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Numerical investigation of modified solar still using nanofluids and external condenser
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Theoretical with experimental validation of modified solar still using nanofluids and external condenser A.E. Kabeel a,∗, Z.M. Omara b, F.A. Essa b a b
Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt Mechanical Engineering Department, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh, Egypt
a r t i c l e
i n f o
Article history: Received 6 April 2016 Revised 8 January 2017 Accepted 20 January 2017 Available online xxx Keywords: Distillation Solar still Nanofluids Nanomaterials Numerical, Statistical paired t-test
a b s t r a c t The effects of using nanofluids and integrating the solar still with external condenser have been studied numerically. The performance of the modified desalination system is evaluated and compared with that of the conventional one under the same meteorological conditions. Theoretical analysis of heat and mass transfer mechanisms for the solar stills has been developed. Numerical calculations had been performed on the solar stills in Kafrelsheikh city, Egypt (31.07°N latitude and 30.57°E longitude) for different nanomaterial concentrations and providing low pressure to study the effects of these parameters on the daily productivity of the system. The analyses are conducted in the weight concentrations range from 0.02 to 0.3% for aluminum oxide (Al2 O3 ) and cuprous oxide (Cu2 O) nanoparticles. Thermo-physical properties of the nanofluid are considered by assuming nanofluid is a single-phase fluid. The simulation results are in a good agreement with the published experimental data. The daily efficiency of the modified still is 84.16% and 73.85% when using Cu2 O and Al2 O3 nanoparticles, respectively, with operating the fan. And the daily efficiency when providing low pressure only is 46.23%. In addition, the conventional stills’ daily efficiency was 34%. © 2017 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction Solar radiation is free, never lasting and available on site. Moreover, using the solar energy reduces fossil fuels consumption and pollutants. Solar stills use the solar radiation for producing freshwater. Solar stills are simple, cheap and need low maintenance, but they suffer from low productivity. Because of their advantages, scientists have conducted studies, which can be classified into two main categories: experimental and theoretical, to enhance the solar still performance. A review of various designs of solar stills was made by Xiao et al. [1] and Ganapathy Sivakumar and Sundaram [2]. Different methods have been carried out in the literature to improve the productivity of solar stills. These methods include adding dyes [3] and charcoal pieces [4] to the basin water, using reflectors [5], external condensers [6] or internal condensers [7], connecting the stills to solar collectors [8] or concentrators [9], etc. Recently, other methods have been carried out to enhance the daily productivity of single effect solar stills.
∗
Corresponding author. E-mail addresses: [email protected], [email protected] (A.E. Kabeel), [email protected] (Z.M. Omara), [email protected] (F.A. Essa).
Several researchers have suggested improvements to the passive solar still with separate condenser and natural circulation of water vapor. Fath and Elsherbiny [10] investigated a single sloped basin solar still integrated with an external condenser. The condenser was located in the shadow zone of the still. They found that the still efficiency was increased. El-Bahi and Inan [11,12] developed a solar still integrated with a separate condenser with double glazing and another solar still integrated with a separate condenser with one glass cover. The condenser was located on the shaded side of the evaporator. A vertical steel reflector was fitted in the top part of the evaporator cast a shadow over the condenser system. It was found that the performance of the solar still with a condenser was better than the one which had no condenser. Gnanadason et al. [13] reported that using nanofluid in a solar still increases its productivity. They examined the effects of adding carbon nanotubes (CNTs) to the water inside a single basin solar still. Their results obtained that adding nanofluid increased the efficiency by 50%. In our recent study, Kabeel et al. [14] conducted the experimental attempts to improve the solar still productivity by providing vacuum fan with integrating an external condenser to the basin and also by using the aluminum oxide–water nanofluid. The results revealed that providing vacuum increased the distillate water productivity by about 53.2%. In addition, using the aluminum oxide– water nanofluid improved the solar still water yield by about 116%,
http://dx.doi.org/10.1016/j.jtice.2017.01.017 1876-1070/© 2017 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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Nomenclatures English symbols A area, m2 Cp specific heat, J/kg K F fan Fs fan speed, rpm FP fan power, W Gr Grashof number h heat transfer coefficient, W/m2 K hfg enthalpy of evaporation at Tw , J/kg K thermal conductivity, W/m.K I ( t) solar radiation on inclined surface, W/m2 L perimeter, m m mass, kg M molecular mass, g/mol P partial pressure, N/m2 Pr Prandtl number Ra Rayleigh number St sticking coefficient t time, S T temperature, °C U heat loss coefficient from basin and sides to ambient, W/m2 K V wind velocity X insulation thickness, m Greek Symbols α absorptivity β volumetric thermal expansion ε emissivity ρ density, kg/m3 σ Stefan–Boltzmann constant, 5.6697 × l0−8 W/m2 K4 δ characteristic length, m ηd the daily efficiency of the still μ dynamic viscosity, N/m2 .s ϕ nanomaterial concentration τ transmissivity Subscripts a ambient b basin bf base fluid c convective e evaporative eff effective fw feed water g glass i insulation nf nanofluid p nanoparticle r radiative s sky v vapor or volume fraction w water or weight fraction
Fig. 1. Schematic diagram of the solar desalination system.
(CrWSS) with internal reflectors, integrated with external condenser and using different types of nanomaterials was investigated by Omara et al. [16]. Investigations clarified that the yield of CrWSS with reflectors when providing vacuum was about 180% higher than that of conventional solar still (CSS). In addition, using the cuprous and aluminum oxides nanoparticles increases the yield of CrWSS with reflectors when providing vacuum by about 285.10% and 254.88%, respectively. Generally, the experimental researches are so costly and time consuming. Therefore, some researchers have focused on mathematical modeling, to find important parameters and better designs of solar stills. Kianifar and Mahian [17] investigated the effect of using low powered fan and reported an improvement in productivity. Al-hussaini and Smith [18] studied theoretically the effects of applying a vacuum inside the solar still on its productivity. Their results showed that the water yield could be increased by 100% when considering complete vacuum. In addition to mathematical modeling, some investigations have been done based on computational fluid dynamic (CFD). CFD has relatively low cost and high speed, while it can also simulate real or ideal conditions. A single sloped passive solar still with an external condenser has been studied theoretically by Madhlopa and Johnstone [19]. Because being the effect of nanomaterials and external condenser on the performance of solar still needs more theoretical research. Then, the main objective of this study is to build a numerical modelling which has the ability of expectation of the effects of nanomaterials and external condenser on the performance of solar still and also has the ability of optimizing the performance based on the considered examined parameters. The considered operating parameters of this investigation are providing low pressure (external condenser) and also using different types of nanomaterials (aluminum oxide (Al2 O3 ) and cuprous oxide (Cu2 O)) with various concentrations (from 0.02 to 0.3%). The output parameters of the solar still performance are the hourly yield and the daily efficiency of the solar stills. So, they are evaluated at various operating conditions. 2. System description and operating principle
with operating the vacuum fan. In another study, Kabeel et al. [15] studied the effects of using the solid nanoparticles of Cu2 O and Al2 O3 with different weight fraction concentrations on the performance of a single basin solar still with and without providing vacuum. The results showed that using the Cu2 O and Al2 O3 nanoparticles, increased the distilled water productivity by about 133.64% and 93.87% and 125.0% and 88.97% with and without operating the vacuum fan, respectively. The performance of hybrid solar distillation system comprising of corrugated wick solar still
A schematic diagram of the examined solar still is shown in Fig. 1. The bottom and side walls of the basin are considered to be well insulated. Purified drinking water is collected from the distilled output collector. The solar radiation transmitted through the glass cover and basin water is absorbed by the basin liner; hence, its temperature increases. Part of thermal energy is transferred by convection to the basin water and the other will be lost by conduction to the ground. The basin water transfers heat to the inner surface of the glass cover by radiation, convection and evaporation.
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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The heat is conducted through the cover and then transfers from the upper surface of the glass cover to surroundings by radiation to the sky and by convection to ambient air. The condensed water vapor trickles down the inclined glass cover to an interior collection trough. From there it is collected into the storage container through distilled output collection port. On the other hand, the fan makes better evaporation rate and lower pressure inside the basin still which cause some more wetted or evaporated air taken out to the condenser through the condensation coil path to be taken as distilled water from the condenser output. The conventional solar still is completely similar to the modified one for the thermal energy distribution.
I (t )Ab αb τg τw = mbC pb .
