Analytical characteristic equation of nanofluid loaded active double slope solar still coupled with helically coiled heat exchanger

Energy Conversion and Management 135 (2017) 308–326

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Analytical characteristic equation of nanofluid loaded active double slope solar still coupled with helically coiled heat exchanger Lovedeep Sahota a,⇑, Shyam a, G.N. Tiwari b a b

Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Bag Energy Research Society (BERS), SODHA BERS COMPLEX, Plot No. 51, Mahamana Nagar, Karaudi, Varanasi (UP) 221005, India

a r t i c l e

i n f o

Article history: Received 10 November 2016 Received in revised form 19 December 2016 Accepted 27 December 2016

Keywords: Active solar still Nanofluid Heat exchanger Thermal energy and exergy efficiency

a b s t r a c t Nanofluids are embryonic fluids and promising thermal energy carrier in solar thermal applications due to their superior thermo-physical and optical properties. In present communication, an analytical expression of the characteristic equation of two different systems viz. (A) active double slope solar still coupled with series connected partially covered N photovoltaic thermal flat plate collectors (N-PVT-FPC) and operating without helical heat exchanger; and (B) active double slope solar still coupled with series connected partially covered N-PVT-FPC and operating with helical heat exchanger has been developed. Analysis has been executed for 0:25% concentration of CuO, Al2O3, TiO2-metallic nanoparticles; four number of collectors; 100 kg basin fluid (BF/NF) mass and 0.03 kg/s mass flow rate. The maximum values of instantaneous gain thermal energy efficiency ðCuO 80:18%; Al2 O3 71:67%; TiO2 74:92%Þ and instantaneous loss thermal energy efficiency ðCuO 64:12%; Al2 O3 59:11%; TiO2 64:77%Þ of the system (A) are found to be significantly higher in comparison the basefluid ðgain 66:81%; loss 52:42%Þ. The productivity of system (A) and system (B) are ðCuO 32%; Al2 O3 19:23%; TiO2 6:47%Þ and ðCuO 31:49%; Al2 O3 26:4%; TiO2 7:26%Þ respectively, higher in comparison to the case using basefluid (water). Moreover, thermal energy and exergy; and thermal exergy efficiency has been evaluated for both the systems. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Potable water is essential for survival of all the creatures on the planet Earth. Moreover, the most important uses of water are in three sectors, viz. (i) domestic, (ii) agriculture and (iii) industrial. Various factors viz. climate change, deforestation, limits to water supply, uneven distribution of water resources, population and pollution; and becoming scare with time which leads to severe water crisis in many parts of the world. Many active organizations like United Nations Development Programme (UNDP), World Health Organization (WHO) and the World Bank (WB) putt efforts to promote the promising projects and policies with time to full-fill the requirement of potable water. Nowadays, advances in science and engineering developed various high and medium techniques (non-conventional methods) to disinfect the contaminated water to produce the potable water. Whereas, solar distillation (passive/active) is the most prominent, environment friendly and economically viable technology can be used for potable water production [1,2]. In literature, various ⇑ Corresponding author. E-mail address: [email protected] (L. Sahota). http://dx.doi.org/10.1016/j.enconman.2016.12.078 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

designs of passive solar stills have been reported in order to improve the performance of the passive stills [3–13]. In active solar stills, external thermal energy (hot water) has been fed into the integrated still. For this purpose, force mode of operation is achieved by using mechanical pump which can be run by non-conventional source of energy such as solar thermal technology or photovoltaic (PV) technology. It makes the active solar stills entirely dependent on renewable energy. External thermal energy from circulated fluid can be transferred to the integrated solar still either directly or via heat exchangers. Coiled tubes are effective heat exchanger as compared to straight tube heat exchangers because of their excellent heat transfer performance, compact size and the enhanced turbulence. Helically coiled heat exchangers (large heat transfer area per unit volume) are frequently used and mostly preferred over the straight tubes due to their excellent heat transfer performance, compact size and enhanced turbulence which intern enhances the heat transfer coefficient of the tube’s internal surface. Soliman [14] suggested the concept (high temperature solar distillation) of feeding external thermal energy into the basin of the still from the solar collector. Later, Rai and Tiwari [15] studied the single basin solar still coupled with flat plate collector and

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

309

Nomenclature Am Ac AgE AgW AB Cp C nf C bf Di dp F0 h1g;E h1g;W h1f ;E h1f ;W hEW hef ;E Lg Lb Lp Mf _f m _ bf M Pgi Pf PF 1 PF 2 PF 3 r 11 r 22 T goE T goW T bf T nf T giE hef ;W hba hFPC hHE hb;f hpf hi ho

area of the PV module, ðm2 Þ area of the glazing, ðm2 Þ surface area of condensing cover of east side of solar still, ðm2 Þ surface area of condensing cover of west side of solar still, ðm2 Þ basin area of solar still, ðm2 Þ specific heat of nanoparticle, ðJ=kg KÞ specific heat of nanofluid, ðJ=kg KÞ specific heat of basefluid, ðJ=kg KÞ diameter of the FPC tube (mm) diameter of nanoparticle (nm) collector efficiency factor total external heat transfer coefficient on east side, (W=m2  C) total external heat transfer coefficient on west side, (W=m2  C) total internal heat transfer coefficient on east side, (W=m2  C) total internal heat transfer coefficient on west side, (W=m2  C) internal radiative heat transfer coefficient between glass covers, (W=m2  C) evaporative heat transfer coefficient on east side, (W=m2  C) thickness of condensing cover, ðmÞ thickness of basin, ðmÞ thickness of the absorption plate ðmÞ mass of fluid in the basin of solar still mass flow rate of the fluid ðkg=sÞ yield obtained from the system ðkg=hÞ partial saturated vapor pressure of the inner glass cover, ðN=m2 Þ partial saturated vapor pressure of the fluid, ðN=m2 Þ penalty factor due to glass covers of the module penalty factor due to absorption plate below the module penalty factor due to absorption plate for the portion covered by the glazing outer diameter of the heat exchanger tube (mm) inner diameter of the heat exchanger tube (mm) outer condensing cover temperature of east side solar still, ð CÞ outer condensing cover temperature of west side solar still, ð CÞ basefluid temperature, ð CÞ nanofluid temperature, ð CÞ inner condensing cover temperature of east side of solar still, ð CÞ evaporative heat transfer coefficient on west side, (W=m2  C) heat transfer coefficient between basin liner and ambient air, (W=m2  C) convective heat transfer in the flat plate collector, (W=m2  C) convective heat transfer in the heat exchanger, (W=m2  C) heat transfer coefficient between basin liner and fluid, (W=m2  C) heat transfer coefficient from blackened plate to ambient, (W=m2  C) heat transfer coefficient for space between absorption plate and glazing, (W=m2  C) heat transfer coefficient from top of PV water collector to ambient, (W=m2  C)

ISE ISW ISW Kp kp knf kbf Kg L T nf Tv Ta T giW

DT DSSS DT FPC DT HE Dt U tp;a U L;m U L;c U tc;a U ga U ba U gaE U gaW U tc;p X

solar intensity on east side of the glass cover, ðW=m2 Þ solar intensity on west side of the glass cover, ðW=m2 Þ solar intensity on FPC, ðW=m2 Þ thermal conductivity of the absorption plate ðW=m KÞ thermal conductivity of nanoparticle, ðW=m KÞ thermal conductivity of nanofluid, ðW=m KÞ thermal conductivity of basefluid, ðW=m KÞ thermal conductivity of condensing cover, (W=m  C) length of the helical heat exchanger ðmmÞ fluid temperature, ð CÞ vapor temperature, ð CÞ ambient temperature, ð CÞ inner condensing cover temperature of west side solar still, ð CÞ temperature difference between NF and BF in DSSS, ð CÞ temperature difference between NF and BF at the outlet of PVT collectors, ð CÞ temperature difference between NF and BF in heat exchanger, ð CÞ time interval (s) overall heat transfer coefficient from absorption plate to ambient, (W=m2  C) overall heat transfer coefficient from module to ambient, (W=m2  C) overall heat transfer coefficient from glazing to ambient, (W=m2  C) overall heat transfer coefficient from cell to ambient from the top surface, (W=m2  C) overall heat transfer coefficient between condensing cover and ambient air, (W=m2  C) overall heat transfer coefficient between basin liner and ambient air, (W=m2  C) overall heat transfer coefficient between outer condensing cover of east side and ambient air, (W=m2  C) overall heat transfer coefficient between outer condensing cover of west side and ambient air, (W=m2  C) overall heat transfer coefficient from cell to the absorption plate, (W=m2  C) characteristic length of solar still, ðmÞ

