g hw + hb h1g + U wo
4.1. Coefficient of correlation (r) When predicted values are validated with the experimental data, then correlation between predicted and experimental values is presented with a coefficient known as coefficient of correlation. The coefficient of correlation can be evaluated with the following expression [17].
r=
N ∑ xi yi − ∑ ( xi ) ∑ ( yi ) N ∑ xi 2 − ( ∑ xi )
2
N ∑ y i 2 − ( ∑ yi )
2
(11) 4.2. Root mean square of percent deviation (e)
The solution of Eq. (6) is given as
The prediction is done with the help of
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experimental values. The predicted values are validated with experimental data. The closeness of predicted values and experimental data can be presented in terms of root mean square of percent deviation. The expression used for this purpose is as follows [17]:
e=
∑(e )
2
i
(12)
n
where ei =
X pred − Yexp X pred
5. Results and discussion The values of design parameters for validation are given in Tables 2 and 3, which are used as input parameters to calculate the theoretical basin, water, inner and outer glass temperature. Fig. 2 shows the hourly variation of solar radiation on condensing cover and flat plate collector. The hourly variation of ambient air temperature has also been shown in the same figure. Ambient air proportionately increases with increase of solar intensity and decreasing trends was noticed during off-sunshine hours. Eq. (7) has been evaluated for water temperature in the basin for a given design (Tables 2 and 3) and climatic parameters (Fig. 2). After knowing the water temperature, the inner and outer glass cover and the basin liner temperatures have been evaluated from Eqs. (2) and (3b). The hourly variation of basin, water, inner and outer glass temperature and yield is shown in Fig. 3. For comparison, the hourly yield has also been shown in the same figure. It is observed from the figure that the yield increases with an increase of temperature as expected, but a declining trend was observed during off-sunshine hours due to lower temperature differences. The range of temperature decreases in the order of Tb > Tw >Tgi >Tgo as expected. It is further to be noted from Fig. 3 that
Table 2 Design parameters for a single slope solar still Ab, m2 Ag, m2 As, m2 Aw, m2 C Cw, J/kgEC g, m/s Kc, W/mEC Kg, W/mEC Kp, W/mEC Kw, W/mEC K1, W/mEC L L1 , m
1 1 1 1 0.54 4190 9.81 385 0.78 0.16 0.614 0.38 1 0.003
Lc/Lg/Lp, m Mw, kg n v, m/s αNb αNg αNw (ατ)s geff μ, kg/m s ρ, kg/m3 σ αNp
0.003 50 0.25 0–3 0.8 0.05 0.05 0.8 0.82 8.6×10!4 995.8 5.67×10!8 0.05
Table 3 Design parameters for flat plate collectors Ac, m2 Cf, J/kg EC FN m ˙ , kg/s N (ατ)c ULC, W/m2 EC
2 4190 0.8 0.035 2 0.8 6
there is marginal difference between the basin and water temperature due to a high value of convective heat transfer from the basin liner to the water mass as expected. Similarly, the inner glass cover temperature is higher about 0.11– 2.70EC than the outer glass cover temperature due to higher value of wind velocity. This difference becomes significant in the case of PVC as a condensing cover due to low value of its thermal conductivity. The validation of inner and outer glass cover temperature, water temperature and yield are shown in Figs. 4. It can be observed that there is a fair agreement between theoretical and experimental values of these parameters. In all the cases the coefficient of correlation are in the range of
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Fig. 2. Hourly variation of ambient air and solar radiation on still and collector.
Fig. 3. Hourly variation of basin, water, inner and outer glass temperature.
r = 0.97–0.99 and root mean square percent deviation (e) lies between 11.46–36.98%, respectively. The higher value of root mean square deviation is due to very low value of output during the night.
Figs. 5a and 5b show the hourly variation of internal heat transfer coefficient, namely convective and evaporative evaluated by using Dunkle’s relation [18]. The figure indicates that the convective heat transfer coefficient was lower
V. Dimri et al. / Desalination 227 (2008) 178–189
185
Fig. 4a. Hourly variation of theoretical and experimental water temperature and yield.
Fig. 4b. Hourly variation of theoretical and experimental inner glass temperature and yield.
Fig. 4c. Hourly variation of theoretical and experimental outer glass temperature and yield.
Fig. 4d. Hourly variation of theoretical and experimental yield at 0.05 m water depth.
between 13:00 to 20:00 hours due to decrease in the temperature differences between the water and inner glass cover. Higher evaporative heat transfer coefficient was noticed at 12:00 due to prevailing higher temperature differences and at night time decreasing trend was observed due to lower temperature differences. The hourly variation of radiative heat transfer coefficient is shown in Fig. 5c. Convective heat transfer coefficient mainly depends on wind velocity; it increases with the increase of wind velocity and vice-versa. One can concluded that there is a reasonable agreement between heat transfer coefficient
evaluated by experimental observation and theoretical value with the correlation coefficient and root mean square deviation of 0.90, 0.99 and 0.98 and 18.81, 15.26 and 3.22%, respectively. Similar agreement has been observed for total internal heat transfer coefficient as shown in Fig. 5d. Theoretical total heat transfer coefficients were verified with the experimental values in term of coefficient of correlation and root mean square percent deviation. Coefficients of correlation and root mean square percent deviation are r = 0.99 and e = 10.57%, respectively. Fig. 6 shows the variations of daily yield for
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V. Dimri et al. / Desalination 227 (2008) 178–189
Fig. 5a. Hourly variation of theoretical and experimental convective heat transfer coefficient at 0.05 m depth.
