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Eﬀect of wind speed on active and passive solar stills A.A. El-Sebaii

*

Department of Physics, Faculty of Science, Tanta University, Tanta, Egypt Received 13 January 2003; received in revised form 28 June 2003; accepted 27 September 2003

Abstract The eﬀect of wind speed V on the daily productivity Pd of some active and passive solar stills is studied by computer simulation. Numerical calculations have been carried out on typical summer and winter days in Tanta in order to correlate Pd with V for diﬀerent masses of basin water mw for the passive stills and various thicknesses dw or mass ﬂow rates m_ w of the ﬂowing brine for the active stills. It is found that for the active and multi-eﬀect passive stills, Pd increases with the increase of V up to a typical velocity Vt beyond which the increase in Pd becomes insigniﬁcant. However, for all the investigated single eﬀect passive stills, there is a critical mass (depth) of basin water beyond which Pd increases as V increases until Vt . For basin water masses less than the critical mass, Pd is found to decrease with increasing V until Vt . After Vt , the change in Pd is unimportant in a similar behavior to that obtained for the active and multi-eﬀect passive stills. The critical mass (depth) of basin water for the investigated single eﬀect passive stills is found to be 45 kg (4.5 cm). Moreover, the typical velocity Vt is independent on the still shape and the mode of operation (active or passive) but it shows some seasonal dependence. For the investigated stills, Vt is found to be 10 and 8 m/s on typical summer and winter days, respectively. Comparisons with the results reported in the previous studies about the eﬀect of wind speed on productivity have been carried out. 2003 Elsevier Ltd. All rights reserved. Keywords: Passive solar stills; Active solar stills; Wind speed; Productivity

1. Introduction One major problem for the whole world and, in particular, in the third world is the availability of pure clean and healthy water especially in remote areas. Desalination systems using solar energy have been used in many countries to produce fresh water. The working of solar distillation

*

Fax: +20-40-3350804. E-mail address: [email protected] (A.A. El-Sebaii).

0196-8904/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.09.036

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Nomenclature A c dw , m_ w Gr k Ls Le , Lw m Ph Pd Pr r s Sc T x a e r q u w s l Dt

surface area (m2 ) speciﬁc heat of water (J/kg K) thickness (m) and mass ﬂow rate (kg/s) of ﬂowing water for the VS Grashof number thermal conductivity (W/m K) length of the VS (m) gap spacing between the absorber plate and the glass cover of the east and west channels of the VS (m) mass of basin water (kg) hourly productivity (kg/m2 h) daily productivity (kg/m2 day) Prandtl number width of the glass cover (m) height of the mirror (m) Schmidt number temperature (K) glass cover thickness (m) absorbitivity emissivity Stefan–BoltizmannÕs constant (W/m2 K4 ) mirror reﬂectivity glass cover tilt angle (degree) angle between mirror and glass cover (degree) transmissivity dynamic viscosity (kg/m s) a selected time interval (s)

Subscripts 1, 2, 3 lower, middle and upper basins for the SSTBS g glass l, u lower and upper basins of the SSDBS m mirror p absorber plate w water, west

units has been broadly classiﬁed into active and passive modes of operation. It is reported that the overall thermal eﬃciency of a passive distiller is higher than of an active one due to the lower operating temperature range [1]. Several researchers [2–8] have investigated the eﬀects of climatic, operational and design parameters on the performance of single, double and multi-eﬀect active and passive solar stills. It has been concluded that the productivity of the solar stills increases with