Greek letters ag fraction of solar energy absorbed by condensing cover aB fraction of solar energy absorbed by basin surface af fraction of solar energy absorbed by fluid ac fraction of solar energy absorbed by solar cell sg fraction of solar energy transmitted by top glass cover of the PVT-FPC 2g emissivity of condensing cover 2bf emissivity of the fluid 2eff effective emissivity of fluid r Stefen-Boltzman’s constant, ðW=m2 K4 Þ up volume fraction of nanoparticles (%) gc efficiency of the PVT-FPC collector ð%Þ b packing factor bp thermal expansion coefficient of nanoparticle, ðK1 Þ bnf thermal expansion coefficient of nanofluid, ðK1 Þ bbf thermal expansion coefficient of basefluid, ðK1 Þ lbf dynamic viscosity of basefluid, ðN s=m2 Þ lnf dynamic viscosity of nanofluid, ðN s=m2 Þ qp density of nanoparticle, ðkg=m3 Þ qnf density of nanofluid, ðkg=m3 Þ qbf density of basefluid, ðkg=m3 Þ

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Subscripts a ambient B basin surface gi inner glass cover go outer glass cover f fluid BF/bf basefluid NF/nf nanofluid HE heat exchanger FPC flat plate collector DSSS double slope solar still p particle c convection

found that productivity decreases with increase in mass flow rate. Lawrence and Tiwari [16] analytically analyzed the active solar distillation system under natural circulation mode by incorporating heat exchanger to develop the empirical relation for internal heat transfer coefficients. They found that the integration of collector enhances the operating temperature of the system which intern improves the overall efficiency of the system; also, the efficiency decreases with increase in water depth. Kumar and Tiwari [17] optimized the daily yield, mass flow rate and other parameters for an active double effect solar distillation system. They found maximum yield at 1:8 m=s flow velocity over the condensing cover; also, the overall thermal efficiency decreases with increase in number of collectors due to higher operating temperature range. Gaur and Tiwari [18] optimized the number of PVT collectors of hybrid solar still. They reported that the maximum productivity occurs for N ¼ 4 and 50 kg basin water mass on the basis of exergy efficiency. Eltawil and Omara [19] reported the improvement in the performance of active solar still by integrating PVT-FPC and hot air. Feilizadeh et al. [20] experimentally investigated the annual performance of basin type multi-stage active solar still; and the effect of different number of collectors on the basin area ratio (CBA) on productivity. Their results show that the system coupled with single collector ðCBA ¼ 3:45Þ gives 11:56 kg of distillate output; whereas the addition of second ðCBA ¼ 6:90Þ and third collector ðCBA ¼ 10:35Þ to the system increases the productivity by 96% and 23% respectively in winter conditions. On the other hand, the enhancement in productivity of 48% and 23% were observed on including second and third collector, respectively in case of summer conditions. Shyam et al. [21] derived the analytical expression of temperature dependent electrical efficiency of series connected N-PVT water collectors for two different configurations and conclude that both configurations gives almost same outcomes for large number of series connected PVT water collectors (mass flow rate, ð0:04 kg=sÞ. Later they performed the experiment [22] for the validation of theoretical model and found good agreement between both studies. Jafarkazemi and Ahmadifard [58] reported the theoretical and comprehensive model for energy and exergy analysis of flat plate solar collectors; and experimentally verify the model. They studied the effect of different parameters viz. fluid flow rate and temperature; type of working fluid; and thickness of the back insulation; moreover, they found the optimal working condition of the system. For the improvement in design and performance of the solar stills, the concept of efficiency is really important. Tamini [23] made the first attempt to characterize the performance of solar still and; Boukar and Harmim [24] explicitly explain the characteristic curve for one-sided vertical solar stills. Various researchers extensively developed and analyzed the characteristic equations of the passive solar stills [25–28]. Later, on the basis of annual experi-

e v E W

evaporation vapor east side west side

Abbreviation HTC heat transfer coefficient DSSS double slope solar still FPC flat plate collector NP nanoparticle HE heat exchanger NF nanofluid BF basefluid

mental observations, Dev and Tiwari [29] established the characteristic equation of hybrid (PVT) solar still. Due to lower root mean square (RMS) percentage error, they recommended to use the nonlinear characteristic equation for the thermal testing of hybrid (PVT) solar still over the characteristic equation obtained by matrix method. Tiwari and Sahota [30] reported a detailed review on the energy and economic efficiencies of distillation systems in which characteristic equation of different passive and active solar distillation systems have been analyzed. Nanofluids are the ultrafast heat transfer fluid with various other features (lower pumping power, better stability, superior lubrication, low friction coefficient and erosion), efficiently improves the system performance and found to be promising thermal energy carrier in solar thermal applications in recent times. The better heat transfer capability of nanofluids is due to their superior thermo-physical and optical properties. In literature, researchers extensively investigated the thermo-physical properties of different nanofluids [31–39]; and studied their effect in water heating systems and heat exchangers [40–44]. Moreover, nanoparticles (NPs) can be prepared more attractive by changing their size and shape for the use in various applications. Baker [45] reported that the most probable mode of water heating in solar collector tubes is mixed convection. A one dimensional transient heat transfer analysis has been carried by Chen et al. [46] to examine the efficiency of direct absorber solar collectors with silver NPs; moreover, they analyze the effects of volume fraction, material of the NPs, collector height, solar flux, and solar radiation time. An et al. [47] experimentally investigated the performance of concentrating PVT collector using Cu9S5 (oleylamine solution) nanoparticles in spectral filter to harvest the moderate temperature heat. They found that the PV efficiency of Si-cell itself can be enhanced using Cu9S5 nanofluid as an optical filter in the collector; their proposed PVT collector system gives 17:9% higher overall thermal efficiency as compared to the system without operating optical filter. Mahian et al. [48] studied the performance of micro-channel based solar collector using CuO, Al2O3, TiO2, and SiO2- water based nanofluids. They observed that heat transfer coefficient is higher for all the nanofluids except SiO2-water based nanofluids; also, the linear enhancement in outlet temperature with nanofluids follows the order as CuO > TiO2 > Al2O3 > SiO2water based nanofluids. They also reported that the entropy generation decreases on including NPs; and considerable drop has been found with CuO-water based nanofluids. Mwesigye et al. [49] numerically analyzed performance of a high concentration ratio (CR-118, rim angle 80 ) parabolic trough solar collector by incorporating Cu-Therminol VP-1 nanofluid. They have observed around 12.5% improvement in thermal efficiency of the system on increasing volume fraction from 0 to 6%; also, the entropy generation rates reduce in the receiver on increasing the volume fraction of NPs for some range of Reynolds numbers.

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

Huminic and Huminic [40] summarized the different correlations of convective heat transfer coefficients in heat exchangers (plate heat exchangers, shell and tube heat exchangers, compact heat exchangers and double pipe heat exchangers) for different nanofluids. Khairul et al. [41] analytically studied CuO, Al2O3, and ZnOwater based nanofluids flowing in a helically coiled heat exchanger and reported that the heat transfer coefficient increases with increase in concentration of metallic NPs and volume flow rate while the entropy generation rate decrease. Faizal et al. [50] investigated the thermal performance and cost analysis of nanofluid based solar collector. They reported that an average 200 MJ embodied energy, 2:4 years payback period and around 170 kg less CO2 emissions can be saved from each collector with nanofluids. Sahota and Tiwari [51] studied the effect of different nanofluids on the performance of passive double slope solar still (DSSS) by developing the characteristic equation. From the analysis, thermal energy and exergy; productivity (yield); instantaneous thermal energy and exergy has been found to be higher with Al2O3-water based nanofluid. Some other studies also investigate the effect of NPs on the performance of passive solar stills [52–54] but no such literatures are available on active solar stills. In present communication, the effect of different nanofluids (Al2O3, TiO2, CuO-water) on the performance of following active solar stills has been studied with characteristic curve: System (A): Active double slope solar still without heat exchanger System (B): Active double slope solar still with helically coiled heat exchanger 2. System description Schematic diagram of system (A), system (B) and helically coiled heat exchanger is depicted in Figs. 1–3. The proposed active systems comprises of double slope solar still (east-west oriented) made of fibre reinforced plastic ðarea 2  1 m2 Þ with top cover of toughen glass (inclination 30 ), partially covered (semitransparent)