3
d Tb + Qc.b−w + Qloss dt
(1)
The transient energy balance equation for the basin water is given as [22,23],
d Tw + Qc.w−g + Qr.w−g dt + Qe.w−g + Q f w
I (t )Aw αw τg + Qc.b−w = mwC pw
(2)
Energy balances for the glass cover [22],
d Tg + dt Qr.g−s + Qc.g−a
I (t )Ag αg + Qc.w−g + Qr.w−g + Qe.w−g = mgC pg .
3. Statistical test parameters
(3)
The hourly yield is given by the following equation, 1. The EFF test is proposed to measure the agreement between the predicted and reference values, Mayer and Butler [20].
(Mean Square Error (MSE )) EF F = 1 − V ( ariance o f re f erence data) Negative EFF test values indicate that there is no agreement. EFF Test values between 0 and 1 indicate that there is agreement; preferable values are those that are close to unity. 2. Paired-difference t-test, Schlotzhauer [21]. A paired t-test is conducted to elucidate the significance of the differences of the mean values of each evaluation parameter prior to and post modification to confirm whether or not the stepped solar still system is enhanced post-modification. Some of the evaluation parameters that are to be tested include evaporation heat transfer coefficient, convective heat transfer coefficient, radiative heat transfer coefficient, productivity and efficiency of solar still. For the t-test, there are two possible results based on the corresponding p-value. If it is less than the reference probability, the result is regarded as being statistically significant, and there is no null hypothesis. However, if it exceeds the reference probability, the result is regarded as not being significant. In this study, the reference probability is assumed to be 0.05. The paired t-statistic is calculated and converted to determine the p-value using the ttable or another utility program. The test statistic for the paireddifference t-test is calculated and provided for in a manner similar to equation, Schlotzhauer [21].
S t = X¯ − μ0 / √ n
where X¯ the average difference, s is the standard deviation of the difference, and n is the sample size. In paired testing, the null hypothesis is assumed when μ0 is 0, meaning that there are no differences between groups. 4. Theoretical analyses In this section, a complete mathematical model that describes the heat and energy processes in the basin solar still is presented as shown in Fig. 1. These models will assist to determine the hourly distillate output productivity and the daily efficiency of the solar stills. The technical specifications of the solar still and parameters used in the computer model are summarized in Table 2. 4.1. The conventional basin still The analytical results are obtained by solving of the energy balance equations for the absorber plate, saline water and glass cover of the solar still. The saline water temperature, basin plate temperature and glass cover temperature can be evaluated at every instant. Energy balance for the basin plate [22],
˙ ew = he.w−g m
(Tw − Tg ) × 3600 hfg
,
(4)
where, he.w − g is the evaporative heat transfer coefficient between water and glass and hfg is the water latent heat. The convective heat transfer between basin and water [24,25],
Qc.b−w = hc.b−w Ab (Tb − Tw ),
(5)
where, hc.b − w is the convective heat transfer coefficient between basin and water and Ab is the basin base surface area. The convective heat transfer coefficient between basin and water, hc,b-w , is given by the following equation, [26].
hc.b−w = 0.54
K w
δ
Ra0.25 ,
(6)
where, Kw is the water thermal conductivity and δ is the characteristic length. In addition, the Rayleigh number, Ra, is calculated from the relation:
Ra =
2 3 g.β (Tb − Tw ).ρw δ
.
μ
2 w
μw .C pw Kw
where, the thermal expansion coefficient of the nanofluid is given as: β = T +2Tw The heat losses by convection through the basin base b
and sides to the ground and surrounding, are given as [27],
Qloss = Ub (Ab + Asides )(Tb − Ta )
(7)
where, U b = Ki and Ki and Li are thermal conductivity and the Li thickness of the insulation; respectively [28]. The convective heat transfer between water and glass is given by [24,25],
Qc.w−g = hc.w−g Aw (Tw − Tg )
(8)
where the convective heat transfer coefficient between water and glass, hc,w − g , is given by [29],
hc.w−g = 0.884 Tw − Tg +
(Pw − Pg )(Tw + 273.15) 268900 − Pw
13
,
(9)
where, Pw and Pg is the partial pressure of the water and glass, respectively. The radiation heat transfer from the basin to glass cover is predicted from [23],
Qr.w−g = σ
εe f f Aw (Tw + 273.15)4 − (Tg + 273.15)4 ,
(10)
where, σ is the Stefan–Boltzmann constant, ε eff is the water-glass effectiveemissivity and Aw is the water surface area. The evaporative heat transfer between water and glass is given by [24,25],
Qe.w−g = he.w−g Aw (Tw − Tg )
(11)
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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A.E. Kabeel et al. / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–10 Table 1 Measured specifications of the cuprous and aluminum oxides nanoparticles. Material
Chemical symbol
True density (kg/m3 )
Thermal conductivity (W/m.K )
Average particle size (nm)
Aluminum oxide Cuprous oxide
Al2 O3 Cu2 O
3900 6320
46 76.5
10 − 14 10 − 14
Table 2 Technical specifications of the solar still [37].
where, the evaporative heat transfer coefficient between water and glass, he,w − g , is given by [24,25],
he.w−g =
0.016237 × hc.w−g (Pw − Pg ) (Tw − Tg )
(12)
Category
Property (Unit)
Value
Basin
αb
0.95 1 460 7800 14 5 0.002016 3 30° 0.05 0.85 0.88 1.18 840 2500 0.05 0.9 0.96 1 4190 1027 0.613 2,350,0 0 0
It is also assumed that, the makeup water is at atmospheric temperature and takes heat from basin. The heat taken by the replaced water is estimated from [23],
Q f w = meC p w (Tw − Ta )
(13)
where, Cpw is the specific heat of water at constant pressure. The radiative heat transfer between glass and sky is given by [24,25],
Qr.g−s = hr.g−s Ag (Tg − Ta ),
Glass
(14)
hr.g−s = εg σ
(Tg + 273.15) − (Ts + 273.15) 4
4
Water
Tg − Ta
(15)
(16)
The convective heat transfer between glass and ambient air, Qc.g − s is given by [30],
Qc.g−a = hc.g−a Ag (Tg − Ta )
(17)
where Ag is the glass surface area. In addition, the convective heat transfer coefficient between glass and ambient, hc.g − s , is taken from [18],
hc.g−a = 5.7 + 3.8 V
(18)
In the case of providing vacuum/low pressure inside the solar still [18], the heat transfer coefficient due to convection, between water and glass cover, becomes zero. Since there is no diffusion of vapor through the air, the evaporation heat transfer coefficient is calculated using the thermal balance equation at the glass cover. Steady state heat transfer through the glass is assumed at the glass cover without any appreciable error. So, he.w − g is found by [18];
(19)
where, Tw and Tg at the end of the interval are then found using Eqs. (2) and (19) again. Eq. (4) is then used to obtain the produced distilled water from the modified solar still with vacuum or low pressure. 4.3. The modified basin still when using nanofluids In the case of using the cuprous oxide and aluminum oxide nanoparticles, the thermo physical properties of nanofluids for a volume concentration (φv ) are calculated at the average bulk temperature of the nanofluid as detailed below. The density of nanofluids (ρnf ) is determined using Pak and Cho’s equation [31],
ρn f = (1 − ϕv )ρb f + ϕv ρ p ,
where φv is the volume concentration of the nanoparticles in the basin water. The effective thermal conductivity of dilute nanofluids (Knf ) can also be evaluated using the Maxwell model [32] for nanofluids with volume fraction less than unity. Maxwell equation is given by;
K p + 2Kb f + 2ϕv K p − Kb f Kn f = Kb f K p + 2Kb f − ϕv K p − Kb f
4.2. The modified basin still with providing low pressure
(hc.g−a + hr.g−s )(Tg − Ta ) he.w−g = − hr.w−g , (Tw − Tg )
αw τw εw
Aw (m2 ) Cp w (J/kg.K) ρ w (kg/m3 ) Kw (W/m.K) hfg w (J/kg.K)
The sky temperature is taken from [29],
Ts = Ta − 6.0
αg τg εg
Ag (m2 ) Cp g (J/kg.K) ρ g (kg/m3 )
where, the radiative heat transfer coefficient between glass and sky, hr,g − s , is given by [24,25],
Ab (m2 ) Cp b (J/kg.K) ρ b (kg/m3 ) Ub (W/m2 .K) Pb (m) Asides (m2 ) Glass thickness. mm Slope of glass
(20)
(21)
The specific heat of the nanofluid (Cpnf ) is calculated using Xuan and Roetzel’s equation [33],
(ρC p)n f = (1 − ϕv )(ρC p)b f + ϕv (ρC p) p
(22)
The viscosity of the dilute nanofluid (μnf ) can also be determined using the viscosity correlation proposed by Einstein [34],
μn f = μb f (1 + 2.5ϕv )
(23)
