Thermal Modeling of Solar Still Coupled with Heat Pipes and Experimental Validation

Water is the basis of the existence of all kinds of life, so obtaining it with good quality represents a challenge to human existence and development especially in the desert and remote cities because these areas contain small populations and water purification requires great materials and huge amounts of fossil fuels resulting pollution of the environment. Cheap and environmentally friendly desalination methods have been done by using solar distillations. Passive solar stills have low yields, so in this research, the problem is overcome by connecting four heat pipes which are installed on the parabolic concentrator reflector with passive solar still to increase the temperature of hot water to more than 90°C, as a result, the yield increases. An extensive theory is studied to manufacture two systems: the first consists of passive solar still has dimensions are 1000 mm × 500 mm and the glass cover tilted at the angle 33°. It is approximately equal to the latitude of the city of Baghdad [(Latitude: (33.34° N) Longitude:  (44.4° E)].  This gives 5.04 kg/m2.day, the second solar still which is associated with 4 heat pipes gives a water yield of about 7. 2 kg/m2.day. This means that the improvement in the daily production of distilled water is 50 % over the productivity of the passive solar still All results above are calculated when the depth of water is 1. 5 cm. In addition, heat balance for each part of the system is achieved and calculations of the performance of the solar still are done by using the program in the language of Matlab. All these results are compared with the experimental ones of different depths of water (1.5 cm, 2 cm, 3 cm, and 4 cm) which are taken from the experimental part to ensure the system reliability at different weather conditions in Baghdad throughout the year and to give a good approach. The system associated with heat pipes gives promising results and can be widely used for its abundant productivity and durability of its components. (TDS) and (pH) value are carried out in the laboratory and it is found that water is safe and pure for drinking.


INTRODUCTION
The crisis of processed water represents the greatest challenge concerned with growth and development in the world. For example, although water covers two -thirds of the planet, drinking water is less than 1%. (Sampath, et al., 2013). The rested water, is snow or groundwater that may be close to the surface of the earth or deep groundwater which is far from the surface of the earth, is difficult to reach or extract and it is very expensive too. As a result, many methods must be developed to obtain potable water such as reverse osmosis, multistage flash distillation and thinfilm distillation, but these methods are expensive in terms of the high cost of the station. The used tools and fuel cause several major hazards including pollution. The use of renewable energy method is the main idea of this research to benefit from the solar radiation which is coming from the sun for water purification that considerably abundant to solve the problem of drinking water in Iraq. (Masoud, et al., 2010), studied theoretically of solar still in the city of Chabahar-Iran. The dimensions of solar still are 2000 mm× 500 mm and the glass cover tilted at the angle 25°. A heat balance of energy equations of solar still is solved under certain minor assumptions. The temperatures of the glass cover, the saline water, and the basin are calculated. The researcher finds that productivity is high in the summer months and it is a function of solar radiation. They find distilled water is approximately 4.81 liters as a daily yield in July and 3.67 liters as a daily yield in December and the efficiency reaches its maximum value in the noon. (Sampath, et al., 2011), studied thermal modeling of single basin solar still. The researcher concluded that can increase the production of water distillation to about 72 % as a result of high temperature due to the coupled flat plate collector with the evacuated tube. (Kiam Beng Yeo et al 2014), performs a numerical investigation to study the heat balance of energy equations on a single slope basin solar still to get clean water from brackish water in an enclosed space. Critical parameters have been studied, such as a slope angle of the glass cover, the quantity of water in basin and wind speed. Simulation is carried