311

N-PVT-FPC (south facing; inclination 45 ), mechanical pump operated by DC motor, and copper heat exchanger (helical). The heat exchanger must be inserted or dipped properly inside the basin water of DSSS for the proper utilization of its transferred heat into the basin water. Therefore, it is essential to fix the exact position of the heat exchanger inside the DSSS according the basin water depth. To retrieve the maximum solar irradiation, base and sides of the DSSS is painted mat black. The detailed specifications of each component of both the systems are given in Table 1. Attenuation of the solar flux via basin fluid (BF/NF) mass occurs with direct absorption of penetrated solar irradiation. Blackened surface (basin liner) of the still absorbs the rest of the solar irradiation and acts as a thermal energy storage system. It plays a significant role to raise the fluid (BF/NF) temperature by transferring the stored thermal energy to the basin fluid (BF/NF) mass. Assisting metallic NPs interact with electromagnetic waves; produce intense absorption accredited to the electrons mutual oscillation on the surface of the particle termed as plasmon resonance. The resonant frequency can be tuned by tailoring the size and shape of the NPs. Moreover, the energy of incident light is converted to heat after absorption by the NPs. Ultimately, the plasmon resonance of NPs has high absorption modes in the spectral regions of ultraviolet and infrared. Consequently, nanofluids absorb directly the penetrated solar irradiation due to toning between the spectrum of optical absorption (nanofluids) and solar irradiation. At higher concentration, the assisting metallic NPs spread more contributes to higher surface area in the given basin nanofluid/heat exchanger volume raises the nanofluid temperature. Thus, the basin liner, natural circulation mode (external thermal energy transfer), and assisting metallic NPs mutually elevates the temperature of the basin fluid (BF/NF) mass which significantly enhances the internal heat transfer mechanism. After releasing the latent heat, vapors gets condensed at the inner surface of the top cover (toughen glass). Eventually, the condensed potable water droplets drip into the measuring jars at lower ends of the systems [55,56]. Here, it is important to mention that though the mixing of metallic NPs in the basefluid of the conventional solar stills

Fig. 1. Schematic view of active double slope solar still without heat exchanger, system (A).

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Fig. 2. Schematic view of active double slope solar still with heat exchanger, system (B).

Fig. 3. Systematic view of helically coiled heat exchanger (copper).

enhances the productivity but it makes the system more complex due to the problem of sedimentation, dispersion and clustering of NPs which demands or causes complex maintenance of the still. Therefore, some advance and sophisticated equipment have been required to overcome this issue which may increase the cost of the conversional solar stills. Moreover, the separation of metallic nanoparticles from the rejected brine is one of the issues which also cause complex maintenance of the solar stills. Various separation methods have been developed depends on the size, shape, volume fraction, and thermo-physical properties of the metallic nanoparticles; and type/class and thermo-physical properties of the basefluid. Among all, filtration, centrifugation, electrophoresis, magnetic separation, chromatography, and chemical methods are the most widely used techniques for this purpose. Therefore, incorporation of NPs sets the constraints to reuse the rejected brine over a longer period with additional saline water (according to the requirement) in the still to avoid the complexity issue.

3. Thermal modeling Following assumption given by Sahota and Tiwari [54], the characteristic equation of the system (A) and system (B) has been developed as given below: 3.1. System (A): Without operating helically coiled heat exchanger The energy balances of different components of the system (A) are expressed as (a) East side


 AB  hEW ðT giE  T giW ÞAgE 2

ag ISE AgE þ h1f ;E ðT f  T giE Þ ¼


 Kg ðT giE  T gOE ÞAgE Lg

ð1Þ

313

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326 Table 1 Different parameters used in computation. Parameter

Numerical value

Parameter

Numerical value

ag ab aBF ac ap

0:05 0:8 0:6 0:9 0:80 0:89 0.95 0.95

Am Ac Lp Kp Ki Li hi h0 U tc;p

0:605 m2 1:395 m2 0:002 m 64 ðW=m KÞ 0:166 ðW=m KÞ 0:1 m 5:7 ðW=m2 KÞ 9:5 ðW=m2 KÞ 5:58 ðW=m2 KÞ

U tc;a U tp;a U L;m U L;c PF 1 PF 2 PF c

9:20 ðW=m2 KÞ 4:74 ðW=m2 KÞ 7:58 ðW=m2 KÞ 4:52 ðW=m2 KÞ 0:378 0:934 0:955 0:15

b 2g 2bf

5:67  108 ðW=m2 K4 Þ 0:780 ðW=m  CÞ 0:035 ðW=m  CÞ 0:004 0:005 m 0:0045=K 0:33 m 0:95 0:968

r Kg KB Lg Lb b0 X

sg F0 Metallic Al2 O3 nanoparticles Parameter

g0

Numerical value

qp

3

3:89  10 ðkg=m Þ 20 nm

dp bp

3

Parameter

Numerical value

Cp

880 ðJ=kg KÞ

kp

40 ðW=m KÞ

8:1  106 ðK1 Þ

Double slope solar still Area of the glass cover ðAgE and AgE Þ

1:025 m  1:025 m

Basin areaðAb Þ Inclination of the coverðhÞ

2m 1m 30

Flat Plate Collectorsðtube in plate typeÞ Parameter

Numerical value

Parameter

Numerical value 48 kg 0:968 45 0:004 m ðToughenedÞ Dc shunt motor

Area of each collector Tube material Tube diameter Plate thickness Riser-outer diameter Riser thickness

0:56  103

Thickness of insulation Weight of the collector Collector efficiency factor Angle of Collectors Thickness of top glass Motor used for water pump

ð18 V;40 W and 2800 rpmÞ Spacing between two risers Effective area of collector under PV module

0:112 m

effective area of collector under glass

1:34 m2

0:66 m2

PV Module (under standard test conditions) Area of single solar cell Size of PV module No of solar cells

0:007 m2 1:25 m  0:55 m 36

Fill factor Efficiency of module Max Power Rating Pmax

0:8 12% 40 W

Helical heat exchanger (copper) Length of the heat exchanger Diameter of the coil tube

0:937 m 0:0125 m

Diameter of the coil Number of turns

0:045 m 12

2

2:00 m Copper tubes 0:0125 m 0:002 m 0:0127 m


 Kg ðT giE  T gOE ÞAgE ¼ h1gE ðT goE  T a ÞAgE Lg (b) West side




ag ISW AgW þ h1f ;W ðT f  T giW Þ

AB 2

ð2Þ

ab ðISE þ ISW Þ ¼ 2hb;f ðT b  T f Þ þ 2hba ðT b  T a Þ

 hEW ðT giE  T giW ÞAgW

½A þ T f B H



 dT f AB AB ¼ af ðISE þ ISW Þ þ 2hb;f ðT b  T f Þ dt 2 2

 AB AB  h1f ;W ðT f  T giW Þ þ Q_ uN  h1f ;E ðT f  T giE Þ 2 2

ð3Þ

Mf C f

ð4Þ

ð8Þ

where Q_ uN ¼ Ac F 0 ½ðasÞN;eff Ic  U LN ðT f  T a Þ. Solving Eqs. (7) and (8) using Eqs. (5) and (6), one can get

dT f þ a1 T f ¼ f 1 ðtÞ dt

ð5Þ

and

T giW

ð7Þ

(d) Water mass

On solving Eqs. (1)–(4), one can get

T giE ¼

Unknown terms, A; A0 ; B; B0 ; and H in above equations are given in Appendix A. (c) Basin liner




 Kg ðT giW  T gOW ÞAgW ¼ Lg
 Kg ðT giW  T gOW ÞAgW ¼ h1gW ðT goW  T a ÞAgW Lg

0:1 m

ð9Þ

The solution of first order differential Eq. (9) can be written as

½A0 þ T f B0  ¼ H

ð6Þ

Tf ¼

f 1 ðtÞ ð1  ea1 Dt Þ þ T f 0 ea1 Dt a1

ð10Þ

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where T f 0 is the basin (BF/NF) temperature at t ¼ 0 and f ðtÞ is the average value of f ðtÞ for the time interval 0 and t.




f 1 ðtÞ ¼

 Ab n ½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ awb ÞISW ðtÞ 2H

U g1;eff ¼ H011 ; F 0g1 ¼

þ Ac F 0 ðasÞN;eff Ic ðtÞ þ T a ðH1 þ H2 þ H3 þ H4 þ H5 Þ

¼ o

ð11Þ


a1 ¼

 Ab ½h1bf ;E ðE1 þ E2 Þ þ h1bf ;W ðE01 þ E02 Þ þ ðU ba Ab þ Ac F 0 U L;N Þ 2H ð12Þ

