Evaluating thermal performance of a single slope solar still

Transcription

1 Heat Mass Transfer (27) 43: DOI.7/s ORIGINAL Evaluating thermal performance of a single slope solar still Omar O. Badran Æ Mazen M. Abu-Khader Received: 7 June 25 / Accepted: 25 July 26 / Published online: 6 September 26 Ó Springer-Verlag 26 Abstract The distillation is one of the important methods of getting clean water from brackish and sea water using the free energy supply from the sun. An experimental work is conducted on a single slope solar still. The thermal performance of the single slope solar still is examined and evaluated through implementing the following effective parameters: (a) different insulation thicknesses of, 2.5 and 5 cm; (b) water depth of 2 and 3.5 cm; (c) solar intensity; (d) Overall heat loss coefficient (e) effective absorbtivity and transmissivity; and (f) ambient, water and vapor temperatures. Different effective parameters should be taken into account to increase the still productivity. A mathematical model is presented and compared with experimental results. The model gives a good match with experimental values. List of symbols A s basin liner still area, (m 2 ) A ss side still area (m 2 ) a equation constant, Eqs. 27, 3 h cb basin liner convection heat transfer coefficient (W/m 2 K) O. O. Badran Department of Mechanical Engineering, FET, AL-Balqa Applied University, 58, Marka 34 Amman, Jordan M. M. Abu-Khader (&) Department of Chemical Engineering, FET, AL-Balqa Applied University, 58, Marka 34 Amman, Jordan MAK@accessme.com h b basin liner overall heat transfer coefficient (W/m 2 K) h cg glass cover convection heat transfer coefficient (W/m 2 K) h cw heat loss coefficient by convection from water surface (W/m 2 K) h ew heat loss coefficient by evaporation from water surface (W/m 2 K) h rb basin liner radiative heat transfer coefficient (W/m 2 K) h rg glass cover radiative heat transfer coefficient (W/m 2 K) h rw basin water radiative heat transfer coefficient (W/m 2 K) h tg total glass heat transfer loss coefficient (W/m 2 K) h w convective heat transfer coefficient from basin to water (W/m 2 K) h tw total water surface heat transfer loss coefficient (W/m 2 K) I solar intensity (W/m 2 ) k ins insulation thermal conductivity (W/m K) L ins insulation thickness (m) M total mass productivity/day (kg/day) (MC) w water heat capacity rate of water per unit area (J/m 2 K) P g glass saturated partial pressure (N/m 2 ) P w water saturated partial pressure (N/m 2 ) q g rate of total energy from the glass cover (W/m 2 ) q b rate of total energy from basin liner (W/m 2 ) q bg rate of energy lost from basin liner to the ground (W/m 2 ) q cg rate of energy lost from the glass cover by convective (W/m 2 )

2 986 Heat Mass Transfer (27) 43: q ew rate of energy lost from water surface by evaporation (W/m 2 ) q cw rate of energy lost from water surface by convection (W/m 2 ) q rg rate of energy lost from the glass cover by radiation (W/m 2 ) q rw rate of energy lost from water surface by radiation (W/m 2 ) q s rate of energy lost from the basin liner through the side of the still (W/m 2 ) Tw temperature of basin water (K) Tg in temperature of inside glass (K) Tg out temperature of outside glass (K) T a ambient temperature (K) T b basin liner temperature (K) T g still glass cover (K) T sky sky temperature (K) T v still vapor temperature (K) T w still water temperature (K) t time (s) U b overall bottom heat lost coefficient (W/m 2 K) U t overall top heat loss coefficient (W/m 2 K) U e overall side heat loss coefficient (W/m 2 K) U l overall heat loss coefficient (W/m 2 K) R t thermal resistance (m 2 K/W) V wind speed (m/s) h fg latent heat of vaporization (kj/kg K) Greek symbols a b absorbtivity fraction of energy absorbed by the basin liner a g absorbtivity fraction of energy absorbed by the glass cover a w absorbtivity fraction of energy absorbed by the water surface s transmissivity e g glass emissivity e w water emissivity e eff effective emissivity g i instantaneous efficiency g vol volumetric effeciency b collector tilt angle (deg) r Stephan Boltzman coefficient (W/m 2 k 4 ) D difference Subscript initial value out outlet in inlet Introduction The increase of population and human agricultural and industrial activities make the availability of fresh water in arid and semiarid regions a problem of great importance all over the world. The supply of drinkable water is an important problem for the developing countries. Most of these countries which are characterized by a high intensity of solar radiation make the direct use of solar energy a promising option for their arid communities to reduce the major operating cost for the distillation plant. Solar distillation is one of