The volume fraction of the nanoparticles (ϕ v ) can be estimated as a function of the weight fraction of the nanoparticles (ϕ w ) in nanofluid by the following correlation [35],
1 − ϕv
ϕv
=
1 − ϕw
ϕw
ρp ρb f
(24)
It is well known that the properties of the nanofluids depend on the shape and size of nanoparticles. The aluminum and cuprous oxides nanoparticles were used for the preparation of the nanofluids. The specifications of the nanoparticles are obtained in Table 1. The aluminum and cuprous oxides nanoparticles were characterized by X-ray diffraction technique (XRD-60 0 0, Shimadzu). To make the nanoparticles more stable and remain more dispersed in the basin water and to minimize the nanoparticles aggregation to improve dispersion behavior, Triton X-100 is used as a dispersant. The optimum of homogeneously dispersed nanoparticle powders
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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was found at about 0.021% wt Triton X-100. Therefore, we choose Triton X-100 concentration equal to 0.021% [36]. The daily efficiency, ηd , is obtained by the summation of the hourly condensate production (m), multiplied by the latent heat (hfg ), hence the result is divided by the daily average solar radiation I(t) over the whole area (A) of the device [30]:
ηd =
˙ × hfg m A × I (t ) + F P
(25)
where FP is the consumed power by the vacuum/low pressure fan. 5. Numerical simulation assessment A mathematical model was developed by the computer program, written in FORTRAN, to evaluate the performance of the solar still. This computer program was developed to solve the energy balance equations of the still elements for various nanomaterial concentrations in the brine and for providing low pressure inside the still too. The temperatures of the glass cover, water and absorber plate can be evaluated every time by solving the energy balance equations for the glass cover, brackish water and absorber plate of the solar still, respectively. The fourth order Runge–Kutta method was used to solve the system of nonlinear ordinary differential equations from Eqs. (1) to (18) to find Tg , Tw , Tb and the quantity of distilled water per hour at any time. Numerical calculations were started at 9:00 a.m. assuming the initial temperatures of various components of the still to be equal to ambient temperature which equals to 296 K. Using known initial values for the various temperatures, different internal and external heat transfer coefficients were calculated. Using these values of heat transfer coefficients along with climatic parameters, the basin liner, basin water and outer glass cover temperatures were calculated for a time interval t (1.0 s.) as stated in the program. The hourly productivity and rate of heat transfer from the basin liner Qc,b-w were then calculated by using Eqs. (4) and (5), respectively. The procedures were repeated for an additional time interval t and so on, until 9:00 a.m. of the next day. The daily efficiency was then calculated by using Eq. (25). Numerical calculations had been performed in order to study the effects of using different types of nanomaterials with various concentrations in saline water of the basin still in the range from 0.02 to 0.3%. In addition, the effects of providing low pressure on the productivity of the solar still were also investigated. Thermal performances for the conventional and modified stills were compared under the same metrological conditions. In an attempt to validate the proposed mathematical models, the obtained theoretical results for both the conventional and modified stills were compared with the experimental results presented in the literature [14,15] under the same climatic and operating parameters. The experimental study of Ref. [15] was conducted for a range of weight fraction concentrations from 0.02 to 0.2% only. 6. Model validation The model is validated by comparing theoretical results obtained in the present work with the corresponding results obtained from experimental work by [14,15]. During the current simulation, the experimental determined operational and metrological parameters are used. Fig. 3 shows theoretical and experimental comparison of hourly variations of freshwater productivity for the conventional and modified solar stills with providing low pressure only and when using the nanomaterials of cuprous and aluminum oxides. It can be seen from the results of Fig. 3 that the agreement between the present theoretical results and those found in the literature [14,15] is fairly good. Even though, there are some overestimation by the model due to uncertainties in correlations used for
5
calculations of various heat transfer coefficients and solar radiation incident on the stills covers. Temperature gradient within the basin water, basin liner, and glass cover and also heat capacity of the insulation materials are not considered in the mathematical analyses and they represent another source of error. The deviations between experimental and theoretical results for the conventional still are ranged from 5 to 9%. In addition, the deviations for the modified still with providing low pressure only are ranged from 7 to 12% and that when using nanofluids are ranged from 8 to 15%. In order to validate this further, a statistical test can be used. The results of the statistical EFF-test were found to be 98% and 97% – which is almost similar to unity – for the conventional and modified solar stills, respectively.
7. Results and discussions The mathematical relations presented in the theoretical analysis section were employed to determine the performance of the proposed unit. Numerical calculations have been performed for the investigated stills on typical days from September to December 2013, in Kafrelsheikh (Egypt).
7.1. Effect of solar radiation Fig. 2 shows the variation of glass, basin water, and ambient temperatures and solar radiation for conventional and modified stills as affected by ambient conditions with respect to time of the day. The solar radiation increases in the morning hours reaching its maximum values around midday and then decreases in the afternoon. It can be observed from Fig. 2a that the maximum temperature is obtained during the period from 12 a.m. to 2 p.m. Also, it is observed that the temperatures at all points increase in the morning hours to reach maximum value around midday before it starts to reduce late in the afternoon. In addition, it is obtained for the day time that the water temperature in the modified still when providing low pressure only is less than that of conventional still by 0.0–0.75 °C but the glass temperature in the modified still is less than that of conventional still by 1.65–3.25 °C. As a result of this difference, the ability of condensation, then the production rate in the modified still is more than that of conventional still, and for the night time the production rate of the modified and conventional stills is about the same quantity. It is observed from Fig. 2b that when using the cuprous oxide nanoparticles with a concentration of 0.2% as weight fraction, the saline water temperature of the modified still was more than that of the conventional type by 0.5–4.5 °C and 1.35–5.5 °C with and without operating the fan at a speed of 1350 rpm from 9:00 a.m. to 17:00 p.m., respectively. While the glass temperature of the modified still was increased by 0.25–1.2 °C more than that of the conventional one and is decreased by another 0.35–1.35 °C without and with operating the fan during the daytime respectively. It is observed from Fig. 2c that when using the aluminum oxide nanoparticles with a concentration of 0.2%, the basin water temperature of the modified still was more than that of the conventional type by 0.5–2.7 °C and 1.35–3.55 °C with and without operating the fan at a speed of 1350 rpm from 9:00 a.m. to 17:00 p.m., respectively. While the glass temperature of the modified still was increased by 0.4–1.1 °C more than that of the conventional one and is decreased by another 0.45–1.25 °C without and with operating the fan during the daytime, respectively.
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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Fig. 3. Hourly evaporation and convective heat transfer coefficients Using Cu2 O, ϕ = 0.02%.
7.2. Comparison of hourly evaporation and convective heat transfer coefficients
Fig. 2. The hourly temperature variation and solar radiation for the modified and conventional stills.