" # PF 2 ðasÞm;eff F Rm 1  ð1  K k;A ÞN Am F Rm U L;m ; K k;A ¼ ; ðasÞN;eff ¼ N K k;A m_ f C f " # F Rm U L;m 1  ð1  K K;A ÞN U L;N ¼ N K k;A Unknown terms are given in Appendices A and B. Instantaneous gain thermal energy efficiency ðgg1;th Þ can be written as


 Ab a1 Dt ; and Z 11 e H

hef ;E ðE1 þ E2 ÞAgE þ hef ;W ðE01 þ E02 ÞAgW H011 þ H0022

;

IðtÞ ¼ AgE ISE ðtÞ þ AgW ISW Unknown terms are given in Appendix A. Eq. (16) represents the instantaneous gain thermal energy efficiency (characteristic equation) of active double slope solar still without operating helically coiled heat exchanger. The internal convective and radiative thermal losses from the fluid (BF/NF) surface are minimal in comparison to the heat lost on increasing the basin fluid (BF/NF) temperature (sensible heat). Therefore, the lost thermal energy efficiency (gL1;th ) of the system (A) can be expressed as

gL1;th ¼

M f C f ðT f  T f 0 Þ ðAgE ISE þ AgW ISW Þ

ð17Þ

gg1;th ¼

½hef ;E ðT f  T giE Þ þ hef ;W ðT f  T giW ÞAb AgE ISE ðtÞ þ AgW ISW ðtÞ

gL1;th ¼

" # ½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ afb ÞISW ðtÞ þ Ac F 0 ðasÞN;eff Ic ðtÞ þ T a ðH011 þ H0022 Þð1  ea1 Dt Þ Mf C f a1 Dt þ T ðe  1Þ fo AgE ISE ðtÞ þ AgW ISW ðtÞ H011 þ H0022

ð13Þ

On substituting T f from Eq. (10), one can get

" # ½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ afb ÞISW ðtÞ þ Ac F 0 ðasÞN;eff Ic ðtÞð1  ea1 Dt Þ Mf C f ðT fo  T a Þ 0 00 a1 Dt Þ  ðH11 þ H22 Þð1  e ¼ 0 AgE ISE ðtÞ þ AgW ISW ðtÞ AgE ISE ðtÞ þ AgW ISW ðtÞ ðH11 þ H0022 Þ

Substituting Eqs. (5) and (6) in Eq. (13); one can obtain


  ½hef ;E ðH  BÞ þ hef ;W ðH  B0 ÞT f  ½hef ;E ðAÞ þ hef ;W ðA0 Þ A gg1;th ¼ b H AgE ISE ðtÞ þ AgW ISW ðtÞ



gL1;th ¼ F 0L1 ðasÞL1;eff  U 0L1;eff

 ðT fo  T a Þ IðtÞ

h i 9 8 0 0 f 1 ðtÞ
<½h ðE þ E ÞA þ h a1 Dt Þ þ T f 0 ea1 Dt  ½ðK 01E ISE ðtÞ þ K 01W ISW ðtÞÞ þ T a ðH1 þ H2 þ H3 þ H4 Þ= 1 2 gE ef ;E ef ;W ðE1 þ E2 ÞAgW  a1 ð1  e Ab ¼ ; H : AgE ISE ðtÞ þ AgW ISW ðtÞ

ð18Þ

ð14Þ

Substitute, the expressions of f 1 ðtÞ and a1 in above equation; one can get

gg1;th ¼



 hef ;E ðE1 þ E2 ÞAgE þ hef ;W ðE01 þ E02 ÞAgW Ab 1 ½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ afb ÞISW ðtÞ 0 00 AgE ISE ðtÞ þ AgW ISW ðtÞ H H11 þ H22    þ Ac F 0 ðasÞN;eff Ic ðtÞð1  ea1 Dt Þ  ðK 01E ISE ðtÞ þ K 01W ISW ðtÞÞ þ H011 ðT f 0  T a Þea1 Dt

ð15Þ

o o 8n n 9 0
   a1 D t =  1Þ  ðK 01E ISE ðtÞ þ K 01W ISW ðtÞÞea1 Dt ðT f 0  T a Þ Ab a1 Dt < Z 11 ½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ afb ÞISW ðtÞ þ Ac F ðasÞN;eff Ic ðtÞðe 0 e þ H ¼ : AgE ISE ðtÞ þ AgW ISW ðtÞ 11 ; AgE ISE ðtÞ þ AgW ISW ðtÞ H

Or



gg1;th ¼ F 0g1 ðasÞg1;eff þ

ðT f 0  T a Þ ðU g1;eff Þ IðtÞ



where,

ðasÞg1;eff ¼

Z 11 ½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ afb ÞISW ðtÞ þ Ac F 0 ðasÞN;eff Ic ðtÞðea1 Dt  1Þ  ðK 01E ISE ðtÞ þ K 01W ISW ðtÞÞea1 Dt IðtÞ

ð16Þ

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L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

"

where, F 0L1

Q_ uN ¼ m_ f C f ðK Nk  1Þ

Mf C f ; ðasÞL1;eff ¼ 0 ðH11 þ H0022 Þ

"

dT f dx ¼ ð2pr 11 UÞðT HE  T f Þdx dx

ðK Nk  1Þez

#

Q_ uN ¼ D1 T f þ D2 Ic ðtÞ þ D3 T a

ð24Þ

ð25Þ


   ðK N 1Þez 1ez k where D1 ¼ m_ f C f ðK Nk  1Þ 1K ¼ ðAF ð a s ÞÞ 1 þ ; D 2 R N z 1 e 1K N ez k k    N N z 1K k ðK N 1Þe 1K k k ; and D3 ¼ ðAF R U L Þ1 1 þ 1K . N z 1K 1K e k

The energy balance of the heat exchanger immersed in the fluid (BF/NF) of the solar still can be expressed as

Tf

1  K Nk ez

! 1  K Nk Ic ðtÞ 1  Kk 1  K Nk ez " # ! ðK N  1Þez 1  K Nk þ ðAF R U L Þ1 1 þ k N Ta 1  Kk 1  K k ez

U 0L1;eff ¼ ðH011 þ H0022 Þð1  ea1 Dt Þ

3.2. System (B): Operating with helically coiled heat exchanger

1  ez

þ ðAF R ðasÞÞ1 1 þ

½ðK 1E þ afb ÞISE ðtÞ þ ðK 1W þ afb ÞISW ðtÞ þ Ac F 0 ðasÞN;eff Ic ðtÞð1  ea1 Dt Þ ¼ ; IðtÞ

Unknown terms are given in Appendix A. Eq. (18) represents the instantaneous loss thermal energy efficiency (characteristic equation) of active double slope solar still without operating helically coiled heat exchanger.

!#

k

k

The term ðAF R ðasÞÞ1 is a function of efficiency of the collector ðgc Þ [21,22]. On substituting T giE , T giW , hb;f ðT b  T f Þ, and Q_ uN from Eqs. (5)–

ð19Þ

(7), and Eq.(25) respectively in the water mass equation (Eq.(8)), one can obtain

Boundary conditions: T f ðx ¼ 0Þ ¼ T FoN and T f ðx ¼ LÞ ¼ T fi . Solving Eq. (19) using above boundary conditions, one can get



 

 dT f B Ab B0 Ab þ h1f ;W 1  ¼ T f h1f ;E 1  H dt 2 H 2 
 

 Ab 1 Ab þ 2U b þ ðaf þ 2ab h1 ÞðISE þ ISW Þ  D1 Mf C f 2 2


0 
 A Ab A Ab þ h1f ;W þ D2 Ic ðtÞ þ h1f ;E H 2 H 2
 

 Ab 1 ð26Þ þ D3 T a þ 2U b Mf C f 2

m_ f C f



 2pr 11 UL 2pr 11 UL þ T FoN exp  T fi ¼ T f 1  exp  m_ f C f m_ f C f where U ¼

h

1 hbf

þ

ð20Þ

    i1 r11 1 log rK221 þ rr11 . K1 h 22 bf

The rate of useful thermal energy gain from series connected N-identical PVT water collectors has been calculated using the following relation;

Q_ uN ¼ m_ f C f ðT FoN  T fi Þ

ð21Þ

Following Dubey and Tiwari [57], the outlet water temperature at the end of the N th PVT water collector is given by

T FoN ¼

K Nk

!

K Nk

ð22Þ Unknown terms in above equation are given in Appendix B. Substituting T FoN from Eq. (22) in Eq. (20) and rearranging, one can get

!