the available methods to produce potable water. This process has the advantage of zero fuel cost, but requires more space (for collection) [, 24, 3, 33, 34, 38]. The basic principles of solar water distillation are simple, yet effective, as distillation replicates the way nature purifies water. The sun s energy heats water to the point of evaporation. As the water evaporates, water vapor rises, condensing on the glass surface for collection. This process removes impurities such as salts and heavy metals, and destroys microbiological organisms. The end result is water cleaner than the purest rainwater. The use of solar energy is more economical than the use of fossil fuels in remote areas having low population densities, low rainfall and abundant available solar energy. The productivity of fresh water by solar distillation depends drastically on the intensity of solar radiation, the sunshine hours and the type of the still [4, 5, 23, 24, 27]. Single slope solar stills can be used for water desalination. Probably, they are considered one of the cheapest solutions for fresh water production. However, the amount of distilled water produced per unit area is somewhat low which makes the single-basin solar still unacceptable in some instances. To capture and condense evaporated fresh water, a cold surface (glass cover) is needed. Due to the slope in the glass for solar still, the condensate vapor will flow through the distillation channel then collected in the distillation vessel. 2 Solar stills: an overview An excellent review on the use of renewable energy in various types of desalination systems and a survey of the various types of solar thermal collectors and applications were presented by Kalogirou [2, 22]. Many experimental and theoretical works have been conducted on single basin solar stills for testing the

3 Heat Mass Transfer (27) 43: performance of different enhancement parameters. Different absorbing materials were used by Akash et al. [2], and Nijmeh et al. [29] to study their effect in a solar still, and thus enhance the productivity of water, using a single-basin solar still with double slopes. Akash et al. [3] examined the effect of using a solar still with various cover tilt angles of 5, 25, 35, 45 and 55, and the optimum tilt angle for water production was found to be 35. Also the authors studied the effect of the salinity of water on solar distillation, and concluded that the distilled water production decreased with salinity. Nafey et al. [27] investigated the main parameters affecting solar still performance using four different still design parameters operated under the same weather conditions. A general equation is developed to predict the daily productivity of a single sloped solar still. Whereas, Nafey et al. [28] studied experimentally the use of black rubber or black gravel materials within a single sloped solar still as a storage medium to improve the still productivity. Khalifa et al. [28] conducted an experimental study on new designs of basin type solar stills, and examined the effect of certain modifications on the productivity and efficiency. These modifications included preheating of feed water by means of a solar heater and utilizing external and internal condensers for vapor condensation as well as for feed water preheating. Boukar and Harmim [9, ] studied the effect of desert climatic conditions on the performance of a simple basin solar still and a similar one coupled to a flat plate solar collector. The performance of the simple still is compared with the coupled one. They found that the coupled still is more productive than the simple one. A comparative experimental study was conducted by Al-Karaghouli and Al-Naser [7, 8] between single basin and double decker having the same basin area. The authors concluded the following: () adding 2.5 cm of styrobore insulation material to the solar stills sides causes a noticeable increase in water production; and (2) the daily average still production for the doublebasin still is around 4% higher than the production of the single-basin still. Aboul-Enein et al. [] presented a simple transient mathematical model for a single basin still through an analytical solution of the energy-balance equations for different parts of the still. The authors also investigated the thermal performance of the still both experimentally and theoretically, and the influence of cover slope on the daily productivity of the still. This transient mathematical model was used by El-Sebaii [2] for a vertical solar still to conduct parametric investigation. He found that the daily productivity of the still increases with increase of the still length, width, and wind speed up to typical values. Furthermore, El-Sebaii [3, 