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the increase of solar radiation and ambient temperature [9,10]. However, it should be pointed out that there are conﬂicting results about the eﬀect of wind speed on solar still productivity. Garg and Mann [9], Cooper [11], Rajvanshi [12], Soliman [13] and Malik and Tran [14] have concluded that the increase in wind speed causes an increase in productivity; while Eibling et al. [10], Hollands [15] and Yeh and Chen [16,17] indicated that an increase in wind speed causes a decreases in productivity. It has also been reported by Morse and Read [18] that the wind speed has no signiﬁcant eﬀect on productivity. In our previous study, it has been found that the daily productivity of some designs of single and double basin solar stills [19] as well as for a vertical solar still [20] increases with the increase of wind speed V up to a typical value of V which is assigned as Vt . The value of Vt is independent on the still shape and the heat capacity of brine but it shows some seasonal dependence. Empirical correlations have been proposed for the daily productivity Pd with V for diﬀerent masses of basin water up to 200 kg. To generalize the results which have been achieved in our previous work [19] for various designs of solar stills under diﬀerent modes of operations and heat capacity of brine, comprehensive studies have been carried out by computer simulation for diﬀerent designs of active and passive solar stills. Numerical calculations have been performed for typical summer and winter days in Tanta (Lat. 30470 N) with a wide (nominal) range of wind speed from 0 to 30 m/s for diﬀerent masses (passive stills) or diﬀerent thicknesses and mass ﬂow rates (active stills) of basin water. It has been found that for the active and multi-eﬀect passive solar stills, the daily productivity increases with the increase of V up to the typical velocity Vt for any depth or mass ﬂow rate of basin water. However, for the single eﬀect passive stills, there is a critical mass (depth) of basin water beyond which the productivity increases with the increase of V up to Vt and this behavior is reversed (the productivity decreases as V increases) for basin water depths less than the critical mass (depth). Furthermore, the decrease or the increase in Pd occurs up to the same value of V , Vt , beyond which the productivity becomes almost independent on V . The value of Vt is independent on the still shape, mode of operation and the heat capacity of brine but it shows some seasonal dependence.

2. The investigated stills and numerical calculations Diﬀerent designs of active and passive solar stills have been selected for the present study. The passive systems include, single slope single basin (SSSBS), double slope single basin with (DSSBSMR) and without (DSSBS) outer mirrors, single slope double basin (SSDBS) and single slope triple basin (SSTBS) solar stills. The single slope single basin still with water ﬂowing in the basin (SSSBSA) and the vertical solar (VS) still are choosen as examples for the active solar stills. Fig. 1 shows schematic diagrams of the stills under study. The evaporating surfaces of the stills are assumed to have an area of 1 m2 . The glass covers of basin type solar stills make inclination angles of 10 with respect to the horizontal. The single slope single and multi-eﬀect stills are orientated to face south while the DSSBS, DSSBSMR and VS are oriented to face east–west in order to receive most of the incident solar radiation. Detailed description, thermal analysis and methods of analytical solutions of the energy balance equations for the single and double slope single eﬀect stills can be found in Refs. [21,22]. However, the double slope single eﬀect still with (DSSBSMR) and without (DSSBS) outer mirrors have been presented in Ref. [19]. Also, detailed analysis of the

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Fig. 1. Schematic of the solar stills under study: (a) SSSBS; (b) DSSBSMR; (c) SSDBS; (d) VS; (e) SSTBS and (f) SSSBSA.

VS, SSDBS and SSTBS has been studied in Refs. [20,23,24], respectively. The design and operational parameters of the investigated stills are given as follow:

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Common parameters sg ¼ 0:9;

eg ¼ 0:88;

Ap ¼ 1 m2 ;

ag ¼ 0:05;

ap ¼ 0:9;

ew ¼ 0:95;

xg ¼ 0:003 m;

kg ¼ 0:78 ðW=m KÞ;

cw ¼ 4190 ðJ=kg KÞ

Ag ¼ 1:015 m2 ;

and u ¼ 10

DSSBSMR and DSSBS W ¼ 100 ðsummerÞ;

W ¼ 50 ðwinterÞ;