1e Tf 1  K Nk ez " # ! ðAF R ðasÞÞ1 ðK Nk  1Þez 1  K Nk Ic ðtÞ þ 1þ 1  Kk m_ f C f 1  K Nk ez " # ! ðAF R U L Þ1 ðK N  1Þez 1  K Nk Ta 1þ k N þ 1  Kk m_ f C f 1  K k ez

T FoN  T fi ¼ ðK Nk  1Þ

dT f þ a2 T f ¼ f 2 ðtÞ dt

Therefore, the rate of useful thermal energy gain (Eq. (21)) can be expressed as

f




 Ab

f 2 ðtÞ ¼ ½ðaf þ 2ab h1 ÞH þ K 01E ISE ðtÞ 2H  þ ðaf þ 2ab h1 ÞH þ K 01W ISW ðtÞ þ D2 Ic ðtÞ þ
 1 þ T a ðH011 þ H0044 Þ Mf C f Similar to Eq. (10), the solution of first order differential Eq. (27) can be expressed as

Tf ¼

ð23Þ

ð27Þ

  Ab ðH011 þ H0033 Þ M1C . where a2 ¼ 2H f

!

ðAF R ðasÞÞ1 1  ðAF R U L Þ1 1  Ic ðtÞ þ T a þ K Nk T fi 1  Kk 1  Kk m_ f C f m_ f C f

z

dT f ¼ a2 T f þ f 2 ðtÞ Or dt

f 2 ðtÞ ½1  ea2 Dt  þ T f 0 ea2 Dt a2

ð28Þ

Using thermo-physical properties (Tables 2 and 3) and heat transfer coefficients (Table 4), hourly variation of basin fluid (BF/ NF) temperature of the system (A) and system (B) can be obtained from Eqs. (10) and (28) respectively. On substituting T giE (Eq. (5)), T giW (Eq. (6)) and T f (Eq. (28)) in Eq. (13), the instantaneous gain thermal energy efficiency ðgg2;th Þ of the system (B) can be expressed as

Table 2 Thermo-physical properties of basefluid [59]. Quantity

Symbol

Expression

Density

qbf

5 999:79 þ 0:0683  T bf  0:0107  T 2bf þ 0:00082  T 2:5  T 3bf bf  2:303  10

Specific heat

C bf

6 2 4:217  0:00561  T bf þ 0:00129  T 1:5  T 2:5 bf  0:000115  T bf þ 4:149  10 bf

Viscosity

lbf

1 ð557:8219:408T bf þ0:136T 2bf 3:116104 T 3bf Þ

Thermal conductivity

kbf

6 0:565 þ 0:00263  T bf  0:000125  T 1:5  T 2bf  0:000941  T 0:5 bf  1:515  10 bf

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L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

Table 3 Thermo-physical properties of Al2O3, TiO2, CuO-water based nanofluid. Quantity

Expression

Specific heat

  0:4167  up 2:272 T nf 0:3037 d C nf ¼ 0:8429 1 þ 50 1 þ 50p 1 þ 100 15 < dp < 50 nm; 0 < up < 4%; 20 < T nf < 50  C (Al2O3,and CuO-water) [60]   D  Cp C nf ¼ Aðup ÞB ðT nf ÞC C p;bf C p;bf A ¼ 1:387; B ¼ 0:00425; C ¼ 0:001124; D ¼ 0:21159 dp ¼ 21 nm; 0 < up < 8%; 15 < T nf < 65  C (TiO2-water) [61]

qnf ¼ up qp þ ð1  up Þqbf [62]

Density

h   i kp 47 knf ¼ kbf 1 þ ð1:0112Þup þ ð2:4375Þup dp ðnmÞ  ð0:0248Þup 0:613

Thermal conductivity

0 < up < 10%; 20 < T nf < 70  C; 11 < dp < 150 nm (Al2O3-water) [63]   0:273  0:547  0:234  k T nf 100 knf ¼ kbf 1 þ ð0:135Þ kbfp ðup Þ0:467 20 dp ðnmÞ 0 < up < 10%; 20 < T nf < 70  C; 11 < dp < 150 nm (TiO2-water) [64] 

 l 0:0235  0:2246  u2 u u 1 knf ¼ kbf 0:9843 þ ð0:398Þðup Þ0:467 lnf  ð3:951Þ T nfp þ ð34:034Þ T 3p þ 32:51 T 2p dp ðnmÞ bf

nf

nf

0 < up < 10%; 20 < T nf < 70  C; 11 < dp < 150 nm (CuO-water) [65]

   2  2 u3 u u u lnf ¼ 0:4491 þ 28:837 þ 0:547up  0:163u2p þ ð23:653Þ T nfp þ ð0:0132Þu3p  ð2354:7Þ T 3p þ ð23:498Þ dpp  ð3:018Þ 2p T nf

Viscosity

nf

dp

11 6 up 6 9; 13 6 dp 6 130 nm;20 6 T nf 6 90  C (Al2O3-water) [63]    0:038  dp 0:061 lnf ¼ lbf ð1 þ up Þ11:3 1 þ T70nf 1 þ 170 10 6 up 6 4; 20 6 dp 6 170 nm;0 6 T 6 70  C (TiO2-water) [66]  247:8

Thermal expansion coefficient

lnf ¼ ð2:414  105 Þ  10 Tnf 140 10 6 up 6 10%; 11 6 dp 6 150 nm;20 6 T 6 70  C (CuO-water) [67] bnf ¼ ð1  up Þbbf þ up bp [62]

h i 8 9 0 0 f 2 ðtÞ
<½h ðE þ E ÞA þ h a2 Dt Þ þ T f 0 ea2 Dt  ½ðK 01E ISE ðtÞ þ K 01W ISW ðtÞÞ þ T a ðH1 þ H2 þ H3 þ H4 Þ= 1 2 gE ef ;E ef ;W ðE1 þ E2 ÞAgW  a2 ð1  e Ab gg2;th ¼ ; AgE ISE ðtÞ þ AgW ISW ðtÞ H :

ð29Þ

Substitute, the expressions of f 2 ðtÞ and a2 in Eq. (29), one can get

gg2;th ¼



 hef ;E ðE1 þ E2 ÞAgE þ hef ;W ðE01 þ E02 ÞAgW Ab ea2 Dt f½ðaf þ 2ab h1 ÞH þ K 01E ISE ðtÞ H AgE ISE ðtÞ þ AgW ISW ðtÞ H011 þ H0033    þ ½ðaf þ 2ab h1 ÞH þ K 01W ISW ðtÞ þ D2 Ic ðtÞgðea2 Dt  1Þ  ½K 01E ISE ðtÞ þ K 01W ISW ðtÞÞea2 Dt þ H011 ðT f 0  T a Þ

ð30Þ


 

Z 22 ½½ðaf þ 2ab h1 ÞH þ K 01E ISE ðtÞ þ ½ðaf þ 2ab h1 ÞH þ K 01W ISW ðtÞ þ D2 Ic ðtÞðea2 Dt  1Þ  ½K 01E ISE ðtÞ þ K 01W ISW ðtÞea2 Dt Ab a2 Dt e ¼ H AgE ISE ðtÞ þ AgW ISW ðtÞ    ðT f 0  T a Þ H0 þ AgE ISE ðtÞ þ AgW ISW ðtÞ 11

gg2;th ¼ F 0g2 ½ðasÞg2;eff þ where Z 22 ¼

ðasÞg2;eff ¼

ðT f 0  T a Þ ðU g2;eff Þ IðtÞ

hef ;E ðE1 þE2 ÞAgE þhef ;W ðE01 þE02 ÞAgW ; H011 þH0033

F 0g2 ¼

ð31Þ  Ab ea2 Dt ; U g2;eff ¼ H011 . H

ffZ 22 ½½ðaf þ 2ab h1 ÞH þ K 01E ISE ðtÞ þ ½ðaf þ 2ab h1 ÞH þ K 01W ISW ðtÞ þ D2 Ic ðtÞðea2 Dt  1Þg  ½K 01E ISE ðtÞ þ K 01W ISW ðtÞea2 Dt g AgE ISE ðtÞ þ AgW ISW ðtÞ