4] examined the effect of wind speed on the daily productivity of different designs of single slope solar stills with single, double and triple basins using computer simulation. He found that daily production increases with the increase of wind speed up to a typical velocity beyond which the increase in production becomes insignificant. Most recent work by El-Sebaii [5] is the investigation of the thermal performance using a transient mathematical model of triple basins solar still. Hamdan et al. [9] preformed an experimental and theoretical work to find the performance of single, double and triple basins solar still. Whereas, Jubran et al. [2] developed a mathematical model to predict the productivity and the thermal characteristics of a multistage solar still with an expansion nozzle and heat recovery in each stage of the still. Al-Hinai et al. [5] reported the use of a mathematical model to predict the productivity of a simple solar still under different climatic, design and operational parameters in Oman. Furthermore, Al-Hinai et al. [6] developed two mathematical models to compare the productivity of single-effect and double-effect solar stills under different climatic, design and operational parameters. Mathioulakis et al. [25] suggested a simplified theoretical method for the evaluation of the performance of a typical solar still and the prediction of long-term water production. Moreover, Voropoulos et al. [4] preformed an evaluation for this simple method in three steps, the first being experimental determination of the coefficients and successive prediction of output, the second being calculation of coefficient values through analytical relations and the third being the use of the model in a continuous way. Thermal modeling and characterization of solar still were presented by Tiwari [34], Tiwari and Noor [35], Tiwari and Prasad [36], and Tiwari et al. [37]. A transient analysis of a double basin solar still was studied by Suneja and Tiwari [32]. They investigated the effect of water depth in the lower basin on the performance of the system. The authors observed that the daily yield of an inverted absorber double basin solar still increases with the increase of water depth in the lower basin for a given water mass in the upper basin. Tiwari et al. [39] derived expressions for water and glass temperatures, hourly yield and instantaneous efficiency for both passive and active solar distillation systems. Recently, Tripathi and Tiwari [4] analyzed the distribution of solar radiation, using the concept of solar fraction inside a conventional single slope solar still by

4 988 Heat Mass Transfer (27) 43: using simulation model for a given solar azimuth, altitude and latitude angles, and longitude of the place. Srivastava et al. [3] in their numerical computations showed that there is a significant effect in the plant, water temperatures and distilled output due to change in the fraction of the solar radiation incident on the north wall, depth of water, absorptivity of basin and the inclination of the roof whereas the heat capacity of the plant has a marginal effect on these temperatures and distilled output. Fath et al. [6] presented analytical, thermal and economic comparisons between pyramid and single slope solar stills. They found that the single slope gave higher daily yield (3%) in winter and 3% higher in summer; they attributed this due to the larger radiation losses from the cover surface of the pyramid. Goosen et al. [8] found that the theoretical analysis (i.e., modeling) of different solar desalination systems is an effective tool for predicting system performance. They found that the efficiency of single-basin solar stills is very low compared to the multi-effect solar desalination systems which reuse the latent heat of condensation. They concluded that the increase in efficiency, though, must be balanced against the increase in capital and operating costs compared to the single-basin still. From the above reviewed work on solar stills, it is clear that there is a need to address a comprehensive mathematical model for single slope solar still and all involved interactive parameters. Therefore, the main objectives of this present work are to investigate all modes of heat and mass transfer involved in the single solar still, and to evaluate the various parameters affecting both the efficiency and productivity of the still. Experimental work and validation of mathematical modeling are carried out and compared. 3 Theoretical analysis of a solar still The theoretical analyses were performed by energy balance on various components of the still with the help of MATLAB software. Figure illustrates various energy quantities in the still which have a direct effect on the output yield. To simplify the analysis, the following assumptions are made:. There is no vapor leakage in the still, and this is important to increase the productivity and efficiency. 