Am ¼ Ag ¼ 1:0154 m2 ;

qm ¼ 0:85 and

s ¼ r ¼ 0:508 m VS and SSSBSA Lw ¼ Le ¼ 0:10 m;

sw ¼ 0:95; dw ¼ 0:005–0:05 m and

m_ w ¼ 1:0 103 –2:0 102 kg=s SSDBS and SSTBS mwu ¼ 25 kg;

mwl ¼ 10–200 kg;

mw2 ¼ mw3 ¼ 25 kg

and mw1 ¼ 10–200 kg

Heat transfer inside the solar stills takes occur by convection, radiation and evaporation from the water surface to the inner surface of the still cover. The heat is then transferred by conduction through the thickness of the still cover. For horizontal solar stills, the various internal heat transfer coeﬃcients are calculated using Dunkle correlations [25]. However, Dunkle correlations are not valid for vertical channels. Therefore, for the VS, the internal heat transfer coeﬃcients are calculated using the modiﬁed SpaldingÕs theory [26,27]. Further, heat transfer from a still cover to the environment occurs by radiation to the sky and by convection, due to wind, to ambient air. The correlations which are used for calculating the internal and external heat transfer coeﬃcients are given in the Appendix A. The wind heat transfer coeﬃcient hw is calculated using the following Wattmuf et al. correlation [28] hw ¼ 2:8 þ 3V

for V 6 5 m=s

¼ 6:15V 0:8

for V > 5 m=s

ð1Þ

Numerical calculations have been performed with the aid of the computer programs that are developed for the solution of the energy balance equations for the selected stills. The input parameters to these programs are climatic, design and operational parameters. The proposed theoretical models for the investigated stills have been validated experimentally in previous work [20–24]. Fig. 2 shows the diurnal variations of solar intensities and ambient temperatures on typical summer (5 June) and winter (26 December) days which are employed for calculating the total solar radiation incident on the covers of the various stills and the mirrors of the DSSBSMR. These calculations are made using another computer program developed by the author using the Liu and Jordan correlations for the total solar radiation incident on a tilted surface [29]. The hourly productivity Ph of the still is calculated using the following equation: Ph ¼ hewg ðTw Tg Þ

3600 L

ð2Þ

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Fig. 2. Diurnal variations of solar intensities and ambient temperatures on typical summer and winter days.

where hewg is the evaporative heat transfer coeﬃcient, L is the latent heat of vaporization of water and Tw and Tg are the water and glass cover temperatures. The daily productivity Pd is calculated from X Pd ¼ Ph ð3Þ In an attempt to correlate the daily productivity with the wind speed for diﬀerent heat capacities of the brine, numerical calculations have been carried out for diﬀerent masses (depths) of basin water mw from 10 to 200 kg (1–20 cm) for the passive stills and diﬀerent mass ﬂow rates m_ w in the range 1 · 103 to 2 · 102 kg/s or diﬀerent thicknesses dw of the ﬂowing water changing from 0.5 to 5 cm for the active stills. For double and triple eﬀect stills, calculations are made for diﬀerent masses of the lower basin water keeping the mass of water in the second and third eﬀects constant at 25 kg.

3. Results and discussions Numerical calculations are performed for the stills under study using the same climatic conditions of typical summer and winter days. Here, we will present some examples of the obtained results. 3.1. Passive stills Fig. 3 shows variations of the daily productivity Pd with wind speed V for the SSSBS when the mass of basin water mw equals 10, 20, 30, 40, 45, 50, 75 and 100 kg on a winter day. From the results of Fig. 3 it is clear that Pd decreases as V increases when mw equals 10, 20, 30 and 40 kg up to a typical value of V beyond which the decrease in Pd with increasing V becomes insigniﬁcant.

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Fig. 3. Variations of daily productivity ðPd Þ of the SSSBS with wind speed ðV Þ for diﬀerent masses of basin water ðmw Þ on a winter day.