Unknown terms are given in Appendix A. Eq. (31) represents the instantaneous gain thermal energy efficiency (characteristic equation) of active double slope solar still coupled with helically coiled heat exchanger (system (B)). Further, an expression of instantaneous loss thermal energy efficiency (characteristic equation) of the system (B) can be obtained on substituting Eq. (28) in Eq. (17);




gL2;th ¼

Mf C f AgE ISE ðtÞ þ AgW ISW ðtÞ




 1 ff½ðaf þ 2ab h1 ÞH H011 þ H0033

þ K 01E ISE ðtÞ þ ½ðaf þ 2ab h1 ÞH þ K 01W ISW ðtÞ þ D2 Ic ðtÞgð1  ea2 Dt Þ þ ðH011 þ H0033 ÞðT fo  T a Þðea2 Dt  1Þg



gL2;th ¼ F 0L2 ðasÞL2;eff  U 0L2;eff

 ðT fo  T a Þ IðtÞ

ð32Þ

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L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326 Table 4 Heat transfer coefficients (HTCs) in different regions of the proposed system. HTCs

Relations

Natural convective HTC from the still basin to fluid

Nusselt number: ðNuÞf ¼ Reynold number: ðReÞf ¼

hb;f X k



¼ CðRePrÞn

qv X l f ; Prandlt number: ðPrÞf ¼ h i qv XC p

Rayleigh number: ðRaÞf ¼ ðRePrÞf ¼ Internal HTC from fluid surface to inner surface of the glass cover

k



lC p k

f

f

C = 0.54 and n = ¼ horizontal plate facing upward From the cooper and Dunkle model h i P P Evaporative HTC; heV;f ¼ ð0:016273Þhc;f T ff T gigi Convective HTC: hc;f ¼ ð0:844ÞðDTÞ1=3   h  i ðPf Pgi ÞðT f þ273Þ where; P x ¼ exp 25:317  T x5144 ; DT ¼ ðT f  T gi Þ þ 2:68910 5 þ273 P f

Radiative HTC hr;f ¼ 2eff r½ðT f þ 273Þ2 þ ðT gi þ 273Þ2 ½T f þ T gi þ 546 where; Within Flat plate collector (FPC)

1 2eff

¼ 21w þ 21g  1

In case of basefluid (water) [68]
0:14 1=3 l ½Gzm þ 0:0083ðGr m Pr m Þ0:75  Nu ¼ 1:75 lbfb bf

Arithmetic mean Graetz number: Gzm ¼

_ r C bf m K bf L ; 2

Arithmetic mean Grashof number: Gr m ¼ gDlbDT bf where, T ¼ Bulk temprature difference; D ¼ tube diameter; L = length of heated section of the tube. In case of nanofluid [69] 3 ÞðPrÞnf k ð f ÞððReÞ 10 ffi hFPC ¼ ðNuÞnf Dnfi ; ðNuÞnf ¼ 8 pnfffiffiffiffiffi 1þ12:7 ð8f ÞððPrÞ2=3 1Þ for 3  103 6 ðReÞnf 6 5  105 and 0:55 6 ðPrÞnf 6 2  103 l C

_r ðReÞnf ¼ p4Dm ; ðPrÞnf ¼ nfk nf i lnf nf _ r ¼ Mass flow rate in any riser and f = Darcy friction factor. m Petukhov correlation for smooth tubes [70] 2

f ¼ ½0:79 ln ðReÞnf  1:64

Colebrook correlation for roughness of the tubes [71]  i p1 ffiffi ¼ 2log 2=D þ 2:51pffiffi for 4  103 6 ðReÞnf 6 105 and 3:7 ðReÞnf

f

Within heat exchanger

f

0 <2 =Di < 0:05 (relative roughness) In case of basefluid (water) [42] ðNuÞnf ¼ ð2:153 þ 0:318ðDeÞ0:643 ÞPr 0:177 For 20 < De < 2  103 and 0:7 < Pr < 200 qffiffiffiffi _r Deans number: ðDeÞnf ¼ ðReÞnf ddci ; Reynold number; ðReÞnf ¼ p4dm il

nf

dc ¼ coil diameter; di ¼ r 11 ¼ Inner tube diameter In case of nanofluid [41] ðNuÞnf ¼ 3:67ðDeÞ0:67 d0:009 u1:004 hnf ¼

ðNuÞnf keff ; di

keff ¼ kstatic þ kbrownian i and qffiffiffiffiffiffiffiffiffiffiffiffiffi 4 ¼ ð5  10 Þðbuqbf C bf 2qkb TRnp Þf ðT; uÞ

kstatic ¼ kbf kstatic

h

knp þ2kbf 2uðkbf knp Þ knp þ2kbf þuðkbf knp Þ

np

b ¼ 8:44  ð100uÞe1:07304 for 1 6 u 6 10% (Al2O3 nanoparticles) Modeling function:  f ðT; uÞ ¼ ð2:82  102 u þ 3:91  103 Þ TT0  ð3:069  102 u þ 3:911  103 Þ where, u ¼ Concentration of nanoparticles; and d ¼ ddci T 0 = Reference temperature

where,

F 0L2 ¼

Mf C f f½ðaf þ 2ab h1 ÞH þ K 01E ISE ðtÞ þ ½ðaf þ 2ab h1 ÞH þ K 01W ISW ðtÞ þ D2 Ic ðtÞgð1  ea2 Dt Þ ; ðasÞL2;eff ¼ 00 IðtÞ þ H33 Þ

ðH011

U 0L2;eff ¼ ðH011 þ H0033 Þð1  ea2 Dt Þ Unknown terms are given in Appendix A. Eq. (32) represents the instantaneous loss thermal energy efficiency (characteristic equation) of active double slope solar still coupled with helically coiled heat exchanger (system (B)). For given parameters of the system, the energy and exergy analysis

has been carried out on the basis of first and second law of thermodynamics respectively. Hourly thermal energy ðEhourly;en Þ and exergy ðEhourly;ex Þ of the proposed systems can be obtained from the following equations,

Ehourly;en ¼ ½hef ;E ðT f  T giE Þ þ hef ;W ðT f  T giW ÞAb

ð33Þ

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L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

 
 T f þ 273 Ehourly;ex ¼ hef ;E ðT f  T giE Þ  ðT a þ 273Þln T giE þ 273 
 T f þ 273 Ab ð34Þ þ hef ;W ðT f  T giW Þ  ðT a þ 273Þln T giW þ 273 The hourly thermal energy efficiency ðghourly;en Þ and exergy efficiency ðghourly;ex Þ of the proposed systems can be obtained from the following equations [55,56]

(

)

_ bf  Lv M ½Ac  Ic ðtÞ þ As  Is ðtÞ  3600

ghourly;en ¼

 100

ð35Þ




 100 0:933  As  Is ðtÞ  
 T f þ 273  hef ;E ðT f  T giE Þ  ðT a þ 273Þln T giE þ 273 
 T f þ 273 Ab ð36Þ þ hef ;W ðT f  T giW Þ  ðT a þ 273Þln T giW þ 273

ghourly;ex ¼

The factor 0:933 represents the conversion factor of solar irradiation into exergy. Hourly yield from the proposed systems can be estimated from the equation given below,

_ _ bf ¼ qeg  3600 ¼ heg ðT f  T g Þ  3600 M Lv Lv

ð37Þ

where the latent heat of vaporization ðLv Þ can be expressed as [56],

Lv ¼ 3:1625  106 þ ½1  ð7:616  104  ðT v ÞÞ for

T v > 70

covered PVT-FPC (450 inclination) has been estimated with the help of MATLAB 2012a. The hourly variation of solar irradiation and ambient temperature of a typical day of the month March (New Delhi) is shown in Fig. 4. Following methodology is executed to study the performance of proposed nanofluid (Al2O3, TiO2, and CuO- water) based systems using characteristic curve for N ¼ 4 number of collectors, 100 kg basin fluid (BF/NF) mass, 0:03 kg=s mass flow rate and 0:25% concentration of metallic NPs: Step I. On considering the different initial temperatures (heat exchanger, basin fluid (BF/NF), collector outlet, etc.) equal to the ambient temperature, the initial inputs and output values have been computed using thermo-physical properties of basefluid (Table 2) and nanofluid (Table 3). For the subsequent computation, these estimated initial values are used to evaluate the temperature of basin fluid (BF/NF) (Eqs. (10) and (28)) of DSSS, collector’s outlet fluid (BF/NF) temperature (Eq. ð22Þ), and fluid (BF/NF) temperature in HE (Eq. (20)). Step II. The convective heat transfer coefficients (HTCs) in PVT-FPC, HE, and DSSS (basin to fluid (BF/NF)); and internal HTCs in DSSS has been estimated using heat transfer relations (Table 4). Step III. The thermal energy (Eq. (33)) and thermal exergy (Eq. (34)); Instantaneous gain/loss thermal energy efficiency (Eq. (16), (18), (31), (32)); thermal energy efficiency (Eq. (35)) and thermal exergy efficiency (Eq. (36)); and productivity (Eq. (37)) of both the systems has been estimated for basefluid and nanofluids.