The hourly evaporation and convective heat transfer coefficients of conventional still and modified still with cuprous oxide nanoparticles at a concentration of 0.2% and without operating the fan are illustrated in Fig. 3. The evaporative and convective heat transfer coefficients values of modified still with cuprous oxide always exceed the values of conventional still. Evaporative and heat transfer coefficient values of conventional still and modified still varies from 8 to 35 W/m² °C and 8 to 48 W/m² °C during the day, respectively. Convective heat transfer coefficient values of conventional
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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Table 3 The amount of energy input/output and energy flows for modified still with cuprous oxide. h 9 10 11 12 13 14 15 16 17
Tw (°C) 36 48 60 62.5 65 63 57.5 50 44
Tg (°C) 26 35 38 40 43 40 38 33 30
Tb (°C) 37 50 62 65 67.5 65.5 60 52 46
Ta (°C) 27 27 28 28 30 29 29 28 28
Energy input (W) A I(t) Qfw
Energy output (W) Qr.g − s Ag Rg I(t) m˙ h f g
Qc.g − a
Qloss
Energy flows (W) Qe.w − g Qc.w − g
Qr.w − g
Qc.b − w
600 750 795 810 760 640 420 180 35
0 130 391 489 522 456 378 274 204
34.9 42.2 49.5 56.9 56.5 47.9 41.8 33.8 29.9
55.5 140.1 165 154 163.7 153.3 141.8 133 121.6
16.3 113 413.4 649.8 540.8 369.8 224.2 39.7 15.54
4.8 39.2 63 53.3 61 55.6 51.1 47.3 42.3
219.8 549.5 373.6 527.5 527.5 461.6 351.7 196 66
0 2.3 8 9.9 11.3 9.5 7.6 5.3 2.3
still and modified still varies from 1.65 to 2.58 W/m² °C and 1.65 to 2.8 W/m² °C, respectively. 7.3. External condenser The hourly variations of freshwater productivity per unit area for the modified solar still with external condenser and the conventional solar still are illustrated in Fig. 4a. As expected the hourly variations curve of freshwater productivity is similar to that of solar radiation curve. Also, the figure indicates that the amount of accumulated distillate water for the modified solar still is greater than that of the conventional still. This is mainly due to the existence of the fan that causes higher evaporation rate inside the still. The fan creates an amount of turbulence of the water vapor content of the air above the saline water that can take evaporated water vapor away from the saline water surface. In addition, the fan takes the non-condensable gases away from the still to the condenser, Ref. [14]. In addition, the condenser decreases the heat loss by convection from water to glass as the condenser acts as an additional and effective heat and mass sink. The theoretical results indicated that integrating the solar still with external condenser increases the distillate water yield by about 56% over the conventional still. 7.4. Nanomaterials Nanofluids improve the heat transfer characteristics and evaporative properties of the water. Addition of nanoparticles to the basin water improves the thermal conductivity of the mixture of water and nanomaterial (nanofluid), as well as the convective heat transfer coefficient. In addition, the nanofluids have higher storage material properties than that of water only. For these reasons, the ability of evaporation and condensation, then the production rates in the modified still are more than that of the conventional type, as shown in Fig. 3b and c. Table 3 indicated the amount of energy input/output and energy flows for modified still with cuprous oxide. The theoretical results indicated that when the cuprous oxide nanoparticles are used at a weight fraction concentration of 0.02%, the basin water temperature of the modified still was more than that of the conventional type by 0.0–2.5 °C when the fan was off and by 0.0–2.0 °C when operating the fan. While the glass temperature of the modified still was increased by 0.0–0.35 °C more than that of the conventional one and is decreased by 0.0–0.75 °C without and with operating the fan during the daytime, respectively. In this case, the daily productivity reached approximately 1750 and 2480 ml/m2 /day for the conventional still and 3620 and 4090 ml/m2 /day for the modified still with and without operating the vacuum/low pressure fan at a speed of 1350 rpm during the daytime respectively as shown in Fig. 4b. The increase in distillate production for the modified still was also 106.86% and 64.92%
49.6 61.1 65.3 66.9 62.8 52.8 35.6 14.8 12.2
41.4 48.3 54.9 56.9 59.3 57.9 56.6 52.6 18.2
1.2 14.3 26.3 23.5 25.1 21.5 18.3 14.7 12.2
higher than that for the conventional still respectively as illustrated from the figure. For using aluminum oxide nanoparticles at a weight fraction concentration of 0.02%, the basin water temperature of the modified still was more than that of the conventional type by 0.0– 2.0 °C when the fan was off and by 0.0–1.6 °C when the fan was on. While the glass temperature of the modified still was increased by 0.0–0.25 °C more than that of the conventional one and is decreased by 0.0–0.55 °C without and with operating the fan during the daytime, respectively. In this case, the daily productivity reached approximately 1545 and 1290 ml/m2 /day for the conventional still and 2875 and 1975 ml/m2 /day for the modified still with and without operating the vacuum/low pressure fan at a speed of 1350 rpm during the daytime respectively as shown in Fig. 4c. The increase in distillate production for the modified still was also 86.08% and 53.10% higher than that for the conventional still respectively as observed from the figure. 7.5. Nanomaterial concentrations The theoretical results indicated that when using the Cu2 O and Al2 O3 nanoparticles, the saline water temperature of the modified still was more than that of the conventional one by different values of degrees. These values of degrees depend on the type of the nanoparticles, the concentration of these nanoparticles in the basin water, and either the fan is on or off. The glass temperature of the modified still was either less than or more than that of the conventional one by different values of degrees according to the same above parameters. The comparison between using the Cu2 O and Al2 O3 nanoparticles at different weight fraction concentrations with and without operating the fan is also numerically carried out as shown in Fig. 5. It can be observed from the figure that the increase in productivity as a percentage increases with increasing the concentration of nanoparticles for both of Cu2 O and Al2 O3 . But when using the Cu2 O nanoparticles the increase in productivity is greater than that when using the Al2 O3 nanoparticles for the same concentration. As it can be cleared from the figure that the agreement between the present theoretical and numerical results and those found in the literature [15] is fairly good. In addition, from the numerical constructed program, the authors could investigate the effect of using Cu2 O and Al2 O3 nanoparticles with higher concentrations in the basin water than 0.20% which is found in the literature [15] on the performance of the solar stills as illustrated in Fig. 5. 7.6. Daily efficiency The daily efficiency of the desalination system is theoretically evaluated. Variations of the daily efficiency for the investigated conditions are shown in Fig. 6. The daily efficiency of the modified solar still when integrating the external condenser only and when
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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Fig. 5. Variations of increase in productivity when using nanofluids with and without fan.
Fig. 4. Comparisons of theoretical and experimental productivity.
using the Cu2 O and Al2 O3 nanoparticles at different concentrations with providing low pressure are illustrated in Fig. 6a. While the daily efficiency of the conventional solar still and the modified still when using the Cu2 O and Al2 O3 nanoparticles at different concentrations without providing low pressure are presented in Fig. 6b. It can be observed that the trend of the daily efficiency curve, Fig. 6, is similar to that of variations of increase in the productivity curve, Fig. 5. It can be observed from Fig. 5 that the maximum daily efficiencies of 84.16% and 73.85% occurred when using Cu2 O and Al2 O3 nanoparticles at the concentration of 0.20%, respectively with operating the fan. Applying these conditions improves the thermal properties of the basin water, and hence improves the evaporation and condensation rates yielding an increase in distillate water. In addition, the daily efficiency for the modified still when providing low pressure only without using nanomaterials is 46.23% as obtained from Fig. 6a and that for the conventional still equals to 33% as shown in Fig. 6b.
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9
Table 4 The results of the statistical paired t-test.
1 2 3 4
Evaluation parameters
t-test results
Convective heat transfer coefficient Evaporation heat transfer coefficient Productivity of still Efficiency of still
There There There There
is is is is
a a a a
significant significant significant significant
difference difference difference difference
between between between between
the the the the
mean mean mean mean
values values values values
before before before before
and and and and
after after after after
modification modification modification modification
posed for calculations may be used for investigating the thermal performance of solar stills with these modifications with a reasonable accuracy. 7.7. Significance of enhancement at each evaluation parameters The results of the statistical paired t-test presents in Table 4. It can be seen that the significant differences between the mean values of the implemented evaluation parameters prior to and post modification of the solar stills are validated. Based on the results, it can be concluded that the proposed modified solar still with nanofluids that are enhanced with superior design concepts is excellent in the context of enhancing the performance of the solar still. 8. Conclusions The main conclusions may be summarized as follows: 1. The distillate productivity of the solar still increased when providing low pressure and also when using nanofluids. 2. The results showed that the modified basin still had a daily efficiency of 84.16% and 73.85% when using the cuprous oxide and the aluminum oxide nanoparticles, respectively, with operating the fan. And the daily efficiency when providing low pressure only was 46.23%. In addition, the conventional stills’ daily efficiency was 33%. The results of this study can be considered to optimize the design of solar stills, in which, it can possible to utilize the energy consumption in the best manner by using nanofluids and integrating an external condenser. References
Fig. 6. Daily efficiency variation for the modified still when using nanomaterials at different concentrations with and without fan.