out on the relation between the slope angle and the latitude of the experimental location. Finally, they find that increasing water in the basin leads to a decrease in water production and that wind speed is one of the factors which increases water production. The result shows that the optimum angle is equal to 10° facing south (latitude angle) and predicts that the productivity of solar still is (2 kg. m -2 .day -1 ). (Kalbande, et al., 2016), studied theoretically analysis of solar still integrated with 10 evacuated tubes. The experiment has been achieved in summer; the researcher found that if the basin water depth is 3 cm, distilled water is approximately 8 liters as a daily yield. The maximum daily efficiency is 34.39 %. (Mehul and Piyush, 2016), an experiment was carried out on the single slope solar still connected with the evacuated tubes. A mathematical model is also constructed to solve the energy balance equations for the different component of system. Their study displays that the efficiency without evacuated tubes are: 20%, 19%, 15% and efficiency with evacuated tubes are: 41%, 45%, and 35% respect to water depths which are: 1 cm, 2 cm, and 3 cm respectively. The theoretical and experimental comparisons show a good agreement. (Hitesh, et al., 2017), an experimental study has been developed and conducted on single basin solar still. Then, the researchers can increase the production of water distillation as a result of high temperature due to couple with evacuated tubes. On the other hand, the maximum yield of the solar still coupled with heat evacuated tubes is 4.94 kg/m 2 .day and the yield of the passive solar still is 2. 5 kg/m 2 .day. This means the improvement in the daily production of distilled water was 97.6 % over the productivity of the passive solar still. In the interval from (11-July-2011to 11-June), the result above was taken at depth of water is equal to 3 cm. (Saad and Mohanad, 2017), performed an experiment on the solar still coupled with evacuated tube heat pipes. The study is carried out on a single basin solar still in Bagdad city for certain days in many months to investigate the effect of heat pipes on distillate output and efficiency of the system under local climatic conditions. Many different water samples are used in this study: sea water and river water in the basin for different depths of water (1,2 and 3 cm). The study showed that single basin solar still coupled with 10 heat pipes to enhance the productivity from 3.4724 to 7.0375 kg/m2. day. (Kotebavi et al., 2018), studied solar still coupled with heat pipes and experimental study has been developed and conducted on three types of still namely: passive solar still, coupled with heat pipes, coupled with evacuated tubes. They could increase the production of water distillation to about 40 % over the productivity of the solar still coupled with evacuated tubes as a result of high temperature due to coupling with heat pipes. (Mowaffaq and Najim 2019), an experimental study has been developed and conducted on a single basin solar still in Mosul city (Latitude:35.866°, Longitude:43.296°), In the interval from May to August, they could increase the production of water distillation as a result of good insulation by 20.785% and 19.864% when using thermal insulation of 4 and 5 cm respectively. The daily production of distilled water is increased by 14.147 % as water depth changes from 5cm to 4 cm. While the present work is divided into two sections: The theoretical investigation involves a numerical study of thermal modeling which is carried out on two types of solar stills which are: passive solar still and solar still coupled with 4 heat pipes. The energy balance equations are solved by Matlab program for each component of solar still with several critical factors including reflectivity, transmissivity, the angle of the glass cover, climate condition (ambient temperature, the intensity of the solar radiation, water depth). The present theoretical work covers water depths: (1.5 cm, 2 cm, 3 cm, and 4 cm). The experimental investigation includes a set of experiments carried out on two types of solar still to study the factors affecting on the performance and the efficiency of the solar still by changing the depth of water in the basin liner which are the same water depth used in the theoretical part of this study under various outdoor climatic conditions related to the two types of solar stills.