Lv ¼ 2:4935  106 ½1  ð9:4779  104  ðT v Þ þ 1:3132  107  ðT 2v Þ  4:7974  103  ðT 3v ÞÞ for

T v < 70

4. Methodology In the present manuscript, analysis has been carried out for a typical day of the month March for the New Delhi climatic conditions; and the climatic data has been obtained from the IMD, Pune, India. Using Liu and Jordan formulae [56], solar irradiation at the toughen glass cover (300 inclination) of the DSSS and partially

5. Results and discussion Hourly variation of temperature difference ðDT ¼ T NF  T BF Þ between basefluid and nanofluids in different sections viz. DSSS, outlet of the series connected PVT-FPC, and within heat exchanger of both the systems is presented in Figs. 5–7 respectively. In these portions, the temperature difference is found to be higher in system (A) in comparison to system (B). Also, the difference is higher in case of CuO-water based nanofluids following the enhancement order as CuO > Al2 O3 > TiO2  water, in both the systems. In the

Fig. 4. Hourly variation of solar intensity and ambient temperature for a typical day of the month March of New Delhi climatic conditions.

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

319

Fig. 5. Hourly variation of temperature difference between basefluid and nanofluid of DSSS of (i) system (A) and (ii) system (B).

Fig. 6. Hourly variation of temperature difference between basefluid and nanofluid at the outlet of series connected PVT-FPC of (i) system (A) and (ii) system (B).

Fig. 7. Hourly variation of temperature difference between basefluid and nanofluid in the portion of helically coiled heat exchanger (system (B)).

section of series connected PVT-FPCs (Fig. 6), the flowing fluid (BF/NF) through it mutually receives the thermal energy from the blackened plate and assisting NPs in sunshine hours and gets heated; when it passes through the HE, it transfers thermal energy to fluid (NF/BF) available in the DSSS (Fig. 5). Hence, the fluid (NF/BF) temperature is higher at the outlet of the PVT-FPC compared to temperature of fluid in HE (Fig. 7) and basin fluid (BF/NF) of the DSSS. The improvement in the temperature of water based nanofluids is credited to their better thermo-physical and optical properties, thanks to conductivity. Basically, the higher temperature of fluid (BF/NF) in DSSS of system (A) is due to direct feeding of external thermal energy from the PVT-FPC whereas, it is done via HE in case of system (B). In system (A), the nanofluid is openly exposed to the solar irradiation, therefore, metallic NPs, in sunshine hours, directly absorbs more solar radiation resulting higher fluid (BF/NF) temperature in comparison to system (B). Moreover, the suspended metallic NPs in the host fluid/basefluid increases the surface area which intern enhances the thermal conductivity and eventually improves the heat transfer efficiency. The higher thermal conductivity of nanofluids is due to various factors such as brownian motion of NPs, liquid layering at liquid-particle interface, and effect of NPs clustering.

320

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

Hourly variation of convective HTC in DSSS (basin to fluid (BF/NF)); series connected PVT-FPC ðhFPC Þ; and heat exchanger ðhHE Þ of both the systems is presented in Figs. 8–10 respectively. It has been observed that the convective HTC is higher for system (A); also, it is found to be higher in case of CuO-water based nanofluids following the enhancement order as CuO > Al2 O3 > TiO2  water, in the studied portions of both the systems. Higher volume fraction of metallic NPs and mass flow rate reduces the entropy generation which intern improves the convective HTC (Reynolds number), hence, energy/exergy efficiency; and it is found to be higher using the CuO-water based nanofluids over the others [41,72,73]. The series connected PVT-FPCs gives higher values of convective HTCs following heat exchanger and DSSS (basin to fluid) which is due to better thermal conductivity of nanofluids as explained earlier. In addition to this, the dispersed metallic NPs also change the flow and thermal fields that improves the HTC. However, viscous forces limit the maximum value of HTCs which increases continuously on increasing the volume fraction due to thermal conductance forces. Consequently, the balance between these

Fig. 10. Hourly variation of convective HTC within helically coiled heat exchanger for basefluid and nanofluid (system (B)).

Fig. 8. Hourly variation of natural convective HTC from basin to fluid (BF/NF) of DSSS in (i) system (A) and (ii) system (B).

Fig. 9. Hourly variation of convective HTC within PVT-FPC of (i) system (A) and (ii) system (B) for basefluid and nanofluid.

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326

forces determines the optimal point. In helical heat exchanger, the thermal boundary layer formation on the tube surface is disturbed by the chaotic motion of the metallic NPs which intern enhances the HTCs. Moreover, the swirl flow in helical heat exchanger induces the centrifugal forces which initiate the secondary flow pattern. It originates the two different vertices perpendicular to the axial flow direction; consequently, the heat transfer mechanism occurs via diffusion and convection. It explains that the heat transfer rate per unit length of the tube is strongly influenced or improved due to contribution of such secondary convective transport. Hourly variation of internal evaporative HTC (east and west side) of the system (A) and system (B) is depicted in Figs. 11 and 12 respectively. It has been observed that the evaporative HTC is higher in system (A) for both basefluid and nanofluid. The evaporative HTC for the west side are marginally higher in comparison to the east side; moreover, the CuO-water based nanofluids give significantly higher values of evaporative HTC than others in both the systems.

321

The hourly variation of thermal energy and exergy of system (A) and system (B) is presented in Fig. 13. Daily thermal energy ðCuO 14:71 kW h;Al2 O3 11:96 kW h;TiO2 11:03 kW hÞ and thermal exergy ðCuO 1:61 kWh;Al2 O3 1:44 kW h;TiO2 1:35 kW hÞ of the system (A) is found to be significantly higher in comparison the basefluid ð10:42 kW h and 1:27 kW hÞ, whereas, for system (B), the thermal energy and thermal exergy respectively are found to be ðCuO 13:70 kW h;Al2 O3 10:58 kW h;TiO2 9:88 kW hÞ and ðCuO 1:39 kW h;Al2 O3 1:11 kW h;TiO2 0:92 kW hÞ, which are significantly higher than the basefluid ð8:85 kW h and 0:89 kW hÞ. Percentage enhancement in daily thermal energy and exergy is depicted in Table 5. Fig. 14 presents the variation of instantaneous gain and instantaneous loss thermal energy efficiency of both the systems with  T 0 T a reduced temperature f IðtÞ . It has been observed that nanofluid loaded both the systems give better instantaneous thermal energy efficiency (gain) in comparison to the basefluid; also, better improvement have been observed in both the systems with

Fig. 11. Hourly variation of internal evaporative heat transfer coefficient of (i) east and (ii) west side of system (A) using basefluid and nanofluid.

Fig. 12. Hourly variation of internal evaporative heat transfer coefficient of (i) east and (ii) west side of system (B) using basefluid and nanofluid.

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Fig. 13. Hourly variation of thermal energy and exergy of (i) system (A) and (i) system (B) using basefluid and nanofluid.

Table 5 Enhancement in the daily thermal energy and exergy of both the active systems using different nanofluids. Enhancement ð%Þ

Thermal energy and exergy ðkW hÞ Basefluid

TiO2 + Water

Al2O3 + Water

CuO + Water

TiO2 + Water

Al2O3 + Water

CuO + Water

(a) With heat exchanger Daily thermal energy ðkW hÞ Daily thermal exergy ðkW hÞ

8:85 0:89

9:88 0:92

10:58 1:11

13:70 1:39

11:6 3:37

19:54 24:7

54:8 56:19

(b) Without heat exchanger Daily thermal energy ðkW hÞ Daily thermal exergy ðkW hÞ

10:42 1:27

11:03 1:35

11:96 1:44

14:71 1:61

5:85 6:29

14:77 13:38

41:11 26:77

Fig. 14. Variation of instantaneous gain and loss thermal energy efficiency with reduced temperature of (i) system (A) and (i) system (B) using basefluid and nanofluid.

CuO- water based nanofluid than the other nanofluids (Table 6). It is credited to the improved thermo-physical and optical properties of these water based nanofluids as explained earlier. Moreover, for both the systems, the instantaneous loss thermal energy efficiency is higher for nanofluids (CuO > Al2 O3 > TiO2  water) than the basefluid which is attributed to higher HTCs of the nanofluids. The maximum values of instantaneous gain thermal energy

efficiency ðCuO 80:18%; Al2 O3 71:67%; TiO2 74:92%Þ and instantaneous loss thermal energy efficiency ðCuO 64:12%; Al2 O3 59:11%; TiO2 64:77%Þ of the system (A) are found to be significantly higher in comparison the basefluid ðgain 66:81%; loss 52:42%Þ, whereas, for system (B), the maximum values of instantaneous gain and loss thermal energy efficiency respectively are found to be ðCuO 76:18%; Al2 O3 67:67%; TiO2

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L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326 Table 6 Maximum instantaneous gain and loss thermal energy efficiency; and thermal exergy efficiency of both the systems loaded with basefluid and nanofluids. With heat exchanger

Without heat exchanger

Instantaneous energy eff.