Fig. 5b. Hourly variation of theoretical and experimental evaporative heat transfer coefficient at 0.05 m depth.
Fig. 5c. Hourly variation of theoretical and experimental radiative heat transfer coefficient at 0.05 m depth.
Fig. 5d. Hourly variation of theoretical and experimental total heat transfer coefficient (convective, radiative and evaporative) at 0.05 m depth.
different thickness of glass cover in active and passive mode. It is clearly indicated from the figure that daily yield decreases with the increase of glass cover thickness due to reduction in the top loss coefficient [Uwo of Eq. (2b)]. This reduction is significant for both passive and active solar stills. Fig. 7 indicates the variation of daily yield for five numbers of collectors in active mode. From this figure, it is observed that yield increases with increase of collector surface area due to increasing high operating temperature range. However, the increase in yield is marginal
due to higher value of inner glass cover temperature. This indicates that one collector is optimum for present design parameters of an active solar still [19]. Effect of wind on daily yield is shown in Fig. 8. It clearly indicates that wind blowing over the glass cover causes faster evaporation. As the wind velocity increases, the convective heat transfer coefficient from the glass cover to ambient air increases and simultaneously the glass cover temperature decreases which increases the water-glass cover temperature differences and ultimately increased the overall
V. Dimri et al. / Desalination 227 (2008) 178–189
187
Fig. 9. Variation of yield on effects of 0.05 m water depth. Fig. 6. Variation of yield on different thickness of glass cover.
Fig. 10. Effect of condensing cover material on the performance of an active solar still. Fig. 7. Variation of yield on effects of collector absorbing surface.
Fig. 8. Variation of yield on effects of wind velocity.
yield. Similar observations were also found [20]. The effect of water depth on daily yield in active and passive mode is shown in Fig. 9. It is seen from the figure that the yield decreases with increase of water mass from 20 to 150 kg. The decrease in yield may be attributed to higher specific heat capacity of water by the increased water mass. This is in accordance with the results previously reported [20]. The effect of different condensing cover material on daily yield is shown in Fig. 10. It is observed that the yield is maximum in the case of copper condensing cover due to fast release of heat available to it. It is due to the high value of thermal conductivity of copper, which gains
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higher overall heat loss coefficient [Uwo of Eq. (2b)]. In case of PVC, the daily yield is decreased due to reduction in top loss coefficient (Uwo). This attribute is due to the low thermal conductivity of PVC condensing material. These results are in accordance with results reported earlier by various scientists. This strongly justifies using glass as a condensing cover for use of solar energy with cost effectiveness of the system. 6. Conclusions The present study indicates the importance of the active distillation at lower water depth. Inner glass temperature plays a key role to determine the yield. The daily yield is more for active distillation as compared to passive mode using inner glass temperature. Yield is also directly related to thermal conductivity of condensing cover materials; copper gives a greater yield compared to glass and plastic due to higher thermal conductivity. 7. Symbols A Ac Aw C
— — — —
Cf
—
Cw
—
e
—
FN FR g Gr hb
— — — — —
Surface area, m2 Area of collector, m2 Area of water surface, m2 Constant in Nusselt number expression Specific heat of working fluid, J/kgEC Specific heat of water in solar still, J/kgEC Root mean square of percent deviation Collector efficiency factor Heat removal factor Acceleration due to gravity, m/s2 Grashof number Overall heat transfer coefficient from basin liner to ambient air through bottom and side insulation, W/m2 EC)
h1g
—
h1w
—
hcw
—
hew
—
hrw
—
hw
—
Ieff K1
— —
Kg /Kc / — Kp L — — L1 Lg /Lc / — Lp
Mw n
— — — — —
N Pgi
— —
Pr Pw
— —
r t T Ti
— — — —
m ˙ m ˙ ew
ew M