MATH EMATICAL MODELS
The mathematical model is done by using equations of energy balance for all parts of the solar still and heat pipes.

Assumptions
Many assumptions are carried out to simplify the mathematical model for the case under study. Therefore, the following assumptions are used in the modeling: 1-The level of water inside the basin is constant. 2-The system is under quasi steady-state. 3-There are no temperature gradients in all components of solar still. 4-The water vapor is an ideal gas. 5-The system is tight so that no vapor leakage occurs outside.

Governing Equations
2.2.2 Energy Balance of Basin Liner in Passive Solar Still. The energy balance of basin Liner is given by: 2.2.4 Useful Heat Gained by Heated Pipes.
The heat pipes give a useful energy to the given water as follows (Dimir et al., 2008):

Internal Heat Transfer.
In the solar still heat is transferred internally in the system by convection, conduction and radiation.

Convective Heat Transfer Rate.
The heat flux transferred from water to glass cover by free convection is calculated according to the law (Velmurugan, et al., 2007): 2.3.2 Convective Heat Transfer Coefficient. Many models have been designed and developed to find convective heat transfer coefficient between the water and the glass cover. One of these methods is developed by (Dunkel, 1969): Where: = exp (25.317 − 5144 ) = exp (25.317 − 5144 ) (Tiwari, et al., 2005), give the convective heat transfer coefficient between the basin liner and the saline water which is: Due to solar radiation, water gets heated and the evaporative heat transfer coefficient from water to glass can be expressed in the form (Dunkle, 1969): 2.3.4 Evaporative Heat Transfer Rate.
The evaporative heat transfer rate between glass and water is calculated according to the relation (Velmurugan, et al., 2007): 2.3.5 Radiative Heat Transfer Rate.
Radiation heat flux transfer from water to glass cover is calculated according to the following equation (Tiwari, et al., 2005): 2.3.6 Radiative Heat Transfer Coefficient.
Radiative heat transfer coefficient from water to glass cover is given by (Dunkel, 1969): The total heat transfer from water to glass is given by, The total heat transfer coefficient from water to glass is given by, Heat losses from the outer surfaces of the glass cover to the atmospheric are got by convection and radiation. Thus the losses of the upper surface are given by (Dunkel, 1969): 2.4.2 Radiative Heat Transfer Coefficient. Radiative heat transfer coefficient from glass cover to atmospheric is given by (Badran, 2007): 2.4.3 Radiative heat transfer rate. Radiative heat transfer rate from glass cover to atmospheric is given by (Tiwari, et al., 2005): 2.4.4 Convective Heat Transfer Coefficient. Convective heat transfer coefficient from glass cover to atmospheric is given by (Tiwari, et al., 2005): 2.4.5 Convective Heat Transfer Rate. Convective heat transfer rate from glass cover to atmospheric is given by (Tiwari, et al., 2005): When the temperature is greater than 70°, the latent heat of evaporation is given in the following relation (Sampath Kumar, 2011): = 3.1615 × 10 6 [1 − 7.6160 × 10 −4 × ] (27) And when the temperature is below 70°, the latent heat of evaporation is given in the following relationship: = 2.4935 × 10 6 [1 − 9.4779 × 10 −4 × + 1.3132 × 10 −7 × 2 − 4.7974 × 10 −9 × 3 ] (28) 2.5.2 Daily Distillate Output of the Still. Daily distillate output from solar still is given as follow: (29) j = Hours of day.

Efficiency of the Solar Still
Instantaneous energy efficiency is given by the following relationship (Radwn, et al., 2009

NUMERICAL SOLUTIONS 3.1 Numerical Solution Procedure for Passive Solar Still
The system of nonlinear transient equations is solved implicitly to find the system of linear algebraic equations for the ℎ time step 3.1.1. Glass Cover (gc) The energy balance equations (2) for the glass cover of solar still are formulated as follows: T = 10 + 11 T −1 + 12 T (31) Where: C 10 = ∆t ( F gc G g,ef + h c,gc−a T a + h r,gc−sk T sk ) ∆t (A w ℎ ℎ , − + h r,gc−sk ) + m gc CP gc ) C 11 = m gc CP gc ∆t (A w ℎ ℎ , − + h r,gc−sk ) + m gc CP gc ) C 12 = ∆t A w ℎ , − ∆t (A w ℎ ℎ , − + h r,gc−sk ) + m gc CP gc )

Basin Liner (b)
The energy balance equations (4) for the basin liner of solar still are formulated as follows: T = 20 + 21 T −1 + 22 T (32) Where:

Numerical Solution Procedure for Solar Still Coupled with Heat Pipes
The same method is used to derive the temperature equations of the glass cover and the basin that is applied in passive solar still but the equations of water temperature are changed because of the heat that is added from the heat pipes ( ). The energy balance equation (10) for the solar still coupled with heat pipes is formulated as follows: = 40 + 41 −1 + 42 T + 43 (34) Where: A computer program is written in MATLAB (version 10.0) to solve the system of equations. See Table 1 for Reference design and operational parameters for the solar still.

Variations of Biot Numbers for Solar Still Components
The variations of Biot number are within the acceptable limit ( ≤ 0.1) for using the lumped capacitance method.

EXPERIMENTAL SETUP
An experimental rig which is designed, developed and constructed is shown in Fig.2 and it is used in the present work to study the solar still. In the present work, different measurements and instruments have been used such as solar meter, anemometer, electronic balance, and digitals data logger thermometers. The components of rig test are described below.

Basin
The basin is made from galvanized iron with thickness of 1. 5 mm and the basin has an area ( 1 × 0.5 ) and the height of the back wall is 0.525m while the front wall of 0.20m.
The base of the basin is painted black to absorb the largest amount of heat falling on the basin itself while the side walls of the basin are painted white to reflect the heat on the base of the basin. Each solar still is equipped with two valves; one is used for supplying water to the basin and the other used for getting rid of the remaining water. It is also used for cleaning basin from the salts and dirty in order to be used again.