2. There is no temperature gradient along the glass cover thickness and in water depth. Also the absorbed energy by the glass cover is negligible. 3. The level of water in the basin is maintained at constant level. 4. The condensation that occurs at the glass trough is a film-type. When conducting energy balance in terms of (W/m 2 ) for passive still, the following assumptions are taken into consideration:. An optimum Inclination of the glass cover 2. The heat capacity of the glass cover, the absorbing material and the Insulation (bottom and sides) are negligible. 3. The solar distiller unit is vapor-leakage-proof. The energy balances for each of the three main components are presented as follows: (a) The solar still glass cover: a g It ðþþðq rw þ q cw þ q ew Þ ¼ q rg þ q cg (b) The solar basin bottom plate (basin liner): A s a b It ðþ¼q b þ q bg þ q s (c) α g (Absorbed) α b A ss The solar still water mass: dt w a w It ðþþq b ¼ ðmcþ w dt 3. External heat transfer Rg (Reflected) q τ g (Transmitted) q rg q cg ðþ ð2þ þ ðq rw þ q cw þ q ew Þ ð3þ The external heat transfer is mainly governed by conduction, convection and radiation processes which are independent of each other. ew q cw Rw Fig. Energy flow through a single basin solar still q cb q rw q s

5 Heat Mass Transfer (27) 43: This process covers exchanges between the outside of the solar still and the surroundings, for example heat transfer from the glass to the ambient, the heat transfer from water in the basin to the ambient and the bottom and sides insulation. The following heat transfer coefficients are considered: 3.. I- top loss coefficient Due to the small thickness of the glass cover (4 mm), the temperature of the glass may be assumed to be uniform. The external radiation and convection losses from the glass cover to outside atmosphere can be expressed as q g ¼ q rg þ q cg where q rg ¼ h rg T g T a q cg ¼ h cg T g T a ð4þ ð5þ ð6þ The glass cover radiative heat transfer coefficient (h rg ) can be evaluated from the following equation: h rg ¼ e g r Tg 4 T4 sky ð7þ T g T a T sky ¼ T a 6 ð8þ by substituting q cg and q rg into Eq. 4, Eq. 9 can be formulated: q g ¼ h tg T g T a ð9þ where h tg is the convection and radiation heat transfer coefficient or in other words, it is the total glass heat transfer loss coefficient from glass to the ambient, and it is a function of the wind speed: h tg ¼ h rg þ h cg h tg ¼ 5:7 þ 3:8 V ðþ ðþ or side surface of the basin. Hence, the overall bottom loss coefficient (U b ) can be written as U b ¼ where h b ¼ h w þ L ins L ins k ins þ k ins þ ð2þ h rbþh cb h cb h rb ð3þ h rbþh cb h cb h rb The values of h cg + h rg can be obtained from Eq. 4 by substituting V = because there is no wind velocity at the bottom of the insulation. Similarly, the side heat loss coefficient (U e ) can be approximated as A ss U e ¼ U b A s ð4þ If the side still area (A ss ) is very small compared with (A s ), then (U e ) can be neglected [24]. 3.2 Internal heat transfer Heat transfer within the solar still is referred to as internal heat transfer which mainly consists of radiation, convection and evaporation that occurs between the water surface and glass cover [24]. These three modes of internal heat transfer are discussed as follows: 3.2. I- radiation loss coefficient It is known that radiation heat transfer occurs between any two bodies when there is a temperature difference between them, and considering the water surface and glass cover, the radiation between the water and the glass can be given by q rw ¼ h rw T w T g ¼ :96r T 4 w Tg 4 ð5þ where h rw can be obtained from: 3..2 II- bottom and sides loss coefficient Heat is also lost from the water in the basin to the ambient through the insulation and subsequently by convection, radiation and conduction from the bottom hh h rw ¼ e eff r ð T w Þ 2 i 2 i þ T g T w þ T g ð6þ The effective emittance between the water surface and the glass cover can be presented by