For the value of mw equals 45 kg, it is obvious that Pd is almost less dependent on V . When mw becomes higher than 45 kg, Pd is seen to increase with increasing V up to a typical value of V (8 m/ s) which we assigned it as Vt . Pd is found to decrease by 18.4%, 14.1%, 10.2% and 6.6% on increasing V from 0 to Vt when mw ¼ 10, 20, 30 and 40 kg, respectively. However, Pd is decreased by 3.5%, 3.4%, 3.1% and 2.8% on increasing V from Vt to 30 m/s. On a summer day, the corresponding percentage values of the decrease in Pd are obtained as 14.5%, 12.4%, 9.7% and 6.5%, respectively, on increasing V from 0 to Vt . Beyond Vt , the average percentage decrease in Pd is about 3%. Tiwari and Suneja [30] have indicated that wind velocity above a particular value has not much eﬀect on the productivity. On the other hand, when mw ¼ 100 kg (for example) on a summer day, Pd is found to increase by 13.4% on increasing V from 0 to Vt . From Vt to 30 m/s, the increase in Pd was only 1.6%. Similar results have been obtained on typical summer and winter days for the other investigated single eﬀect passive stills; viz. the DSSBS and DSSBSMR. For the DSSBSMR on a winter day, Pd is decreased by 17.8%, 14.1%, 10.3% and 6.7% for wind velocities from 0 to Vt when mw ¼ 10, 20, 30 and 40 kg, respectively. Pd is found to decrease by 1.1%, 0.9%, 0.78% and 0.64% on increasing V from Vt to 30 m/s. For the same still when mw ¼ 100 kg, Pd is increased by 12.9% with increasing V from 0 to Vt . After Vt , the increase was only 1.1%. Therefore, it may be concluded that there is a critical mass (depth) of basin water of the passive single eﬀect basin type solar stills beyond which Pd increases as V increases up to Vt . But, when the mass (depth) of basin water becomes less than the critical mass, Pd decreases as V increases until Vt . For the present single eﬀect passive stills, the critical mass (depth) of basin water is found to be 45 kg (4.5 cm) as is shown in Fig. 3. These results can be explained in terms of the basin water Tw and glass Tg temperatures as well as their temperature diﬀerences ðTw Tg Þ. Hourly variations of basin water Tw and glass Tg temperatures for the SSSBS when mw ¼ 20 kg (as an example) and V ¼ 0, 3,

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5, 8, 10, 12, 15 and 20 m/s on a summer day are presented in Fig. 4. From this ﬁgure, it is obvious that Tg decreases as V increases because the heat is removed more rapidly from the still cover by convection. This lowers the cover temperature that should increase the rate of heat transfer from the basin water to the cover. The water temperature Tw is thereby decreases as V increases. The temperature diﬀerence between the water and glass ðTw Tg Þ for diﬀerent values of V on a summer day is depicted in Fig. 5. It is seen that ðTw Tg Þ increases as V increases during the period from mid-day until sunset; hence, the daylight productivity increases as V increases [19]. It is also seen from the results of Fig. 5 that after sunset, ðTw Tg Þ dramatically decreases due to the increased heat losses due to wind. Therefore, the productivity decrease as V increases during the night. The decrease in productivity during night is considerably greater than the increase during daylight; thus, Pd decreases as V increases for water depths less than the critical depth. However, for basin water depths higher than the critical depth, the temperature diﬀerence ðTw Tg Þ shows a little decrease with increasing V owing to the storage eﬀect of the large basin water depth (see Fig. 7 in Ref. [19]); consequently, Pd increases as V increases. It is also obvious from the results of Figs. 4 and 5 that Tw , Tg and ðTw Tg Þ becomes less dependent on V for values of V higher than Vt (10 m/s). Thus, the increase or the decrease in Pd becomes insigniﬁcant after Vt . With increasing V from 0 to Vt on a summer day, the daily productivity Pd of the DSSBS is found to decrease by 14.5%, 12.5%, 9.8% and 6.6%, respectively, when mw equal 10, 20, 30 and 40 kg. For the values of mw greater than the critical mass (45 kg), Pd of the same system is found to increase by 3.4%, 5.9%, 13.4%, 19.2%, 23.4%, 26.4% and 28.4% when mw equal 50, 75, 100, 125, 150, 175 and 200 kg with increasing V from 0 to Vt . After Vt , Pd is found to change only by about 2.5–3.5%. The latter results also indicate the increasing eﬀect of wind at higher values of mw . Fig. 6 summarizes the variation of Pd with V for the triple basin still (SSTBS) for diﬀerent masses of the lower basin water mw1 when the mass of water in both the middle mw2 and upper mw3 basins

Fig. 4. Hourly variations of basin water ðTw Þ and glass cover ðTg Þ temperatures with wind speed ðV Þ for the SSSBS on a summer day. Curves from up to down for V ¼ 0, 3, 5, 8, 10, 12, 15 and 20 m/s.