Convective and radiative heat transfer coefficient from glass cover to ambient, W/m2 EC Total heat transfer coefficients from water surface to glass cover, W/m2EC Convective heat transfer coefficient from water surface to glass, W/m2EC Evaporative heat transfer coefficient from water surface to glass, W/m2EC Radiative heat transfer coefficient from water surface to glass, W/m2EC Convective heat transfer coefficient from basin liner to water, W/m2EC Effective solar intensity, W/m2 Thermal conductivity of insulation material, W/mEC Thermal conductivity of glass, copper and PVC, W/mEC Latent heat of vaporization, J/kg Thickness of insulation material, m Thickness of glass, copper and PVC, m Flow rate of pump, L/s Hourly output of still, kg/m2 h Daily output of still, kg/m2 h Mass of water in basin, kg Constant in Nusselt number expression Number of observations Partial vapor pressure at inner glass temperature, N/m2 Prandtl number Partial vapour pressure at water temperature, N/m2 Coefficient of correlation Time, s Temperature, EC Average of water and inner glass temperature, EC
V. Dimri et al. / Desalination 227 (2008) 178–189
Tb Tgi Tgo Ub
— — — —
ULC
—
Ut
—
v Xi Yi
— — —
Temperature of basin water, EC Inner glass temperature, EC Outer glass temperature, EC Overall bottom heat loss coefficient, W/m2EC Overall heat transfer coefficient for collector, W/m2EC Overall top loss coefficient from water surface to ambient air, W/m2EC Wind velocity, m/s Theoretical or predicted value Experimental value
Greek Α αN (ατ)
— — —
β ΔT γ μ σ
— — — — —
Absorptivity Fraction of energy absorbed Effective absorptance-transmittance product Expansion factor, K!1 Temperature difference, EC Relative humidity Viscosity of humid air, N.s/m2 Stefan Boltzman constant
Subscripts a b c eff g s w
— — — — — — —
Ambient Basin liner Collector Effective Glass cover Solar still Water
References [1] M.A.S. Malik, G.N. Tiwari, A. Kumar and M.S. Sodha, Solar Distillation, Pergamon Press, Oxford, UK, 1982. [2] H.S Soliman, Solar still coupled with a solar water heater, Mosul University, Mosul, Iraq, 1976, p. 43. [3] T. Kiatsiriroat, P. Wibulswas and S.C. Bhattacharya, Performance analysis of multiple effect vertical solar still with flat plate solar collector. J. Solar Wind
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Technol., 4(4) (1987) 451. [4] G.M. Zaki, A. Al-Turki and M. AI-Fatani, Experimental investigation on concentrator assisted solar stills, J. Solar Energy, 11(1992) 193–199. [5] G.N. Tiwari, Recent Advances in Solar Distillation, Wiley Eastern, New Delhi, India, 1992, Chap. 2. [6] R. Tripathi and G.N. Tiwari, Effect of water depth on internal heat and mass transfer for active solar distillation, Desalination, 173 (2005) 187–200. [7] G.N. Tiwari, S.K. Shukla and I.P. Singh, Computer modeling of passive/active solar stills by using inner glass temperature, Desalination, 154 (2003) 171. [8] G.N. Tiwari, H.N. Singh and R. Tripathi, Present status of solar distillation, Solar Energy, 75(5) (2003) 367–373. [9] M. Kobayashi, A method of obtaining water in arid land, Solar Energy, 7(3) (1963) 93. [10] A.A. Delyannis, Solar stills provide an islands’s inhabitants with water, Sun at Work, 10(1) (1965) 6. [11] G.O.G. Lof, Solar desalination, in: Principle of Desalination, K.S. Spiegler, ed., Academic Press, New York, 1966, Chap. 5. [12] B.W. Tlemat and E.D. Howe, Comparison of plastic and glass condensing covers for solar distillers. Proc. Solar Energy Society, Annual Conference, Arizona, 1967, pp. 1–12. [13] E.Zh. Norov, B.M. Achilov and T.D. Zhuraev, Results of tests on solar film-covered stills, Geliotekhnika, 11(3/4) (1975) 130. [14] G.Ya. Umarov, M.K. Asamov, B.M. Achilov, T.K. Sarros, E.Zh. Norov and N.A. Tsagaraeva, Modified polyethylene films for solar stills, Geliotekhnika, 12(2) (1976) 29. [15] J. Ahmadzadeh, Solar earth water stills, Solar Energy, 20(5) (1978) 387. [16] G.N. Tiwari, Solar Energy: Fundamentals, Design, Modeling and Applications, Narosa, New Delhi, and CRC, New York, 2002. [17] S.C. Chapra and R.P. Canale, Numerical Methods for Engineers, McGraw-Hill, New York, 1989. [18] R.V. Dunkle, Solar water distillation; the roof type still and a multiple effect diffusion still, Internat. Developments in Heat Transfer, ASME Proc., International Heat Transfer, Part V, University of Colorado, 1961, p. 895. [19] H.N. Singh, Estimation of beam and diffuse radiation for Indian climatic conditions and its application for distillation, Ph.D. Thesis, India Institute of Technology, Delhi, 2004. [20] P.I. Cooper, Digital simulation of transient solar still process, Solar Energy, 12 (1969) 313.