It can be noticed from the figure that by increasing the weight fraction concentration of the nanomaterial, the daily efficiency for the modified solar still increases till ϕ = 0.12% and ϕ = 0.16% when using the Cu2 O nanoparticles and ϕ = 0.16% and ϕ = 0.20% when using the Al2 O3 nanoparticles. After these concentrations, the efficiency has no marked increase and seems to be constant. The comparisons shown in Figs. 3–5 clearly confirm that the proposed mathematical model for the modified still when providing low pressure and when using nanofluids and the method pro-
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Theoretical with experimental validation of modified solar still using nanofluids and external condenser A.E. Kabeel a,∗, Z.M. Omara b, F.A. Essa b a b
Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt Mechanical Engineering Department, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh, Egypt
a r t i c l e
i n f o
Article history: Received 6 April 2016 Revised 8 January 2017 Accepted 20 January 2017 Available online xxx Keywords: Distillation Solar still Nanofluids Nanomaterials Numerical, Statistical paired t-test
a b s t r a c t The effects of using nanofluids and integrating the solar still with external condenser have been studied numerically. The performance of the modified desalination system is evaluated and compared with that of the conventional one under the same meteorological conditions. Theoretical analysis of heat and mass transfer mechanisms for the solar stills has been developed. Numerical calculations had been performed on the solar stills in Kafrelsheikh city, Egypt (31.07°N latitude and 30.57°E longitude) for different nanomaterial concentrations and providing low pressure to study the effects of these parameters on the daily productivity of the system. The analyses are conducted in the weight concentrations range from 0.02 to 0.3% for aluminum oxide (Al2 O3 ) and cuprous oxide (Cu2 O) nanoparticles. Thermo-physical properties of the nanofluid are considered by assuming nanofluid is a single-phase fluid. The simulation results are in a good agreement with the published experimental data. The daily efficiency of the modified still is 84.16% and 73.85% when using Cu2 O and Al2 O3 nanoparticles, respectively, with operating the fan. And the daily efficiency when providing low pressure only is 46.23%. In addition, the conventional stills’ daily efficiency was 34%. © 2017 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction Solar radiation is free, never lasting and available on site. Moreover, using the solar energy reduces fossil fuels consumption and pollutants. Solar stills use the solar radiation for producing freshwater. Solar stills are simple, cheap and need low maintenance, but they suffer from low productivity. Because of their advantages, scientists have conducted studies, which can be classified into two main categories: experimental and theoretical, to enhance the solar still performance. A review of various designs of solar stills was made by Xiao et al. [1] and Ganapathy Sivakumar and Sundaram [2]. Different methods have been carried out in the literature to improve the productivity of solar stills. These methods include adding dyes [3] and charcoal pieces [4] to the basin water, using reflectors [5], external condensers [6] or internal condensers [7], connecting the stills to solar collectors [8] or concentrators [9], etc. Recently, other methods have been carried out to enhance the daily productivity of single effect solar stills.
∗
Corresponding author. E-mail addresses: [email protected], [email protected] (A.E. Kabeel), [email protected] (Z.M. Omara), [email protected] (F.A. Essa).
Several researchers have suggested improvements to the passive solar still with separate condenser and natural circulation of water vapor. Fath and Elsherbiny [10] investigated a single sloped basin solar still integrated with an external condenser. The condenser was located in the shadow zone of the still. They found that the still efficiency was increased. El-Bahi and Inan [11,12] developed a solar still integrated with a separate condenser with double glazing and another solar still integrated with a separate condenser with one glass cover. The condenser was located on the shaded side of the evaporator. A vertical steel reflector was fitted in the top part of the evaporator cast a shadow over the condenser system. It was found that the performance of the solar still with a condenser was better than the one which had no condenser. Gnanadason et al. [13] reported that using nanofluid in a solar still increases its productivity. They examined the effects of adding carbon nanotubes (CNTs) to the water inside a single basin solar still. Their results obtained that adding nanofluid increased the efficiency by 50%. In our recent study, Kabeel et al. [14] conducted the experimental attempts to improve the solar still productivity by providing vacuum fan with integrating an external condenser to the basin and also by using the aluminum oxide–water nanofluid. The results revealed that providing vacuum increased the distillate water productivity by about 53.2%. In addition, using the aluminum oxide– water nanofluid improved the solar still water yield by about 116%,
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Nomenclatures English symbols A area, m2 Cp specific heat, J/kg K F fan Fs fan speed, rpm FP fan power, W Gr Grashof number h heat transfer coefficient, W/m2 K hfg enthalpy of evaporation at Tw , J/kg K thermal conductivity, W/m.K I ( t) solar radiation on inclined surface, W/m2 L perimeter, m m mass, kg M molecular mass, g/mol P partial pressure, N/m2 Pr Prandtl number Ra Rayleigh number St sticking coefficient t time, S T temperature, °C U heat loss coefficient from basin and sides to ambient, W/m2 K V wind velocity X insulation thickness, m Greek Symbols α absorptivity β volumetric thermal expansion ε emissivity ρ density, kg/m3 σ Stefan–Boltzmann constant, 5.6697 × l0−8 W/m2 K4 δ characteristic length, m ηd the daily efficiency of the still μ dynamic viscosity, N/m2 .s ϕ nanomaterial concentration τ transmissivity Subscripts a ambient b basin bf base fluid c convective e evaporative eff effective fw feed water g glass i insulation nf nanofluid p nanoparticle r radiative s sky v vapor or volume fraction w water or weight fraction
Fig. 1. Schematic diagram of the solar desalination system.
(CrWSS) with internal reflectors, integrated with external condenser and using different types of nanomaterials was investigated by Omara et al. [16]. Investigations clarified that the yield of CrWSS with reflectors when providing vacuum was about 180% higher than that of conventional solar still (CSS). In addition, using the cuprous and aluminum oxides nanoparticles increases the yield of CrWSS with reflectors when providing vacuum by about 285.10% and 254.88%, respectively. Generally, the experimental researches are so costly and time consuming. Therefore, some researchers have focused on mathematical modeling, to find important parameters and better designs of solar stills. Kianifar and Mahian [17] investigated the effect of using low powered fan and reported an improvement in productivity. Al-hussaini and Smith [18] studied theoretically the effects of applying a vacuum inside the solar still on its productivity. Their results showed that the water yield could be increased by 100% when considering complete vacuum. In addition to mathematical modeling, some investigations have been done based on computational fluid dynamic (CFD). CFD has relatively low cost and high speed, while it can also simulate real or ideal conditions. A single sloped passive solar still with an external condenser has been studied theoretically by Madhlopa and Johnstone [19]. Because being the effect of nanomaterials and external condenser on the performance of solar still needs more theoretical research. Then, the main objective of this study is to build a numerical modelling which has the ability of expectation of the effects of nanomaterials and external condenser on the performance of solar still and also has the ability of optimizing the performance based on the considered examined parameters. The considered operating parameters of this investigation are providing low pressure (external condenser) and also using different types of nanomaterials (aluminum oxide (Al2 O3 ) and cuprous oxide (Cu2 O)) with various concentrations (from 0.02 to 0.3%). The output parameters of the solar still performance are the hourly yield and the daily efficiency of the solar stills. So, they are evaluated at various operating conditions. 2. System description and operating principle
with operating the vacuum fan. In another study, Kabeel et al. [15] studied the effects of using the solid nanoparticles of Cu2 O and Al2 O3 with different weight fraction concentrations on the performance of a single basin solar still with and without providing vacuum. The results showed that using the Cu2 O and Al2 O3 nanoparticles, increased the distilled water productivity by about 133.64% and 93.87% and 125.0% and 88.97% with and without operating the vacuum fan, respectively. The performance of hybrid solar distillation system comprising of corrugated wick solar still
A schematic diagram of the examined solar still is shown in Fig. 1. The bottom and side walls of the basin are considered to be well insulated. Purified drinking water is collected from the distilled output collector. The solar radiation transmitted through the glass cover and basin water is absorbed by the basin liner; hence, its temperature increases. Part of thermal energy is transferred by convection to the basin water and the other will be lost by conduction to the ground. The basin water transfers heat to the inner surface of the glass cover by radiation, convection and evaporation.
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The heat is conducted through the cover and then transfers from the upper surface of the glass cover to surroundings by radiation to the sky and by convection to ambient air. The condensed water vapor trickles down the inclined glass cover to an interior collection trough. From there it is collected into the storage container through distilled output collection port. On the other hand, the fan makes better evaporation rate and lower pressure inside the basin still which cause some more wetted or evaporated air taken out to the condenser through the condensation coil path to be taken as distilled water from the condenser output. The conventional solar still is completely similar to the modified one for the thermal energy distribution.
I (t )Ab αb τg τw = mbC pb .
3
d Tb + Qc.b−w + Qloss dt
(1)
The transient energy balance equation for the basin water is given as [22,23],
d Tw + Qc.w−g + Qr.w−g dt + Qe.w−g + Q f w
I (t )Aw αw τg + Qc.b−w = mwC pw
(2)
Energy balances for the glass cover [22],
d Tg + dt Qr.g−s + Qc.g−a
I (t )Ag αg + Qc.w−g + Qr.w−g + Qe.w−g = mgC pg .