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Fig. 5. Water–glass temperature diﬀerence ðTw Tg Þ as a function of time for the SSSBS for various wind speed ðV Þ when mw ¼ 20 kg on a summer day.

Fig. 6. Variations of Pd of the SSTBS with V for diﬀerent masses of the lower basin water ðmw1 Þ on a summer day.

equal 25 kg on a summer day. It is clear from the results of Fig. 6 that Pd increases as V increases up to a typical value of V (10 m/s) for all values of mw1 from 10 to 200 kg. The critical mass (depth) of basin water is not observed for the passive SSTBS as in the case of the passive SSSBS and the productivity increases as V increases for all depths of basins water. It is also seen from the results of

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Fig. 6 that the value of Vt (10 m/s) is independent on the heat capacity of basin water. On a summer day, Pd is found to increase by 13.2%, 15%, 16.4%, 18.1% and 20.6% on increasing V from 0 to Vt (10 m/s) when mw1 ¼ 10, 30, 50, 100 and 150 kg, respectively. From Vt to 30 m/s, Pd is increased by 0.7%, 1.4%, 1.7%, 2.9% and 3.3% for the same values of mw1 . Numerical calculations indicated that, although the temperatures of water and glass covers of the three eﬀects of the SSTBS decrease, the water glass temperature diﬀerences ðTw Tg Þ for the three eﬀects are found to increase as V increases until the value of Vt (10 m/s), especially during the period from noon until the early morning of the next day, as shown in Fig. 7 for the middle (Fig. 7a) and upper (Fig. 7b) basins on a summer day. The increase in ðTw Tg Þ becomes insigniﬁcant after Vt . Therefore, the daily productivity is increased with increasing V due to the increased water-glass temperature diﬀerence more than for the fall in both temperatures. Comparing Figs. 5 and 7 we observe that ðTw Tg Þ increases as V increases even during the night in the case of the SSTBS; hence, the critical depth of basin water does not observed for the multi-eﬀect stills compared to the single eﬀect stills and the productivity increases for all depths of basin water. Furthermore, the increase in productivity of the SSTBS with increasing V is found mainly due to the increased daily productivities of both the middle and upper basins. For example, when mw1 ¼ mw2 ¼ mw3 ¼ 25 kg, the daily productivities of the lower, middle and upper basins are found to increase by 9.7%, 17.4% and 15%, respectively, with increasing V from 0 to Vt on a summer day. It is worth mentioning here that, similar behavior of Pd vs. V has been obtained for the double eﬀect still (SSDBS) [19]. 3.2. Active stills The systems that are selected as examples of the active solar stills are the SSSBSA and VS. Fig. 8 explains variations of Pd of the SSSBSA with V for diﬀerent mass ﬂow rates m_ w of basin water

Fig. 7. ðTw Tg Þ as a function of time for the middle (a) and upper (b) basins of the SSTBS for diﬀerent values of V on a summer day. Curves from down to up for V ¼ 0, 3, 5, 8, 10, 12, 15 and 20 m/s.

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Fig. 8. Variations of Pd of the SSSBSA with V for diﬀerent mass ﬂow rates ðm_ w Þ of basin water when dw ¼ 0:015 m on a summer day.