Effect of condensing cover material on yield of an active solar still: an experimental validation Vimal Dimria, Bikash Sarkara, Usha Singhb, G.N. Tiwaria* a
Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Tel. +91 (11) 2659-1258/6464; Fax: +91 (11) 2658-1121; email: [email protected] b Department of Physics, University of Rajasthan, Rajasthan, India Received 27 April 2006; Accepted 21 June 2007
Abstract An attempt has been made to evaluate inner and outer glass temperature and its effects on yield. Numerical computations have been performed for a typical day in the month of December, 2005, for the climatic condition of New Delhi (latitude: 28E35N N; longitude: 77E12N E and an altitude of 216 m above mean sea level). Higher yield was observed for an active solar distillation system as compared to the passive mode due to higher operating temperature differences between water and inner glass cover. The parametric study has also been performed to find out the effects of various parameters, namely thickness of condensing cover, collector absorbing surface, wind velocity and water depth of the still. It is observed that there is significant effect on daily yield due to change in the values of collector absorbing surface, wind velocity and water depth. For all the cases, the correlation of coefficients (r) between predicted and experimental values have been verified and they showed fair agreement with 0.90 < r < 0.99 and root mean square percent deviation 3.22% < e < 22.64%. Effect of condensing cover materials, namely copper and polyvinyl chloride (PVC), on daily yield have also been investigated and compared. Keywords: Solar distillation; Active system; Heat transfer coefficient; Parametric studies
1. Introduction Solar distillation is a process to distill brackish/saline water by utilizing solar energy. In general, solar distillation process is carried out in two modes e.g., passive and active. Malik et al. *Corresponding author.
[1] reported on passive solar stills until 1982. Soliman [2] studied the performance of basin type solar stills integrated with a flat plate collector. Kiatsiriroat et al. [3] analyzed the performance of multiple effect vertical solar stills with a flat plate solar collector. Zaki et al. [4] studied an active system of conventional single slope solar still integrated with a flat plate collector under the
0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.06.024
V. Dimri et al. / Desalination 227 (2008) 178–189
thermosyphon mode of operation and found that the maximum increase in the yield was up to 33% when the water in the still was preheated in the collector. Tiwari [5] reviewed the work on passive as well as active solar stills. Tripathi and Tiwari [6] carried out an experiment with the effect of water depth on internal heat and mass transfer for active system. Tiwari et al. [7] worked out computer modeling of passive/active solar stills by using inner glass temperature for limited period. However, they have not considered this effect in thermal modeling. Further, Tiwari et al. [8] reviewed the present status of solar distillation systems for both passive and active modes. In this field a large group of authors reported that the passive solar distillation system is a slow process for purification of brackish water. The yield of this still is about 2 L/day per m2 of still area, which is much less and may not be economically useful. Effect of shape and size by using plastic condensing cover for passive solar still has also been carried out by various scientists [9–15]. They concluded that the daily yield is decreased due to reduction in top loss and large surface tension between condensed water and condensing cover for a same design. However, there is a method to increase the yield by integration of solar collector into the basin. This is generally referred to as active solar stills. These may be flat plat collector, solar concentrator or evacuated collector. These collectors may produce temperatures within the range of 80–120EC depending upon the type of solar collector. However, the range of temperature within solar stills is reduced to about 80EC due to high heat capacity of water mass within the basin. Hence there is a practical application of such active systems to extract the essence of medicinal plants placed under the solar still at about 80EC. The systems used for extraction of the essence of medicinal plants have become economical. Among these, the flat plate collector is becoming more popular due to its easy operation, low
179
cost and easy maintenance. In this system, additional thermal energy is fed into the basin from a collector panel [3,4,6]. Therefore the objectives of the present studies are: C to investigate the effects of inner and outer glass temperature on yield; C to study the effects on various parameters on yield, viz., thickness of glass cover, collector absorbing surface, wind velocity and water depth. C to study the effects of different condensing cover materials.
2. Materials and methods 2.1. Experimental set-up The experiment was carried out at the solar Energy Park at IIT Delhi (latitude: 28E35NN; longitude: 77E12NE and an altitude of 216 m above mean sea level) [6]. The cross sectional view of an active solar still is shown in Fig. 1. The bottom surface of the still was painted black for higher absorptivity and a glass cover of 0.003 m thickness covers the still. The area of the still was taken to be 1 m2. The still was coupled by using well insulated pipes to two flat plate collectors of effective area 4 m2. The depth of water in the basin has been kept equal to 0.05 m. 2.2. Instrumentation and observations Parameters such as water, inner glass, outer glass and ambient temperatures, total and diffuse radiations on the glass cover and collector and the yield were measured hourly. Water and glass temperatures were recorded with the help of calibrated copper-constantan thermocouples and a digital temperature indicator having the least count of 0.1EC. The ambient temperature and the yield were recorded with the help of calibrated mercury thermometer having a least count of 0.1EC and with a measuring cylinder of least count 10 ml, respectively. The solar intensity was
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V. Dimri et al. / Desalination 227 (2008) 178–189
Fig. 1. Cross sectional view of an active solar still coupled with a flat plate collector.
measured with the help of calibrated solarimeter of least count 2 mW/cm2. During the active distillation process, the hot water from the collector was pumped into the basin of the still to increase the temperature difference between the glass and water surface. The pump was operated only for the sunshine hours (9 am to 4 pm) to avoid the heat losses caused by reverse flow during off-sunshine hours. Table 1 shows the experimental observations for particular days for hourly variation of solar intensity, water, glass and ambient temperature and yield for 0.05 m depth. Experiments were conducted from 9 am to 8 am (i.e., 24 h) and validation was done for a clear typical day — December 7, 2005 — for 0.05 m water depth. A computer program in MATLAB was made to calculate various heat transfer coefficients, the values of which were then used to calculate the theoretical values of water, inner, outer glass temperature and the yield, by providing the initial values of water and glass temperature and the effective solar intensity values.