6 99 Heat Mass Transfer (27) 43: e eff ¼ ð7þ e w þ e g The values of the constants will be w =.96, g =.88 given in [26] II- convective loss coefficient Free convection occur across the humid air in the enclosure, due to the temperature difference between the water surface and the glass cover. The convective heat transfer rate can be obtained from the following equation [7, 24]: q cw ¼ h cw T w T g ð8þ where the convective heat loss coefficient h cw will be obtained from the following expression [34]: h cw ¼ :884 T w T g þ P = w P g ð Tw Þ 3 268:9 3 ð9þ P w where P w and P g are the vapor pressures at glass and water temperatures. They can be expressed by the following equations respectively: P g ¼ e 25:37544 Tg ð2aþ P w ¼ eð 25:37544 Tw Þ ð2bþ III- evaporation loss coefficient It is necessary for the evaporation loss coefficient to find out the evaporation pressure occurring inside the still and acting on the glass and the water surfaces. Due to condensation of the rising vapor on the glass cover, there is heat loss by evaporation between the water surface and the glass cover. This can be expressed by the following empirical equation [34]: q ew ¼ h ew T w T g ð2þ where h ew ¼ 6:273 3 P w P g h cw ð22þ T w T g Equations 8 and 2 are evaluated at initial water and glass temperatures. Then the total internal heat transfer coefficient between water surface and glass cover can be expressed as h tw ¼ h rw þ h cw þ h ew 3.3 Overall heat transfer ð23þ By substituting Eqs. 5, 6, 9, 8, 2 into Eqs., 2 and 3, the overall energy balance equations become: a g It ðþþh tw T w T g ¼ htg T g T a dt w a w It ðþþh w ðt b T w Þ ¼ ðmcþ w dt þ h tw T w T g ð24þ ð25þ a b It ðþ¼h w ðt b T w Þþ h b ðt b T a Þ ð26þ By substituting the values of T g and T b in Eqs. 24 and 26 into Eq. 25, then dt w dt þ at w ¼ fðþ t where a ¼ U l ðmcþ and fðþ¼ t ðas w Þ eff It ðþþu lt a ðmcþ w ð27þ (as) eff and U l can be represented by following equations: h w ðasþ eff ¼ a b þ a w þ a g h w þ h b U l ¼ U b þ U t where R t is equal to R t ¼ þ h tw h tg and h twh tg U t ¼ ¼ R t h tw þ h tg h tw h tw þ h tg ð28þ ð29þ ð29aþ ð29bþ In order to obtain an approximate analytical solution, the following assumptions have been made:. The time interval Dt ( < t < Dt) is small. 2. a is constant during the time interval Dt. 3. The side heat loss coefficient U e was neglected because of the use of rock wool insulator and the fixed side mirrors. 4. The function f (t) is constant, i.e. f ðtþ ¼ _ f ðtþ for the time Interval Dt.

7 Heat Mass Transfer (27) 43: By using the following boundary condition: At t =, T w(t=) = Tw and T g(t=) = Tg An approximate solution for T w can be obtained: T w ¼ f ðtþ a ð expðatþþþtw expðatþ ð3þ where Tw is the temperature of basin water and f ðtþ is the average value of f (t) for time interval Dt at a value of.2 [39]. The average glass temperature can be evaluated using the following equation: Table Technical specification of the solar still Specification Basin area (m 2 ) Glass area (m 2 ).46 Glass thickness (mm) 4 Number of glass Slope of glass 32 Dimensions T g ¼ a git ðþþh tw T w þ h tg T a ð3þ h tw þ h tg The instantaneous efficiency for passive solar still is h twh tg g i ¼ q ew It ðþ ¼ ðt w T a Þ ð32þ h tw þ h tg and by substituting Eq. 3 into Eq. 32, then h twh tg g i ¼ : h tw þ h tg U l " # ðtw T a Þ ðasþ eff ð exp ðatþþþu l exp ðatþ It ðþ ð33þ The glass window used is 4 mm thickness with an average transmissivity (s) of.88. whereas, the volumetric efficiency, which represents the productivity, can be found by the following equation: g vol ¼ h fg P M P As I ð34þ where (I) is the daily solar radiation, (M) is the total productivity of the day, (h fg ) is the latent heat of vaporization, (A s ) is the still area. 4 Experimental set-up The still was constructed from a large variety of local materials to reduce the overall cost and ease of construction. The solar still has side mirrors to enhance the productivity through the re-reflectivity of the rays on water surface and the incident solar radiation [4]. The still technical specifications are shown in Table, and Fig. 2 shows the geometrical dimension of the solar still used in the experiments. Fig. 2 Schematic diagram of the single slope solar still (dimensions are in cm) The basin liner is made of galvanized iron sheet of 9 cm 2 with maximum height of 5 cm, and.4 mm thickness. The galvanized basin was painted by red-lead primer then by matt-type black paint. There are certain specifications needed for the used glass cover in the still, and they are (a) Minimum amount of absorbed heat, (b) Minimum amount of reflection for solar radiation energy, (c) Maximum transmittance for solar radiation energy, and (d) high thermal resistance for heat loss from the basin to the ambient. Glass covers have been sealed with silicon rubber which plays an important role to promote efficient operation as it can accommodate the expansion and contraction between dissimilar materials. Rock wool of 5 cm thickness with thermal conductivity of.45 W/m K is used as an insulating material to reduce the heat losses from the bottom and the side walls of the solar still. A small feeding tank is installed in the system as a constant head tank which is used to control the level of water inside the still (maintain the water level in the basin constant along time) by a floating ball.