when the thickness of the ﬂowing water dw ¼ 0:015 m on a summer day. Of course, with increasing the mass ﬂow rate of the ﬂowing brine, the residence time of the brine in the still decreases. This eﬀect has been taken into consideration in the thermal analysis of the active stills (see for example Eq. (5) in Ref. [20]). It is seen from the results of Fig. 8 that Pd increases as V increases up to the typical velocity Vt (10 m/s). Values of the percentage increase in Pd on a summer day are obtained as 30.5%, 37.8%, 39.9% and 40.6% on increasing V from 0 to Vt when m_ w ¼ 0:001, 0.002, 0.003 and 0.004 kg/s. Pd is increased only by 2.3%, 3.1%, 4.2% and 4.8% on increasing V from Vt to 30 m/ s. Similar trends of Pd vs. V have been obtained for diﬀerent values of dw at a constant mass ﬂow rate. On a winter day, Pd is increased by 29.3%, 39.3% and 42.2% with increasing V from 0 to Vt when dw ¼ 0:5, 1.0 and 1.5 cm and m_ w is kept constant at 0.005 kg/s. Pd is found to increase only by 1.5%, 2.5% and 3.4% on increasing V from Vt to 30 m/s. Figs. 9 and 10 represent the diurnal variations of the water Tw and glass Tg temperatures, Fig. 9, as well as their temperature diﬀerences ðTw Tg Þ, Fig. 10, for diﬀerent values of V when dw ¼ 0:02 m and m_ w ¼ 0:005 kg/s. From the results of Fig. 9 it is clear that as V increases Tw and Tg decrease due to the same reasons described earlier for the passive SSSBS. However, ðTw Tg Þ increases with an increase of V until Vt . After Vt , ðTw Tg Þ becomes less dependent on V ; hence the increase in productivity is insigniﬁcant may be because at higher velocities, the limitation on heat transfer is imposed by conductance of the glass and not by the external heat transfer coeﬃcient. The same conclusion was drawn by Rajvanshi [12]. Similar trends have been obtained for the variation of Pd with V for the VS on typical summer and winter days [19]. Thus, it can be concluded that the productivity of the active solar stills increases with increasing wind velocity up to Vt for all thicknesses and/or mass ﬂow rates of the ﬂowing water. The critical heat capacity of brine of the active systems does not exist probably because their overnight productivities equal zero. From the results which have been achieved in

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Fig. 9. Hourly variations of basin water ðTw Þ and glass cover ðTg Þ temperatures with wind speed ðV Þ for the SSSBSA when m_ w ¼ 0:005 kg/s and dw ¼ 0:02 m on a summer day. Curves from up to down for V ¼ 0, 3, 5, 8, 10, 12, 15 and 20 m/s.

Fig. 10. Hourly variations of ðTw Tg Þ for the SSSBSA for diﬀerent values of V on a summer day.

Sections 3.1 and 3.2 it can be concluded that for all investigated solar stills, the values of Vt equal 8 and 10 m/s for the winter and summer seasons, respectively. The values of Vt are independent on the still shape and the heat capacity of basin water.

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3.3. Correlations of Pd with V In order to correlate Pd of the investigated stills with V for various heat capacities of basin water, the Pd may be expressed as: For passive stills Pd ¼ ambw V c

ð4Þ

For active stills Pd ¼ adwb V c ;

m_ w ¼ const

ð5aÞ

Pd ¼ am_ bw V c ;

dw ¼ const

ð5bÞ

or

where a, b and c are constants to be determined from the numerical results using the method of least square. Detailed description of the steps of determination of the constants a, b and c can be found elsewhere [19]. Figs. 11–13 give three examples of the obtained correlations for the passive SSSBS for basin water depth less than the critical depth, active SSSBSA and the SSTBS, respectively, on a summer day. Table 1 summarizes the obtained values of the constants a, b and c and the proposed correlations for Pd with V , mw and dw or m_ w on typical summer and winter days. These correlations are valid for 0 < mw1 6 200 kg for the SSDBS and the SSTBS. For the single eﬀect passive stills (SSSBS, DSSBS and DSSBSMR), the correlations are valid for 0 < mw 6 45 kg (critical mass of basin water). For active stills (SSSBSA and VS), the correlations are valid for 0 < dw 6 0:05 m and 0 < m_ w 6 2 102 kg/s. The correlations which are obtained for the VS as well as for the SSDBS and the single eﬀect passive stills for water masses greater than the critical mass have been present in our previous work [19]; therefore they are not given in this paper to prevent repetition. The correlations are obtained by least square curve ﬁtting. The accuracy of the ﬁtting is

Fig. 11. Proposed correlations for Pd with V (a) and mw (b) for the SSSBS on a summer day.

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Fig. 12. Proposed correlations for Pd with V (a) and dw (b) for the SSSBSA when m_ w ¼ 0:005 kg/s on a summer day.