3. Statistical test parameters
(3)
The hourly yield is given by the following equation, 1. The EFF test is proposed to measure the agreement between the predicted and reference values, Mayer and Butler [20].
(Mean Square Error (MSE )) EF F = 1 − V ( ariance o f re f erence data) Negative EFF test values indicate that there is no agreement. EFF Test values between 0 and 1 indicate that there is agreement; preferable values are those that are close to unity. 2. Paired-difference t-test, Schlotzhauer [21]. A paired t-test is conducted to elucidate the significance of the differences of the mean values of each evaluation parameter prior to and post modification to confirm whether or not the stepped solar still system is enhanced post-modification. Some of the evaluation parameters that are to be tested include evaporation heat transfer coefficient, convective heat transfer coefficient, radiative heat transfer coefficient, productivity and efficiency of solar still. For the t-test, there are two possible results based on the corresponding p-value. If it is less than the reference probability, the result is regarded as being statistically significant, and there is no null hypothesis. However, if it exceeds the reference probability, the result is regarded as not being significant. In this study, the reference probability is assumed to be 0.05. The paired t-statistic is calculated and converted to determine the p-value using the ttable or another utility program. The test statistic for the paireddifference t-test is calculated and provided for in a manner similar to equation, Schlotzhauer [21].
S t = X¯ − μ0 / √ n
where X¯ the average difference, s is the standard deviation of the difference, and n is the sample size. In paired testing, the null hypothesis is assumed when μ0 is 0, meaning that there are no differences between groups. 4. Theoretical analyses In this section, a complete mathematical model that describes the heat and energy processes in the basin solar still is presented as shown in Fig. 1. These models will assist to determine the hourly distillate output productivity and the daily efficiency of the solar stills. The technical specifications of the solar still and parameters used in the computer model are summarized in Table 2. 4.1. The conventional basin still The analytical results are obtained by solving of the energy balance equations for the absorber plate, saline water and glass cover of the solar still. The saline water temperature, basin plate temperature and glass cover temperature can be evaluated at every instant. Energy balance for the basin plate [22],
˙ ew = he.w−g m
(Tw − Tg ) × 3600 hfg
,
(4)
where, he.w − g is the evaporative heat transfer coefficient between water and glass and hfg is the water latent heat. The convective heat transfer between basin and water [24,25],
Qc.b−w = hc.b−w Ab (Tb − Tw ),
(5)
where, hc.b − w is the convective heat transfer coefficient between basin and water and Ab is the basin base surface area. The convective heat transfer coefficient between basin and water, hc,b-w , is given by the following equation, [26].
hc.b−w = 0.54
K w
δ
Ra0.25 ,
(6)
where, Kw is the water thermal conductivity and δ is the characteristic length. In addition, the Rayleigh number, Ra, is calculated from the relation:
Ra =
2 3 g.β (Tb − Tw ).ρw δ
.
μ
2 w
μw .C pw Kw
where, the thermal expansion coefficient of the nanofluid is given as: β = T +2Tw The heat losses by convection through the basin base b
and sides to the ground and surrounding, are given as [27],
Qloss = Ub (Ab + Asides )(Tb − Ta )
(7)
where, U b = Ki and Ki and Li are thermal conductivity and the Li thickness of the insulation; respectively [28]. The convective heat transfer between water and glass is given by [24,25],
Qc.w−g = hc.w−g Aw (Tw − Tg )
(8)
where the convective heat transfer coefficient between water and glass, hc,w − g , is given by [29],
hc.w−g = 0.884 Tw − Tg +
(Pw − Pg )(Tw + 273.15) 268900 − Pw
13
,
(9)
where, Pw and Pg is the partial pressure of the water and glass, respectively. The radiation heat transfer from the basin to glass cover is predicted from [23],
Qr.w−g = σ
εe f f Aw (Tw + 273.15)4 − (Tg + 273.15)4 ,
(10)
where, σ is the Stefan–Boltzmann constant, ε eff is the water-glass effectiveemissivity and Aw is the water surface area. The evaporative heat transfer between water and glass is given by [24,25],
Qe.w−g = he.w−g Aw (Tw − Tg )
(11)
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A.E. Kabeel et al. / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–10 Table 1 Measured specifications of the cuprous and aluminum oxides nanoparticles. Material
Chemical symbol
True density (kg/m3 )
Thermal conductivity (W/m.K )
Average particle size (nm)
Aluminum oxide Cuprous oxide
Al2 O3 Cu2 O
3900 6320
46 76.5
10 − 14 10 − 14
Table 2 Technical specifications of the solar still [37].
where, the evaporative heat transfer coefficient between water and glass, he,w − g , is given by [24,25],
he.w−g =
0.016237 × hc.w−g (Pw − Pg ) (Tw − Tg )
(12)
Category
Property (Unit)
Value
Basin
αb
0.95 1 460 7800 14 5 0.002016 3 30° 0.05 0.85 0.88 1.18 840 2500 0.05 0.9 0.96 1 4190 1027 0.613 2,350,0 0 0
It is also assumed that, the makeup water is at atmospheric temperature and takes heat from basin. The heat taken by the replaced water is estimated from [23],
Q f w = meC p w (Tw − Ta )
(13)
where, Cpw is the specific heat of water at constant pressure. The radiative heat transfer between glass and sky is given by [24,25],
Qr.g−s = hr.g−s Ag (Tg − Ta ),
Glass
(14)
hr.g−s = εg σ
(Tg + 273.15) − (Ts + 273.15) 4
4
Water
Tg − Ta
(15)
(16)
The convective heat transfer between glass and ambient air, Qc.g − s is given by [30],
Qc.g−a = hc.g−a Ag (Tg − Ta )
(17)
where Ag is the glass surface area. In addition, the convective heat transfer coefficient between glass and ambient, hc.g − s , is taken from [18],
hc.g−a = 5.7 + 3.8 V
(18)
In the case of providing vacuum/low pressure inside the solar still [18], the heat transfer coefficient due to convection, between water and glass cover, becomes zero. Since there is no diffusion of vapor through the air, the evaporation heat transfer coefficient is calculated using the thermal balance equation at the glass cover. Steady state heat transfer through the glass is assumed at the glass cover without any appreciable error. So, he.w − g is found by [18];
(19)
where, Tw and Tg at the end of the interval are then found using Eqs. (2) and (19) again. Eq. (4) is then used to obtain the produced distilled water from the modified solar still with vacuum or low pressure. 4.3. The modified basin still when using nanofluids In the case of using the cuprous oxide and aluminum oxide nanoparticles, the thermo physical properties of nanofluids for a volume concentration (φv ) are calculated at the average bulk temperature of the nanofluid as detailed below. The density of nanofluids (ρnf ) is determined using Pak and Cho’s equation [31],
ρn f = (1 − ϕv )ρb f + ϕv ρ p ,
where φv is the volume concentration of the nanoparticles in the basin water. The effective thermal conductivity of dilute nanofluids (Knf ) can also be evaluated using the Maxwell model [32] for nanofluids with volume fraction less than unity. Maxwell equation is given by;
K p + 2Kb f + 2ϕv K p − Kb f Kn f = Kb f K p + 2Kb f − ϕv K p − Kb f
4.2. The modified basin still with providing low pressure
(hc.g−a + hr.g−s )(Tg − Ta ) he.w−g = − hr.w−g , (Tw − Tg )
αw τw εw
Aw (m2 ) Cp w (J/kg.K) ρ w (kg/m3 ) Kw (W/m.K) hfg w (J/kg.K)
The sky temperature is taken from [29],
Ts = Ta − 6.0
αg τg εg
Ag (m2 ) Cp g (J/kg.K) ρ g (kg/m3 )
where, the radiative heat transfer coefficient between glass and sky, hr,g − s , is given by [24,25],
Ab (m2 ) Cp b (J/kg.K) ρ b (kg/m3 ) Ub (W/m2 .K) Pb (m) Asides (m2 ) Glass thickness. mm Slope of glass
(20)
(21)
The specific heat of the nanofluid (Cpnf ) is calculated using Xuan and Roetzel’s equation [33],
(ρC p)n f = (1 − ϕv )(ρC p)b f + ϕv (ρC p) p
(22)
The viscosity of the dilute nanofluid (μnf ) can also be determined using the viscosity correlation proposed by Einstein [34],
μn f = μb f (1 + 2.5ϕv )
(23)
The volume fraction of the nanoparticles (ϕ v ) can be estimated as a function of the weight fraction of the nanoparticles (ϕ w ) in nanofluid by the following correlation [35],