3. Thermal modeling The energy balance equations in terms of various heat transfer coefficient of an active solar still [16] are as follows: C Inner and outer glass cover:
α′g I effs + h 1w (Tw − Tgi ) = Kg Lg
(T
gi
Kg Lg
(T
gi
− Tgo )
− Tgo ) = h1g (Tgo − Ta )
(1a)
(1b)
Simplifying Eqs. (1a) and (1b), one gets
α′g I effs + h 1w Tw + Tgi =
and
h 1w +
Kg Lg
Kg Lg
Tgo (2a)
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V. Dimri et al. / Desalination 227 (2008) 178–189 Table 1 Hourly variation of solar intensity, water, glass, ambient temperature and yield for 0.05 m water depth in the basin Time (h)
Ieffs (W/m2)
Ieffc (W/m2)
Tw (EC)
Tgi (EC)
Tgo (EC)
Ta (EC)
m ˙ ew (kg/m2 h)
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8
369.55 570.47 680.96 747.05 660.00 433.34 318.00 94.04 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
533.0 779.0 895.0 967.0 862.0 589.0 438.0 170.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19.1 40.6 50.0 56.0 67.9 62.6 60.5 49.4 42.6 37.4 32.5 29.5 26.3 24.1 22.4 20.8 19.4 18.4 17.5 16.8 16.1 15.6 15.2 15.1
23.0 32.6 40.8 48.3 57.7 56.9 50.8 41.6 32.9 27.7 23.6 21.3 19.4 18.1 16.9 15.6 14.7 14.0 13.4 13.1 12.8 12.6 12.5 14.9
14.0 18.0 22.0 23.0 24.0 25.0 25.0 26.0 26.0 26.0 26.0 26.0 24.0 20.0 15.0 11.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.0
14.0 18.0 22.0 23.0 24.0 25.0 25.0 26.0 26.0 26.0 26.0 26.0 24.0 20.0 15.0 11.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.0
0.000 0.068 0.281 0.495 0.590 0.570 0.450 0.340 0.180 0.120 0.090 0.060 0.053 0.047 0.030 0.027 0.021 0.018 0.016 0.014 0.013 0.011 0.011 0.011
Tgo =
α′g I effs h k + U woTw + h 1g Ta h 1g + U wo
C Water mass: (2b)
+α′ (1- α′ ) I + h ( T − T ) Q u w g effs w b w = ( M C )w
C Basin liner:
α′b (1- α′g ) (1- α′w ) I effs = hw ( Tb − Tw ) + hb ( Tb − Ta )
α′− b I effs + hwTw + hbTa hw + hb
(4)
where (3a)
After simplifying the above equation, one gets
Tb =
d Tw + h1w ( Tw − Tgo ) dt
(3b)
= A F ⎡( ατ ) ⎤ I − U ( T − T ) Q u c R ⎣ LC w a c⎦ c
(5)
Substituting the values of Tgi and Tb from Eqs. (2) and (3b) in Eq. (4) and after simplifying, we get
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V. Dimri et al. / Desalination 227 (2008) 178–189
d Tw + aTw = f ( t ) dT
(6)
UAeff
( MC )w
Ut =
f (t ) =
;
h1w h1g
( IA)eff
;
hw hb ; hw + hw
= NAc FR ( ατ )effc I effc + ( ατ )effs I effs
h1w U wo =
( IA)eff + (UA)eff Ta ( MC )w
; Ub =
h1g + U wo
Kg
h1w +
(UA)eff
Lg Kg
qew = hew (Tw − Tg )
(8)
and the hourly output is given by
h ew (T w - T g ) × 3600 kg/ m 2h ) ( L
24
ew = ∑ m ew M 4. Statistical analyses
U LS = U b + U t
Kg h1w +
Kg
;
hw =
Kw n C ( Gr Pr ) L
Lg
α′− b = (1 − α′g ) (1 − α′w )
= α′b
(10)
i =1
= U LS + NAC FRU LC
Lg
(9)
The daily yield is given by
Lg
−1
( ατ )eff
where Tw0 is the temperature of basin water at t = 0 and f (t ) is the average value of f(t) for the time interval between 0 and t. Inner, outer glass and basin temperatures in terms of water temperature can be calculated using Eqs. (2a), (2b) and (3b), respectively. Now the rate of evaporation is given by:
ew = m
⎡L 1 ⎤ hb = ⎢ 1 + ⎥ ; ⎣⎢ K1 h1g ⎥⎦
hk =
f (t ) ⎡1 − exp ( −a Δt )⎤⎦ + Tw 0 exp ( -a Δt ) a ⎣
(7)
where
a=
Tw =
hw h1w hk + α′w + α′g hw + hb h1g + U wo
4.1. Coefficient of correlation (r) When predicted values are validated with the experimental data, then correlation between predicted and experimental values is presented with a coefficient known as coefficient of correlation. The coefficient of correlation can be evaluated with the following expression [17].