Basin Cover
In this present work, the cover is made from a glass plate whose thickness effects the performance of the solar still. The researchers (Hitesh and Shah 2011), used identical glass plates with different thicknesses (4mm, 8mm, and 12mm). They find that the lower glass thickness of 4mm is better because of increasing the evaporative heat transfer coefficients, water temperature, the efficiency of a solar still, convective heat transfer coefficient as well as the distillate water output. Consequently, the thickness which is used in this experiment is 4mm. The best angle of the glass surface is 10° to ensure that the drop of condensed droplets inside the trough and to ensure that it does not fall back and also affect on the optimal utilization of solar radiation So, normally = for annual performance (Abdul Jabbar, 2011). Thus the angle of the glass cover is taken as 33.34° and approximately is equal to the latitude of the city of Baghdad [( : (33.34° ) : (44.4° )] gives maximum yield production which are shown in Fig. 3.

Distillate Trough
A rectangular channel with dimensions (50 × 2 × 3 ) (made of galvanized steel) was installed inside the galvanized iron box, which lies on the lower edge of each condensing surface to collect distilled water.

Sealant:
Sealants should be used in special conditions such as: remain resilient at very low temperatures, durable, low cost and easily applicable. The materials that are used include tapes silicon, tars, and Putty. Sealant foam is put between the glass cover and the basin material to absorb the shock and silicone material that fills the gap between them to seal and prevent leakage.

Insulation
The loss of heat from the sides and bottom of the basin is undesirable because it reduces the performance of the solar still. Therefore, the heat losses should be reduced by the use of good insulators that have low thermal conductivity (K). In this present work, two-layer insulation is used, the first layer from Polystyrene has a thickness of 5 cm and the second layer of plywood has a thickness of 11mm which are shown in Fig. 3.

Instrumentation
In this research, used measuring devices are calibrated by the Ministry of Science and Technology to take readings of the intensity of solar radiation, wind speed, the mass of water, total dissolved solids (TDS) and pH of water, and temperatures of water, basin, glass cover, and ambient air temperature.