1 − ϕv
ϕv
=
1 − ϕw
ϕw
ρp ρb f
(24)
It is well known that the properties of the nanofluids depend on the shape and size of nanoparticles. The aluminum and cuprous oxides nanoparticles were used for the preparation of the nanofluids. The specifications of the nanoparticles are obtained in Table 1. The aluminum and cuprous oxides nanoparticles were characterized by X-ray diffraction technique (XRD-60 0 0, Shimadzu). To make the nanoparticles more stable and remain more dispersed in the basin water and to minimize the nanoparticles aggregation to improve dispersion behavior, Triton X-100 is used as a dispersant. The optimum of homogeneously dispersed nanoparticle powders
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was found at about 0.021% wt Triton X-100. Therefore, we choose Triton X-100 concentration equal to 0.021% [36]. The daily efficiency, ηd , is obtained by the summation of the hourly condensate production (m), multiplied by the latent heat (hfg ), hence the result is divided by the daily average solar radiation I(t) over the whole area (A) of the device [30]:
ηd =
˙ × hfg m A × I (t ) + F P
(25)
where FP is the consumed power by the vacuum/low pressure fan. 5. Numerical simulation assessment A mathematical model was developed by the computer program, written in FORTRAN, to evaluate the performance of the solar still. This computer program was developed to solve the energy balance equations of the still elements for various nanomaterial concentrations in the brine and for providing low pressure inside the still too. The temperatures of the glass cover, water and absorber plate can be evaluated every time by solving the energy balance equations for the glass cover, brackish water and absorber plate of the solar still, respectively. The fourth order Runge–Kutta method was used to solve the system of nonlinear ordinary differential equations from Eqs. (1) to (18) to find Tg , Tw , Tb and the quantity of distilled water per hour at any time. Numerical calculations were started at 9:00 a.m. assuming the initial temperatures of various components of the still to be equal to ambient temperature which equals to 296 K. Using known initial values for the various temperatures, different internal and external heat transfer coefficients were calculated. Using these values of heat transfer coefficients along with climatic parameters, the basin liner, basin water and outer glass cover temperatures were calculated for a time interval t (1.0 s.) as stated in the program. The hourly productivity and rate of heat transfer from the basin liner Qc,b-w were then calculated by using Eqs. (4) and (5), respectively. The procedures were repeated for an additional time interval t and so on, until 9:00 a.m. of the next day. The daily efficiency was then calculated by using Eq. (25). Numerical calculations had been performed in order to study the effects of using different types of nanomaterials with various concentrations in saline water of the basin still in the range from 0.02 to 0.3%. In addition, the effects of providing low pressure on the productivity of the solar still were also investigated. Thermal performances for the conventional and modified stills were compared under the same metrological conditions. In an attempt to validate the proposed mathematical models, the obtained theoretical results for both the conventional and modified stills were compared with the experimental results presented in the literature [14,15] under the same climatic and operating parameters. The experimental study of Ref. [15] was conducted for a range of weight fraction concentrations from 0.02 to 0.2% only. 6. Model validation The model is validated by comparing theoretical results obtained in the present work with the corresponding results obtained from experimental work by [14,15]. During the current simulation, the experimental determined operational and metrological parameters are used. Fig. 3 shows theoretical and experimental comparison of hourly variations of freshwater productivity for the conventional and modified solar stills with providing low pressure only and when using the nanomaterials of cuprous and aluminum oxides. It can be seen from the results of Fig. 3 that the agreement between the present theoretical results and those found in the literature [14,15] is fairly good. Even though, there are some overestimation by the model due to uncertainties in correlations used for
5
calculations of various heat transfer coefficients and solar radiation incident on the stills covers. Temperature gradient within the basin water, basin liner, and glass cover and also heat capacity of the insulation materials are not considered in the mathematical analyses and they represent another source of error. The deviations between experimental and theoretical results for the conventional still are ranged from 5 to 9%. In addition, the deviations for the modified still with providing low pressure only are ranged from 7 to 12% and that when using nanofluids are ranged from 8 to 15%. In order to validate this further, a statistical test can be used. The results of the statistical EFF-test were found to be 98% and 97% – which is almost similar to unity – for the conventional and modified solar stills, respectively.
7. Results and discussions The mathematical relations presented in the theoretical analysis section were employed to determine the performance of the proposed unit. Numerical calculations have been performed for the investigated stills on typical days from September to December 2013, in Kafrelsheikh (Egypt).
7.1. Effect of solar radiation Fig. 2 shows the variation of glass, basin water, and ambient temperatures and solar radiation for conventional and modified stills as affected by ambient conditions with respect to time of the day. The solar radiation increases in the morning hours reaching its maximum values around midday and then decreases in the afternoon. It can be observed from Fig. 2a that the maximum temperature is obtained during the period from 12 a.m. to 2 p.m. Also, it is observed that the temperatures at all points increase in the morning hours to reach maximum value around midday before it starts to reduce late in the afternoon. In addition, it is obtained for the day time that the water temperature in the modified still when providing low pressure only is less than that of conventional still by 0.0–0.75 °C but the glass temperature in the modified still is less than that of conventional still by 1.65–3.25 °C. As a result of this difference, the ability of condensation, then the production rate in the modified still is more than that of conventional still, and for the night time the production rate of the modified and conventional stills is about the same quantity. It is observed from Fig. 2b that when using the cuprous oxide nanoparticles with a concentration of 0.2% as weight fraction, the saline water temperature of the modified still was more than that of the conventional type by 0.5–4.5 °C and 1.35–5.5 °C with and without operating the fan at a speed of 1350 rpm from 9:00 a.m. to 17:00 p.m., respectively. While the glass temperature of the modified still was increased by 0.25–1.2 °C more than that of the conventional one and is decreased by another 0.35–1.35 °C without and with operating the fan during the daytime respectively. It is observed from Fig. 2c that when using the aluminum oxide nanoparticles with a concentration of 0.2%, the basin water temperature of the modified still was more than that of the conventional type by 0.5–2.7 °C and 1.35–3.55 °C with and without operating the fan at a speed of 1350 rpm from 9:00 a.m. to 17:00 p.m., respectively. While the glass temperature of the modified still was increased by 0.4–1.1 °C more than that of the conventional one and is decreased by another 0.45–1.25 °C without and with operating the fan during the daytime, respectively.
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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Fig. 3. Hourly evaporation and convective heat transfer coefficients Using Cu2 O, ϕ = 0.02%.
7.2. Comparison of hourly evaporation and convective heat transfer coefficients
Fig. 2. The hourly temperature variation and solar radiation for the modified and conventional stills.