r=
N ∑ xi yi − ∑ ( xi ) ∑ ( yi ) N ∑ xi 2 − ( ∑ xi )
2
N ∑ y i 2 − ( ∑ yi )
2
(11) 4.2. Root mean square of percent deviation (e)
The solution of Eq. (6) is given as
The prediction is done with the help of
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experimental values. The predicted values are validated with experimental data. The closeness of predicted values and experimental data can be presented in terms of root mean square of percent deviation. The expression used for this purpose is as follows [17]:
e=
∑(e )
2
i
(12)
n
where ei =
X pred − Yexp X pred
5. Results and discussion The values of design parameters for validation are given in Tables 2 and 3, which are used as input parameters to calculate the theoretical basin, water, inner and outer glass temperature. Fig. 2 shows the hourly variation of solar radiation on condensing cover and flat plate collector. The hourly variation of ambient air temperature has also been shown in the same figure. Ambient air proportionately increases with increase of solar intensity and decreasing trends was noticed during off-sunshine hours. Eq. (7) has been evaluated for water temperature in the basin for a given design (Tables 2 and 3) and climatic parameters (Fig. 2). After knowing the water temperature, the inner and outer glass cover and the basin liner temperatures have been evaluated from Eqs. (2) and (3b). The hourly variation of basin, water, inner and outer glass temperature and yield is shown in Fig. 3. For comparison, the hourly yield has also been shown in the same figure. It is observed from the figure that the yield increases with an increase of temperature as expected, but a declining trend was observed during off-sunshine hours due to lower temperature differences. The range of temperature decreases in the order of Tb > Tw >Tgi >Tgo as expected. It is further to be noted from Fig. 3 that
Table 2 Design parameters for a single slope solar still Ab, m2 Ag, m2 As, m2 Aw, m2 C Cw, J/kgEC g, m/s Kc, W/mEC Kg, W/mEC Kp, W/mEC Kw, W/mEC K1, W/mEC L L1 , m
1 1 1 1 0.54 4190 9.81 385 0.78 0.16 0.614 0.38 1 0.003
Lc/Lg/Lp, m Mw, kg n v, m/s αNb αNg αNw (ατ)s geff μ, kg/m s ρ, kg/m3 σ αNp
0.003 50 0.25 0–3 0.8 0.05 0.05 0.8 0.82 8.6×10!4 995.8 5.67×10!8 0.05
Table 3 Design parameters for flat plate collectors Ac, m2 Cf, J/kg EC FN m ˙ , kg/s N (ατ)c ULC, W/m2 EC
2 4190 0.8 0.035 2 0.8 6
there is marginal difference between the basin and water temperature due to a high value of convective heat transfer from the basin liner to the water mass as expected. Similarly, the inner glass cover temperature is higher about 0.11– 2.70EC than the outer glass cover temperature due to higher value of wind velocity. This difference becomes significant in the case of PVC as a condensing cover due to low value of its thermal conductivity. The validation of inner and outer glass cover temperature, water temperature and yield are shown in Figs. 4. It can be observed that there is a fair agreement between theoretical and experimental values of these parameters. In all the cases the coefficient of correlation are in the range of
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V. Dimri et al. / Desalination 227 (2008) 178–189
Fig. 2. Hourly variation of ambient air and solar radiation on still and collector.
Fig. 3. Hourly variation of basin, water, inner and outer glass temperature.
r = 0.97–0.99 and root mean square percent deviation (e) lies between 11.46–36.98%, respectively. The higher value of root mean square deviation is due to very low value of output during the night.
Figs. 5a and 5b show the hourly variation of internal heat transfer coefficient, namely convective and evaporative evaluated by using Dunkle’s relation [18]. The figure indicates that the convective heat transfer coefficient was lower
V. Dimri et al. / Desalination 227 (2008) 178–189
185
Fig. 4a. Hourly variation of theoretical and experimental water temperature and yield.
Fig. 4b. Hourly variation of theoretical and experimental inner glass temperature and yield.
Fig. 4c. Hourly variation of theoretical and experimental outer glass temperature and yield.