Fig. 13. Proposed correlations for Pd with V (a) and mw1 (b) for the SSTBS on a summer day.

indicated by the regression coeﬃcients (RC) whose values are higher than 0.96 (see Table 1) which indicate excellent ﬁtting. From the results of Table 1 it is seen that for all stills under study, the values of the constant a during the summer are higher than those during the winter due to the increased solar intensity and ambient temperature and, thus, a higher productivity. Also, the constant b has negative values, which indicate decreasing of the still productivity with the increase of the heat capacity of brine as is expected. It is found also that Pd is inversely proportional to V to the power 0.04 for the investigated single eﬀect passive still when the mass of basin water less than the critical mass (45 kg or 4.5 cm). However, Pd is directly proportional to V to the power 0.05 for basin water masses

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Table 1 Proposed correlations for the investigated solar stills System

Season

a

b

c

Correlation

RC

SSSBS

Summer Winter

8.87 4.73

)0.037 )0.078

)0.045 )0.049

Pd ¼ Pd ¼

DSSBS

Summer Winter

8.97 3.67

)0.036 )0.085

)0.046 )0.041

Pd ¼ 8:97m0:036 V 0:046 w 0:085 0:041 Pd ¼ 3:67mw V

0.966 0.968

DSSBSMR

Summer Winter

10.91 5.25

)0.033 )0.080

)0.049 )0.048

Pd ¼ 10:91m0:033 V 0:049 w 0:080 0:048 Pd ¼ 5:25mw V

0.968 0.982

SSTBS mw2 ¼ mw3 ¼ 25 kg

Summer Winter

93.58 30.78

)0.573 )0.532

0.044 0.012

Pd ¼ 93:58m0:573 V 0:044 w1 0:532 0:012 Pd ¼ 30:38mw1 V

0.980 0.980

SSSBSA dw ¼ 0:015 m

Summer Winter

5.81 2.97

)0.283 )0.347

0.145 0.066

Pd ¼ 5:81m_ 0:283 V 0:145 w 0:347 0:066 Pd ¼ 2:97m_ w V

0.975 0.959

SSSBSA m_ w ¼ 0:005 kg/s

Summer Winter

11.02 4.48

)0.720 )0.799

0.134 0.056

Pd ¼ 11:02dw0:720 V 0:134 Pd ¼ 4:48dw0:799 V 0:056

0.980 0.990

8:87m0:037 V 0:045 w 0:078 0:049 4:73mw V

0.977 0.966

higher than the critical mass [19]. For the SSSBSA and SSTBS the obtained values of the constant c during the summer are higher than those during the winter indicating increasing eﬀect of wind during the summer. Similar trends have been obtained for the SSDBS and the VS [19]. 3.4. Comparison with previous work The results presented in the previous sections indicate that the daily productivities Pd of the multi-eﬀect stills, active stills and the single eﬀect passive stills (for the values of mw higher than the critical mass) are increase as V increases until Vt . These results are agree with those reported by Garg and Mann [9], Cooper [11], Rajvanshi [12] and Malik and Tran [14]. They have investigated a passive single eﬀect stills with basin water depths higher than the critical depth (4.5 cm). Soliman [13] has studied a single eﬀect still under forced convection conditions. He outlined that increasing wind speed will increase the productivity. Minasian and Al-Karaghouli [31] have reported an increase of productivity of a wick-type ﬂoating vertical solar still with an increase of wind speed. These results are agree with our results obtained for the active and vertical stills. A suggested decrease in productivity with increasing wind speed in Refs. [10,15,17,32,33] probably because the authors have studied single eﬀect passive stills with shallow water depths less than the critical depth (4.5 cm). It is seen that all conclusions given in the previous work clearly conﬁrm our ﬁndings about the eﬀect of wind speed on the daily productivity of various active and passive solar stills.