The hourly evaporation and convective heat transfer coefficients of conventional still and modified still with cuprous oxide nanoparticles at a concentration of 0.2% and without operating the fan are illustrated in Fig. 3. The evaporative and convective heat transfer coefficients values of modified still with cuprous oxide always exceed the values of conventional still. Evaporative and heat transfer coefficient values of conventional still and modified still varies from 8 to 35 W/m² °C and 8 to 48 W/m² °C during the day, respectively. Convective heat transfer coefficient values of conventional
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7
Table 3 The amount of energy input/output and energy flows for modified still with cuprous oxide. h 9 10 11 12 13 14 15 16 17
Tw (°C) 36 48 60 62.5 65 63 57.5 50 44
Tg (°C) 26 35 38 40 43 40 38 33 30
Tb (°C) 37 50 62 65 67.5 65.5 60 52 46
Ta (°C) 27 27 28 28 30 29 29 28 28
Energy input (W) A I(t) Qfw
Energy output (W) Qr.g − s Ag Rg I(t) m˙ h f g
Qc.g − a
Qloss
Energy flows (W) Qe.w − g Qc.w − g
Qr.w − g
Qc.b − w
600 750 795 810 760 640 420 180 35
0 130 391 489 522 456 378 274 204
34.9 42.2 49.5 56.9 56.5 47.9 41.8 33.8 29.9
55.5 140.1 165 154 163.7 153.3 141.8 133 121.6
16.3 113 413.4 649.8 540.8 369.8 224.2 39.7 15.54
4.8 39.2 63 53.3 61 55.6 51.1 47.3 42.3
219.8 549.5 373.6 527.5 527.5 461.6 351.7 196 66
0 2.3 8 9.9 11.3 9.5 7.6 5.3 2.3
still and modified still varies from 1.65 to 2.58 W/m² °C and 1.65 to 2.8 W/m² °C, respectively. 7.3. External condenser The hourly variations of freshwater productivity per unit area for the modified solar still with external condenser and the conventional solar still are illustrated in Fig. 4a. As expected the hourly variations curve of freshwater productivity is similar to that of solar radiation curve. Also, the figure indicates that the amount of accumulated distillate water for the modified solar still is greater than that of the conventional still. This is mainly due to the existence of the fan that causes higher evaporation rate inside the still. The fan creates an amount of turbulence of the water vapor content of the air above the saline water that can take evaporated water vapor away from the saline water surface. In addition, the fan takes the non-condensable gases away from the still to the condenser, Ref. [14]. In addition, the condenser decreases the heat loss by convection from water to glass as the condenser acts as an additional and effective heat and mass sink. The theoretical results indicated that integrating the solar still with external condenser increases the distillate water yield by about 56% over the conventional still. 7.4. Nanomaterials Nanofluids improve the heat transfer characteristics and evaporative properties of the water. Addition of nanoparticles to the basin water improves the thermal conductivity of the mixture of water and nanomaterial (nanofluid), as well as the convective heat transfer coefficient. In addition, the nanofluids have higher storage material properties than that of water only. For these reasons, the ability of evaporation and condensation, then the production rates in the modified still are more than that of the conventional type, as shown in Fig. 3b and c. Table 3 indicated the amount of energy input/output and energy flows for modified still with cuprous oxide. The theoretical results indicated that when the cuprous oxide nanoparticles are used at a weight fraction concentration of 0.02%, the basin water temperature of the modified still was more than that of the conventional type by 0.0–2.5 °C when the fan was off and by 0.0–2.0 °C when operating the fan. While the glass temperature of the modified still was increased by 0.0–0.35 °C more than that of the conventional one and is decreased by 0.0–0.75 °C without and with operating the fan during the daytime, respectively. In this case, the daily productivity reached approximately 1750 and 2480 ml/m2 /day for the conventional still and 3620 and 4090 ml/m2 /day for the modified still with and without operating the vacuum/low pressure fan at a speed of 1350 rpm during the daytime respectively as shown in Fig. 4b. The increase in distillate production for the modified still was also 106.86% and 64.92%
49.6 61.1 65.3 66.9 62.8 52.8 35.6 14.8 12.2
41.4 48.3 54.9 56.9 59.3 57.9 56.6 52.6 18.2
1.2 14.3 26.3 23.5 25.1 21.5 18.3 14.7 12.2
higher than that for the conventional still respectively as illustrated from the figure. For using aluminum oxide nanoparticles at a weight fraction concentration of 0.02%, the basin water temperature of the modified still was more than that of the conventional type by 0.0– 2.0 °C when the fan was off and by 0.0–1.6 °C when the fan was on. While the glass temperature of the modified still was increased by 0.0–0.25 °C more than that of the conventional one and is decreased by 0.0–0.55 °C without and with operating the fan during the daytime, respectively. In this case, the daily productivity reached approximately 1545 and 1290 ml/m2 /day for the conventional still and 2875 and 1975 ml/m2 /day for the modified still with and without operating the vacuum/low pressure fan at a speed of 1350 rpm during the daytime respectively as shown in Fig. 4c. The increase in distillate production for the modified still was also 86.08% and 53.10% higher than that for the conventional still respectively as observed from the figure. 7.5. Nanomaterial concentrations The theoretical results indicated that when using the Cu2 O and Al2 O3 nanoparticles, the saline water temperature of the modified still was more than that of the conventional one by different values of degrees. These values of degrees depend on the type of the nanoparticles, the concentration of these nanoparticles in the basin water, and either the fan is on or off. The glass temperature of the modified still was either less than or more than that of the conventional one by different values of degrees according to the same above parameters. The comparison between using the Cu2 O and Al2 O3 nanoparticles at different weight fraction concentrations with and without operating the fan is also numerically carried out as shown in Fig. 5. It can be observed from the figure that the increase in productivity as a percentage increases with increasing the concentration of nanoparticles for both of Cu2 O and Al2 O3 . But when using the Cu2 O nanoparticles the increase in productivity is greater than that when using the Al2 O3 nanoparticles for the same concentration. As it can be cleared from the figure that the agreement between the present theoretical and numerical results and those found in the literature [15] is fairly good. In addition, from the numerical constructed program, the authors could investigate the effect of using Cu2 O and Al2 O3 nanoparticles with higher concentrations in the basin water than 0.20% which is found in the literature [15] on the performance of the solar stills as illustrated in Fig. 5. 7.6. Daily efficiency The daily efficiency of the desalination system is theoretically evaluated. Variations of the daily efficiency for the investigated conditions are shown in Fig. 6. The daily efficiency of the modified solar still when integrating the external condenser only and when
Please cite this article as: A.E. Kabeel et al., Theoretical with experimental validation of modified solar still using nanofluids and external condenser, Journal of the Taiwan Institute of Chemical Engineers (2017), http://dx.doi.org/10.1016/j.jtice.2017.01.017
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Fig. 5. Variations of increase in productivity when using nanofluids with and without fan.
Fig. 4. Comparisons of theoretical and experimental productivity.
using the Cu2 O and Al2 O3 nanoparticles at different concentrations with providing low pressure are illustrated in Fig. 6a. While the daily efficiency of the conventional solar still and the modified still when using the Cu2 O and Al2 O3 nanoparticles at different concentrations without providing low pressure are presented in Fig. 6b. It can be observed that the trend of the daily efficiency curve, Fig. 6, is similar to that of variations of increase in the productivity curve, Fig. 5. It can be observed from Fig. 5 that the maximum daily efficiencies of 84.16% and 73.85% occurred when using Cu2 O and Al2 O3 nanoparticles at the concentration of 0.20%, respectively with operating the fan. Applying these conditions improves the thermal properties of the basin water, and hence improves the evaporation and condensation rates yielding an increase in distillate water. In addition, the daily efficiency for the modified still when providing low pressure only without using nanomaterials is 46.23% as obtained from Fig. 6a and that for the conventional still equals to 33% as shown in Fig. 6b.
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Table 4 The results of the statistical paired t-test.
1 2 3 4
Evaluation parameters
t-test results
Convective heat transfer coefficient Evaporation heat transfer coefficient Productivity of still Efficiency of still
There There There There
is is is is
a a a a
significant significant significant significant
difference difference difference difference
between between between between
the the the the
mean mean mean mean
values values values values
before before before before
and and and and
after after after after
modification modification modification modification
posed for calculations may be used for investigating the thermal performance of solar stills with these modifications with a reasonable accuracy. 7.7. Significance of enhancement at each evaluation parameters The results of the statistical paired t-test presents in Table 4. It can be seen that the significant differences between the mean values of the implemented evaluation parameters prior to and post modification of the solar stills are validated. Based on the results, it can be concluded that the proposed modified solar still with nanofluids that are enhanced with superior design concepts is excellent in the context of enhancing the performance of the solar still. 8. Conclusions The main conclusions may be summarized as follows: 1. The distillate productivity of the solar still increased when providing low pressure and also when using nanofluids. 2. The results showed that the modified basin still had a daily efficiency of 84.16% and 73.85% when using the cuprous oxide and the aluminum oxide nanoparticles, respectively, with operating the fan. And the daily efficiency when providing low pressure only was 46.23%. In addition, the conventional stills’ daily efficiency was 33%. The results of this study can be considered to optimize the design of solar stills, in which, it can possible to utilize the energy consumption in the best manner by using nanofluids and integrating an external condenser. References
Fig. 6. Daily efficiency variation for the modified still when using nanomaterials at different concentrations with and without fan.
It can be noticed from the figure that by increasing the weight fraction concentration of the nanomaterial, the daily efficiency for the modified solar still increases till ϕ = 0.12% and ϕ = 0.16% when using the Cu2 O nanoparticles and ϕ = 0.16% and ϕ = 0.20% when using the Al2 O3 nanoparticles. After these concentrations, the efficiency has no marked increase and seems to be constant. The comparisons shown in Figs. 3–5 clearly confirm that the proposed mathematical model for the modified still when providing low pressure and when using nanofluids and the method pro-
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