Fig. 4d. Hourly variation of theoretical and experimental yield at 0.05 m water depth.
between 13:00 to 20:00 hours due to decrease in the temperature differences between the water and inner glass cover. Higher evaporative heat transfer coefficient was noticed at 12:00 due to prevailing higher temperature differences and at night time decreasing trend was observed due to lower temperature differences. The hourly variation of radiative heat transfer coefficient is shown in Fig. 5c. Convective heat transfer coefficient mainly depends on wind velocity; it increases with the increase of wind velocity and vice-versa. One can concluded that there is a reasonable agreement between heat transfer coefficient
evaluated by experimental observation and theoretical value with the correlation coefficient and root mean square deviation of 0.90, 0.99 and 0.98 and 18.81, 15.26 and 3.22%, respectively. Similar agreement has been observed for total internal heat transfer coefficient as shown in Fig. 5d. Theoretical total heat transfer coefficients were verified with the experimental values in term of coefficient of correlation and root mean square percent deviation. Coefficients of correlation and root mean square percent deviation are r = 0.99 and e = 10.57%, respectively. Fig. 6 shows the variations of daily yield for
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V. Dimri et al. / Desalination 227 (2008) 178–189
Fig. 5a. Hourly variation of theoretical and experimental convective heat transfer coefficient at 0.05 m depth.
Fig. 5b. Hourly variation of theoretical and experimental evaporative heat transfer coefficient at 0.05 m depth.
Fig. 5c. Hourly variation of theoretical and experimental radiative heat transfer coefficient at 0.05 m depth.
Fig. 5d. Hourly variation of theoretical and experimental total heat transfer coefficient (convective, radiative and evaporative) at 0.05 m depth.
different thickness of glass cover in active and passive mode. It is clearly indicated from the figure that daily yield decreases with the increase of glass cover thickness due to reduction in the top loss coefficient [Uwo of Eq. (2b)]. This reduction is significant for both passive and active solar stills. Fig. 7 indicates the variation of daily yield for five numbers of collectors in active mode. From this figure, it is observed that yield increases with increase of collector surface area due to increasing high operating temperature range. However, the increase in yield is marginal
due to higher value of inner glass cover temperature. This indicates that one collector is optimum for present design parameters of an active solar still [19]. Effect of wind on daily yield is shown in Fig. 8. It clearly indicates that wind blowing over the glass cover causes faster evaporation. As the wind velocity increases, the convective heat transfer coefficient from the glass cover to ambient air increases and simultaneously the glass cover temperature decreases which increases the water-glass cover temperature differences and ultimately increased the overall
V. Dimri et al. / Desalination 227 (2008) 178–189
187
Fig. 9. Variation of yield on effects of 0.05 m water depth. Fig. 6. Variation of yield on different thickness of glass cover.
Fig. 10. Effect of condensing cover material on the performance of an active solar still. Fig. 7. Variation of yield on effects of collector absorbing surface.
Fig. 8. Variation of yield on effects of wind velocity.
yield. Similar observations were also found [20]. The effect of water depth on daily yield in active and passive mode is shown in Fig. 9. It is seen from the figure that the yield decreases with increase of water mass from 20 to 150 kg. The decrease in yield may be attributed to higher specific heat capacity of water by the increased water mass. This is in accordance with the results previously reported [20]. The effect of different condensing cover material on daily yield is shown in Fig. 10. It is observed that the yield is maximum in the case of copper condensing cover due to fast release of heat available to it. It is due to the high value of thermal conductivity of copper, which gains
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V. Dimri et al. / Desalination 227 (2008) 178–189
higher overall heat loss coefficient [Uwo of Eq. (2b)]. In case of PVC, the daily yield is decreased due to reduction in top loss coefficient (Uwo). This attribute is due to the low thermal conductivity of PVC condensing material. These results are in accordance with results reported earlier by various scientists. This strongly justifies using glass as a condensing cover for use of solar energy with cost effectiveness of the system. 6. Conclusions The present study indicates the importance of the active distillation at lower water depth. Inner glass temperature plays a key role to determine the yield. The daily yield is more for active distillation as compared to passive mode using inner glass temperature. Yield is also directly related to thermal conductivity of condensing cover materials; copper gives a greater yield compared to glass and plastic due to higher thermal conductivity. 7. Symbols A Ac Aw C
— — — —
Cf
—
Cw
—
e
—
FN FR g Gr hb
— — — — —