4. Conclusions On the basis of the results obtained for the various active and passive solar stills, the following conclusions may be drawn: (i) The daily productivities Pd of the active basin type, wick-type and vertical solar stills increase as wind speed increases up to the typical velocity Vt , possibly because

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their overnight productivities equal zero. Therefore, it is advisable to install such stills in windy places. (ii) The daily productivities Pd of the multi-eﬀect passive solar stills are found to increase with an increase of V until Vt may be because the upper basin protects the lower ones against heat losses due to wind especially during the night. (iii) For the passive single eﬀect basin type stills, it is found that there is a critical mass (depth) of basin water beyond which Pd increases as V increases up to Vt . For shallow depths less than the critical depth, Pd decreases as V increases until Vt . (iv) The value of the critical mass (depth) for the investigated single eﬀect passive stills is found to be 45 kg (4.5 cm). (v) After the typical velocity Vt , the change in Pd becomes insigniﬁcant. (vi) The value of Vt is independent on the still shape, mode of operation (active or passive) and the heat capacity of brine, but it shows some seasonal dependence. Vt is found to be 10 and 8 m/s on typical summer and winter days, respectively. (vii) The results which have been achieved in the present study may be used to explain the conﬂicting results which are reported in the previous studies [9–18,31–33] about the eﬀect of wind speed on the daily productivity of the solar stills. Appendix A A.1. Horizontal stills The following Dunkle correlations [25] are used for calculating the total internal heat transfer coeﬃcient ðh1 Þ h1 ¼ hrwg þ hcwg þ hewg

ðA:1Þ

hrwg ¼ 0:9rðTw2 þ Tg2 ÞðTw þ Tg Þ

ðA:2Þ

hcwg

1=3 ðPw Pg ÞTw ¼ 0:884 ðTw Tg Þ þ 2016 Pw 7

hewg ¼ 9:15 10

hcwg ðPw Pg ÞL Tw Tg

ðA:3Þ

ðA:4Þ

where hrwg , hcwg and hewg are the radiative, convective and evaporative heat transfer coeﬃcients between the water surface and the inner surface of the glass cover. Pw and Pg are the partial pressures of saturated vapor at the water and glass cover temperatures, respectively. L is the latent heat of vaporization of water. The conductive heat transfer coeﬃcient Ug through the thickness of the still cover is Ug ¼ kg =xg

ðA:5Þ

The total external heat transfer coeﬃcient h2 is given by h2 ¼ hrgs þ hw

ðA:6Þ

The radiative heat transfer coeﬃcient hrgs from the still cover to the sky is given by hrgs ¼ eg rðTg2 þ Ts2 ÞðTg þ Ts Þ where Ts is the sky temperature. hw is calculated using Eq. (1).

ðA:7Þ

A.A. El-Sebaii / Energy Conversion and Management 45 (2004) 1187–1204

1203

Hence, the overall heat transfer coeﬃcient Ut through the top of the still can be calculated using the following formula: Ut1 ¼ ðh1 Þ1 þ ðxg =kg Þ þ ðh2 Þ1

ðA:8Þ

A.2. Vertical still For the vertical still hewg is calculated, using the modiﬁed SpaldingÕs theory, [26,27] for the west channel of the still as follow: Ph;w ¼ gw lnð1 þ Bw Þ

ðA:9Þ

where Bw is the mass transfer driving force and gw is the mass transfer conductance calculated using the following correlation [26] gw Lw =ðl=ScÞ ¼ 0:271ðLs =Lw Þ0:21 ðGr ScÞ0:25

ðA:10Þ

Hence hewg ¼ Ph;w L=ðTw;w Tg;w ÞDt

ðA:11Þ

hcwg is calculated from the following correlation [34] hcwg ¼ 0:271ðkw =Lw ÞðLs =Lw Þ0:21 ðGr PrÞ0:25 ; 5 103 6 Gr Pr 6 1:2 106 ;

ðA:12Þ

hrwg is given by 2 2 hrwg ¼ rðTw;w þ Tg;w ÞðTw;w þ Tg;w Þ=½ð1=ew Þ þ ð1=eg Þ 1:

ðA:13Þ

The external and overall heat transfer coeﬃcients for the west channel can be calculated using Eqs. (A.6)–(A.8). The corresponding relations which are used for calculating the various heat transfer coeﬃcients for the east channel can be simply written on replacing the subscript ÔwÕ by ÔeÕ in Eqs. (A.9)–(A.13).

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