DISCUSSION AND RESULT
The research focuses on the energy analysis of the passive solar still and solar still coupled with heat pipes that are studied in Baghdad city. The temperature of the two types of solar stills, the quantity of produced water, the efficiency of energy, the pressure, the absorptivity and the heat transfer coefficients by evaporative, radiative and convective have been investigated. It is found that the active solar still produces more distilled water per unit area of basin than the conventional solar still. The theoretical results are compared with the experimental results and gave a good approach. On the other hand, the results are compared with other researchers of the credibility of the results. Figs. (5 & 6) show the hourly variation of the theoretical values of heat transfer coefficients from water in the basin to the glass cover (as a result of evaporation, radiation, and evaporation) of passive solar still and solar still coupled with heat pipes respectively. The evaporation heat transfer coefficient increases gradually until it reaches its maximum values which are: (27.85 W/m 2 .°C and 41.31 W/m 2 .°C) at 2 p.m. and then the evaporation heat transfer coefficient of the two types of solar stills mentioned above decrease. The convective and radiative heat transfer coefficients are much smaller than the evaporation heat transfer coefficient. The maximum values of convective heat transfer coefficients are (3.22 W/m 2 . °C and 3.52 W/m 2 . °C) of the two types of solar stills respectively. The corresponding values of radiative heat transfer coefficients are (6.43 W/m 2 . °C and 6.98 W/m 2 . °C) respectively. It is obvious that the patterns of theoretical for heat transfer coefficients are the same. Fig. 7 shows the hourly variation of the theoretical values of evaporation heat transfer coefficients from water in the basin to the glass cover (as a result of evaporation) of passive solar still and solar still coupled with heat pipes respectively. It is very clear that the evaporation heat transfer coefficients increase with the time and reaches its maximum values of the two types mentioned above at 2 p.m. which are: (27.85 W/m 2 .°C and 41.31 W/m 2 .°C ) respectively and then decrease. The values of evaporation heat transfer coefficients of solar still coupled with heat pipes are greater than passive solar still by 48.33%. It is very close to the increment of distillate output. Figs. (8 & 9) show the hourly variation of the ambient, basin, glass cover and saline water temperatures of passive solar still and solar still coupled with heat pipes respectively, which are recorded according to the simulation program of a typical day (3 -April -2018) at water depth (2 cm). It is very obvious that the temperatures have the following tendency: temperatures start initially together and then gradually go up as a result of increasing the intensity of solar radiation until temperatures reach their maximum values after 1 p.m. Then temperatures begin to decrease. In other words, the daylight can be divided into three intervals as follows: In the first interval (from 6 a.m. to 9 a.m.) hourly variation of temperatures is insignificant because of the low intensity of solar radiation while during the second interval (from 9 a.m. to 2 p.m.) is relatively high temperatures variation because the solar radiation is high. In the third interval after 2 p.m., the solar radiation decreases and temperatures decrease too. It is clear from the figure that the basin temperature is slightly more than saline water due to some physical properties which are: high absorption coefficient, low transmissivity, and high thermal conductivity. On the other hand, the basin of solar still is insulated by two layers which are: plywood and polystyrene to reduce heat loss from system to the environment leading to an increase of basin temperature in addition to the factors mentioned above. The obtained conclusion is that both solar radiation and temperature have the same behavior. Figs. (10 & 11) show the instantaneous energy efficiencies of passive solar still and solar still coupled with heat pipes respectively. In the passive solar still, see Fig. 10, the energy efficiency goes up from (0%) at 8 a.m. and reaches its maximum value is (27%) when its maximum quantity of evaporative heat is (195.64W/m 2 ) at 2 p.m. In solar still coupled with heat pipes see Fig. 11, the energy efficiency goes up from (0) and reaches its value is (77.86%) when its maximum quantity of evaporative heat is (1152.8W/m 2 ) at 2 p.m. Fig. 12 shows the variation of saturated water pressures at glass cover and water temperatures as a function of time. The change of saturated water pressure starts increasing since the early morning hours until it reaches the maximum value after 1 p.m. and then it starts gradually to decrease until it reaches the lowest value in the dark of both cases mentioned above. This means that the saturated water pressure at water temperature starts from 2590 N/m 2 at 7 a. m and reaches its maximum value 10532 N/m 2 after 1 p.m. while saturated water pressure glass temperature starts from 2200 N/m 2 at 7 a.m. and reaches its maximum value 7000 N/m 2 after 1 p.m. As a result, the growth of saturated water pressure is the same trend of growth of solar radiation. It is very clear that the figure shows the same behavior as solar radiation. Figs. (13 & 14) show the variation of theoretical and experimental cumulative distillate production of passive solar still and solar still coupled with heat pipes at the University of Baghdad. It should be noted that these observations conform to the computed levels of effective irradiance. Productivity is estimated from the present theoretical work which is closer to the experimental data. It should also be mentioned that theoretical productivity is more than the experimental one. Passive solar still and solar still coupled with heat pipes overestimate the distillate yield slightly by about 5%, 6% respectively due to vapor and distillate leakage from practical solar still and measurement errors. It is very clear that the hourly distillate output is relatively low of the two solar stills when the level of insolation is low. As a result, it is difficult to measure the distillate yield with higher accuracy. So, the daily distillate outputs are found to be more reliable in all seasons except winter. Figs. (15 & 16) show the theoretical comparison between present work and theoretical work achieved by other researchers that the behavior of evaporative heat transfer coefficients of current work during solar distillation is the same as the behavior of (Dunkle, 1969), (Hitesh, 2011) and(Medugu, 2009) and that the difference in values is due to different hypotheses and weather conditions. It is shown by comparison that the behavior of heat transfer coefficients of current work during solar distillation is the same as the behavior of (Dunkle, 1969), (Hitesh Panchal, 2011) and that the difference in evaporative heat transfer coefficients and convective heat transfer coefficients is due to different hypotheses and weather conditions.

CONCLUSIONS
Theoretical and experimental investigations of the passive solar still and solar still coupled with heat pipes under Baghdad, climate conditions have been performed in the present work. The following conclusions have been drawn from the present investigation: 1-The highest productivity obtained for each system are as follows: 4.8 liters in the passive solar still and 7.2 liters in the solar still coupled with heat pipes because increasing the rate of heat transfers to water coming from heat pipes. 2-The output of the solar still coupled with the heat pipes installed above the reflector increases approximately by 50% due to more solar radiation which is absorbed by the heat pipes. 3− The distillate of water decreases in months (June, July, and August) because of the high temperature of the glass. As a result, it decreases the difference temperature between the glass cover and saline water. 4-The depth of the water affects on distillation productivity. In all experiments, it is found that increasing the depth of water reduces distillate productivity because increasing the mass of water in the basin needs to absorb a large amount of heat to raise its temperature and then delays the process of evaporation and condensation.