Surface area, m2 Area of collector, m2 Area of water surface, m2 Constant in Nusselt number expression Specific heat of working fluid, J/kgEC Specific heat of water in solar still, J/kgEC Root mean square of percent deviation Collector efficiency factor Heat removal factor Acceleration due to gravity, m/s2 Grashof number Overall heat transfer coefficient from basin liner to ambient air through bottom and side insulation, W/m2 EC)
h1g
—
h1w
—
hcw
—
hew
—
hrw
—
hw
—
Ieff K1
— —
Kg /Kc / — Kp L — — L1 Lg /Lc / — Lp
Mw n
— — — — —
N Pgi
— —
Pr Pw
— —
r t T Ti
— — — —
m ˙ m ˙ ew
ew M
Convective and radiative heat transfer coefficient from glass cover to ambient, W/m2 EC Total heat transfer coefficients from water surface to glass cover, W/m2EC Convective heat transfer coefficient from water surface to glass, W/m2EC Evaporative heat transfer coefficient from water surface to glass, W/m2EC Radiative heat transfer coefficient from water surface to glass, W/m2EC Convective heat transfer coefficient from basin liner to water, W/m2EC Effective solar intensity, W/m2 Thermal conductivity of insulation material, W/mEC Thermal conductivity of glass, copper and PVC, W/mEC Latent heat of vaporization, J/kg Thickness of insulation material, m Thickness of glass, copper and PVC, m Flow rate of pump, L/s Hourly output of still, kg/m2 h Daily output of still, kg/m2 h Mass of water in basin, kg Constant in Nusselt number expression Number of observations Partial vapor pressure at inner glass temperature, N/m2 Prandtl number Partial vapour pressure at water temperature, N/m2 Coefficient of correlation Time, s Temperature, EC Average of water and inner glass temperature, EC
V. Dimri et al. / Desalination 227 (2008) 178–189
Tb Tgi Tgo Ub
— — — —
ULC
—
Ut
—
v Xi Yi
— — —
Temperature of basin water, EC Inner glass temperature, EC Outer glass temperature, EC Overall bottom heat loss coefficient, W/m2EC Overall heat transfer coefficient for collector, W/m2EC Overall top loss coefficient from water surface to ambient air, W/m2EC Wind velocity, m/s Theoretical or predicted value Experimental value
Greek Α αN (ατ)
— — —
β ΔT γ μ σ
— — — — —
Absorptivity Fraction of energy absorbed Effective absorptance-transmittance product Expansion factor, K!1 Temperature difference, EC Relative humidity Viscosity of humid air, N.s/m2 Stefan Boltzman constant
Subscripts a b c eff g s w
— — — — — — —
Ambient Basin liner Collector Effective Glass cover Solar still Water
References [1] M.A.S. Malik, G.N. Tiwari, A. Kumar and M.S. Sodha, Solar Distillation, Pergamon Press, Oxford, UK, 1982. [2] H.S Soliman, Solar still coupled with a solar water heater, Mosul University, Mosul, Iraq, 1976, p. 43. [3] T. Kiatsiriroat, P. Wibulswas and S.C. Bhattacharya, Performance analysis of multiple effect vertical solar still with flat plate solar collector. J. Solar Wind
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Technol., 4(4) (1987) 451. [4] G.M. Zaki, A. Al-Turki and M. AI-Fatani, Experimental investigation on concentrator assisted solar stills, J. Solar Energy, 11(1992) 193–199. [5] G.N. Tiwari, Recent Advances in Solar Distillation, Wiley Eastern, New Delhi, India, 1992, Chap. 2. [6] R. Tripathi and G.N. Tiwari, Effect of water depth on internal heat and mass transfer for active solar distillation, Desalination, 173 (2005) 187–200. [7] G.N. Tiwari, S.K. Shukla and I.P. Singh, Computer modeling of passive/active solar stills by using inner glass temperature, Desalination, 154 (2003) 171. [8] G.N. Tiwari, H.N. Singh and R. Tripathi, Present status of solar distillation, Solar Energy, 75(5) (2003) 367–373. [9] M. Kobayashi, A method of obtaining water in arid land, Solar Energy, 7(3) (1963) 93. [10] A.A. Delyannis, Solar stills provide an islands’s inhabitants with water, Sun at Work, 10(1) (1965) 6. [11] G.O.G. Lof, Solar desalination, in: Principle of Desalination, K.S. Spiegler, ed., Academic Press, New York, 1966, Chap. 5. [12] B.W. Tlemat and E.D. Howe, Comparison of plastic and glass condensing covers for solar distillers. Proc. Solar Energy Society, Annual Conference, Arizona, 1967, pp. 1–12. [13] E.Zh. Norov, B.M. Achilov and T.D. Zhuraev, Results of tests on solar film-covered stills, Geliotekhnika, 11(3/4) (1975) 130. [14] G.Ya. Umarov, M.K. Asamov, B.M. Achilov, T.K. Sarros, E.Zh. Norov and N.A. Tsagaraeva, Modified polyethylene films for solar stills, Geliotekhnika, 12(2) (1976) 29. [15] J. Ahmadzadeh, Solar earth water stills, Solar Energy, 20(5) (1978) 387. [16] G.N. Tiwari, Solar Energy: Fundamentals, Design, Modeling and Applications, Narosa, New Delhi, and CRC, New York, 2002. [17] S.C. Chapra and R.P. Canale, Numerical Methods for Engineers, McGraw-Hill, New York, 1989. [18] R.V. Dunkle, Solar water distillation; the roof type still and a multiple effect diffusion still, Internat. Developments in Heat Transfer, ASME Proc., International Heat Transfer, Part V, University of Colorado, 1961, p. 895. [19] H.N. Singh, Estimation of beam and diffuse radiation for Indian climatic conditions and its application for distillation, Ph.D. Thesis, India Institute of Technology, Delhi, 2004. [20] P.I. Cooper, Digital simulation of transient solar still process, Solar Energy, 12 (1969) 313.