8 992 Heat Mass Transfer (27) 43: Measuring devices The measuring devices used in the system are as follows:. A Pyranometer is used to measure the solar radiation. This device measures the instantaneous intensity of radiation in (kw/m 2 ) with a range from to.2 kw/m Five thermocouples (type-k) coupled to digital thermometer with a range from to 99.9 C with ± C accuracy are used to measure the temperatures of the various components of the still system. 3. A digital anemometer is used to measure wind speed. 5 Discussion of results The solar still is operated from 8: am to 5: pm during the months of March and April 24. The measurements of the temperatures, solar radiation intensity, and the production of distilled water are taken hourly to study the effect of each parameter on the still productivity. Then the experimental results are compared with theoretical results to check the mathematical model predictions for validation purposes. In this study various operating conditions have been examined such as; different water depth, insulation thickness, ambient temperature, and solar intensity. The variables such as Tg in, Tg out, T a,t w, T b, T v, I, V and productivity were measured hourly. The total productivity and solar Intensity for each day were also measured. Also, different experimental tests were carried out at different ambient conditions. The wind speed is found to be around 2 4 m/s. Figure 3 shows the experimental results taken in st of April 24. It can be seen that an increase in the water temperature occurs until it reaches the maximum in the afternoon because the absorbed solar radiation exceed the losses to the ambient. From about 2 pm, water temperature decreases due to the losses from the solar still which becomes larger than the absorbed solar radiation. It can be noted that the basin temperature get closer to the water temperature because of the continuous contact between them which lead to heat equilibrium. Also, Fig. 3 shows that vapor temperature is the largest temperature in the solar still because at this temperature the particles have enough energy to evaporate. It can also be seen from Fig. 3 that the inner and outer glass temperatures have almost the same value, which means that the difference between them is very small DT = Tg in Tg out. Therefore, the assumption made earlier that the absorbed energy by the glass is negligible is valid. As the glass temperature is much smaller than the vapor temperature, it causes condensation of vapor on the glass. In the early hours of the morning (8 9 am), the glass temperature is higher than the water and vapor temperatures causing small productivity due to the small energy absorbed by the water at these times. Figure 4 illustrates the increase in the solar intensity in the early morning until it reaches the maximum at around 2 and 3 pm, then decreases in the late afternoon. The solar intensity has an important effect on the solar still productivity. This is shown clearly in Fig. 5. As the solar intensity increases, the productivity increases due to the increase in heat gain for water vaporization inside the still. The productivity rate varies as time passes from early morning until late afternoon. Figure 6 shows that the productivity increases until it reaches the maximum in the afternoon then decreases in the late afternoon. The water temperature can be taken as one of parameters that has a direct effect on the productivity. This is evident in Fig. 6, whereas the depth of water Temperatures (C) Local Standard Time (hr) Tg,in Tw Tv Ta Tg,out Solar Intensity (kw/m 2 ) Standard Local Time (hr) Fig. 3 Relationship among various temperatures and standard local time in st of April Fig. 4 Relationship between solar intensity and standard local time in st of April

9 Heat Mass Transfer (27) 43: Productivity (ml/m 2.hr) Solar Intensity (kw/m 2 ) Fig. 5 Relationship between solar intensity and productivity Productivity ( ml/m 2.hr ) Standard Local Time (hr) 3.5 cm depth 2 cm depth Fig. 6 Relationship between productivity and various water depths at standard local time increases from 2 to 3.5 cm, the daily still output decreases (inversely proportional). This decrease in the productivity of the still is due to the fact that as the depth increases the water will have higher heat capacity rate, which results in a lower temperatures of the basin and water, thus, lower evaporation rate. This is supported by previous researchers [9]. Figure 7 shows the variation of the overall heat loss coefficient through the standard local time using the theoretical model. The results show that there is a strong relationship between solar intensity (Fig. 4), ambient temperature (Fig. 3) and overall heat loss coefficient. As the solar intensity increases the overall heat loss coefficient increases (directly proportional). This is attributed to the high temperature of the solar still at higher solar intensities. This investigation proved the proportional dependency of the overall heat loss coefficient on the solar intensity. The solar still efficiency is considered as the most important parameter to be evaluated as can indicate the best still design. Figure 8 shows that the efficiency increases with time until reaching the maximum value in the afternoon. At the maximum, the incident solar radiation is larger than heat losses early in the afternoon. Then the heat losses starts overcoming the incident solar radiation (which decreases with time) thus the efficiency decreases in the late afternoon. It can be concluded that as the solar intensity increases, the heat loss decreases and the water and ambient temperature difference increases considerably due to the increase of the water temperature through conduction process between the black base and the water. As the ambient temperature increases, the efficiency increases as shown in Fig. 9. In the morning, the temperature of water is low; therefore it needs high energy to change its phase from saturated liquid to saturated vapor phase. The results show that temperature and required heat are inversely proportional. In the early afternoon the temperature of water reaches the maximum so it needs less heat to vaporize, and vise versa in the late afternoon. Based on theoretical calculations of the proposed mathematical model, the insulation thickness has a direct effect on the productivity as shown in Fig.. The efficiency increases when the insulation thickness increases. This is due to the decrease in the heat loss from the still to the surroundings. The theoretical value of absorbtivity multiplied with transmissivity is a function of the solar intensity and the ambient condition. Figure shows its behaviour against local time. It has a maximum value related to the maximum of solar intensity, and then decreases in the late Ui(kW/m 2.C) Efficiency Standard Local Time (hr) Standard Local Time (hr) Fig. 7 Relationship between theoretical overall heat loss coefficient and standard local time in st of April Fig. 8 Change of the efficiency with standard local time at 2 cm depth in st of April

10 994 Heat Mass Transfer (27) 43: Efficiency (Tw - Ta)/ Fig. 9 Change of the efficiency with (T w T a )/I (t) Efficiency Standard Local Time Fig. Insulation thickness effect on the efficiency ατ cm 2.5 cm 5cm Standard Local Time Fig. Relationship between (as) and the standard local time in st of April afternoon. Also a comparison between the theoretical and experimental results of productivity was conducted to validate the proposed mathematical model as shown in Fig. 2 which illustrates that the deviation in the results between the experimental and theoretical results is very narrow. The proposed theoretical model gave a good match with the experimental results. This may help to investigate factors which enhance the productivity of the solar still. Also the agreement between the experimental and the theoretical results Procuctivity (ml/m 2.hr) prove the accuracy of the theoretical model used in the present study. 6 Conclusions In this present study, several conclusions can be obtained as follows; (a) the increase in either ambient temperature and/or the solar intensity can lead to an increase the solar productivity, (b) as the water depth decreases from (3.5 cm) to (2 cm), the productivity increases by (25.7 %), (c) The maximum efficiency occurs in early afternoon due to the high solar radiation at this time, (d) the overall heat loss coefficient increases until it reaches the maximum in the afternoon due to higher solar intensity and ambient temperature, and finally, (e) the proposed mathematical model gave good match with experimental results. Future work can be carried out using this model to enhance the design of single solar stills. References Stand Local Time (hr) Experimental data Theoretical data Fig. 2 Comparison between theoretical and experimental productivity in st of April (the straight and dashed lines are the fitting lines of the experimentaland theoretical data respectively). Aboul-Enein S, El-Sebaii AA, El-Bialy E (998) Investigation of a single-basin solar still with deep basins. Renew Energy 4( 4): Akash BA, Mohsen MS, Osta O, Elayan Y (998) Experimental evaluation of a single-basin solar still using different absorbing materials. Renew Energy 4( 4): Akash BA, Mohsen MS, Nayfeh W (2) Experimental study of the basin type solar still under local climate conditions. Energy Convers Manage 4(9): Al-Hayek I, Badran O (24) The effect of using different designs of solar stills on water distillation. Desalination 69(2): Al-Hinai H, Al-Nassri MS, Jubran BA (22a) Effect of climatic, design and operational parameters on the yield of a simple solar still. Energy Convers Manage 43(3):639 65

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