Basefluid Al2O3 + Water TiO2 + Water CuO + Water

Max. gain ð%Þ

Max. loss ð%Þ

61:09 67:67 72:2 76:18

48:47 55:11 59:76 61:12

Max. exergy eff. ð%Þ

21:92 24:91 23:8 26:5

72:2%Þ and ðCuO 61:12%; Al2 O3 55:11%; TiO2 59:76%Þ, which are significantly higher than the basefluid ðgain 61:09%; loss 48:47%Þ. Hourly variation of thermal exergy efficiency of both the systems is shown in Fig. 15. It has been perceived that the maximum values of thermal exergy efficiency of system (A) ðCuO 27:9%;

Instantaneous energy eff. Max. gain ð%Þ

Max. loss ð%Þ

66:81 71:67 74:92 80:18

52:47 59:11 64:76 64:12

Max. exergy eff. ð%Þ

23:21 26 24:8 27:9

Al2 O3 26%; TiO2 24:8%Þ and system (B) ðCuO 26:5%; Al2 O3 24:91%; TiO2 23:8%Þ are found to be significantly higher in comparison to these systems loaded with basefluid (Table 6). Also, it has been observed that both the systems loaded with CuO-water based nanofluid gives higher thermal exergy efficiency than the other studied nanofluids.

Fig. 15. Hourly variation of thermal exergy efficiency of (i) system (A) and (i) system (B) using basefluid and nanofluid.

Fig. 16. Variation of daily yield (east side, west side, and total) obtained from (i) system (A) and (ii) system (B) using basefluid and nanofluid.

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Table 7 Enhancement in the daily productivity of both the active systems using different nanofluids. Enhancement ð%Þ

Daily productivity ðkgÞ TiO2 + Water

Al2O3 + Water

CuO + Water

TiO2 + Water

Al2O3 + Water

CuO + Water

(a) With heat exchanger 2:25 East side ðkgÞ 2:29 West side ðkgÞ 4:54 Total ðkgÞ

Basefluid

2:39 2:48 4:87

2:79 2:95 5:74

2:91 3:06 5:97

6:22 8:3 7:26

24 28:8 26:4

29:33 33:6 31:49

(b) Without heat exchanger 2:57 East side ðkgÞ 2:68 West side ðkgÞ 5:25 Total ðkgÞ

2:68 2:91 5:59

2:97 3:29 6:26

3:34 3:59 6:93

4:28 8:58 6:47

15:56 22:76 19:23

29:9 33:9 32

Daily productivity (east side, west side and total yield) obtained from both the systems by incorporating basefluid and naofluids is shown in Fig. 16. Productivity is found to be marginally higher for the west side of both the systems in comparison to the east side; also, it is significantly higher for the system (A) than system (B) (Table 7). The better performance of system (A) is credited to higher temperature of basin fluid (BF/NF) in DSSS due to direct feeding of external thermal energy from the series connected PVT-FPC whereas, it is done via HE in case of system (B). Moreover, it has been observed that incorporation of CuO-water based nanofluid as compared to other nanofluids give better productivity of both the systems. Daily productivity of system (A) ðCuO 6:93 kg;Al2 O3 6:26 kg;TiO2 5:59 kgÞ and system (B) ðCuO 5:97 kg;Al2 O3 5:74 kg;TiO2 4:87 kgÞ with nanofluids is found to be significantly higher than productivity obtained with basefluid ðsystemðAÞ  5:25 kg; systemðBÞ  4:54 kgÞ. 6. Conclusions Effect of CuO, Al2O3 and TiO2-water based nanolfluids on the performance of two different active solar distillation systems has been studied analytically using the characteristic curve (characteristic equation). Following conclusions have been withdrawn from the present study: In both the systems, maximum temperature difference; HTCs (convective and evaporative); instantaneous gain and loss thermal energy efficiency; thermal energy and exergy; thermal exergy efficiency; and productivity are found to be higher using CuO-water based nanofluid follows the order as CuO > Al2 O3 > TiO2  water. Moreover, the performance of these studies has been traced to be better for the system (A) in comparison to system (B). The temperature difference ðDT ¼ T NF  T BF Þ between the nanofluid and basefluid in different portions (outlet of the series connected PVT-FPC, helical heat exchanger, and DSSS) of (System B) follows the order of increment ðDTÞFPC > ðDTÞHE > ðDTÞDSSS . The same order has been observed for the system (A) ððDTÞFPC > ðDTÞDSSS Þ. The convective HTC follows the order of, hFPC > hHE > hb;f in system (B) and hFPC > hb;f in system (A). Also, the system (A) gives higher values of the internal evaporative HTC which harvest the higher productivity in comparison to the system (B). The characteristic curve (characteristic equation) shows the improved instantaneous thermal energy efficiency (gain) of both the systems for nanofluids than basefluid. Recommendation Different nanofluids assisted with different metallic NPs; and exergoeconomic and enviroeconomic analysis can be investigated for the present proposed systems. Effect of size and shape of the metallic NPs of different nanofluids can be studied in active solar stills.

Appendix A

 3  3 2 K K h1gE Lgg h1gW Lgg 4 5 4 5;   ; U gaW ¼ ¼ Kg Kg þ h1gE þ h1gW Lg Lg 2

U gaE

U ga ¼

Ub ¼

hb;bf hb;f ; h1 ¼ ; 2ðhb;bf þ hba Þ 2ðhb;f þ hba Þ

hb;f hba ; A ¼ C 1 U 2 þ C 2 ; A0 ¼ C 01 U 1 þ C 02 ; ðhb;f þ hba Þ

C 1 ¼ ag ISE AgE þ U gaE T a AgE C 2 ¼ ag ISW hEW AgE AgW þ U gaW T a hEW AgE AgW ; C 01 ¼ ag ISW AgE þ U gaW T a AgW C 02 ¼ ag ISE hEW AgE AgW þ U gaE T a hEW AgE AgW ;
 AB þ hEW AgE þ U gaE AgE U 1 ¼ h1fE 2
 AB þ hEW AgW þ U gaW AgW ; 2
 AB B ¼ ðh1fE U 2 þ h1fW hEW AgE Þ 2

U 2 ¼ h1fW


 AB 2 ; H ¼ U 1 U 2  hEW AgE AgW ; B0 ¼ ðh1fW U 1 þ h1fE hEW AgE Þ 2
 A afb ¼ b ðaf þ 2ab U ga Þ 2 

  Ab 1 þ hEW 1 þ þ U gaW AgE AgW ag h1f ;E K 1E ¼ h1f ;W h1f ;E 2AgW 

  Ab 1 þ hEW 1 þ þ U gaE AgE AgW ag h1f ;W K 1W ¼ h1f ;E h1f ;W 2AgE
   hef ;W Ab þ hEW ð1 þ K 01E ¼ hef ;W ÞAgW þ U gaW AgW AgE ag hef ;E 2 hef ;E
 
  hef ;E Ab þ hEW 1 þ AgE þ U gaE AgE AgW ag hef ;W K 01W ¼ hef ;E 2 hef ;W H1 ¼


 Ab ðU gaE AgE þ U gaW AgW Þh1f ;E h1f ;W 2

H2 ¼ AgE AgW hEW ðU gaE h1f ;E þ U gaW h1f ;W Þ H3 ¼ AgE AgW U gaE U gaW ðh1f ;E þ h1f ;W Þ

L. Sahota et al. / Energy Conversion and Management 135 (2017) 308–326 2

H4 ¼ AgE AgW hEW ðU gaE h1f ;W þ U gaW h1f ;E Þ; H ¼ U 1 U 2  hEW AgE AgW H011 ¼ H1 þ H2 þ H3 þ H4 ; H0022 ¼

2H ðU b Ab þ Ac F 0 U L;N Þ; Ab

H0033 ¼ U b Ab  D1 ; H0044 ¼ U b Ab þ D3 
 Ab ; E2 ¼ U gaW ðhEW þ U gaE ÞAgE AgW E1 ¼ U gaE hEW þ h1f ;W 2AgW 
 Ab ; E02 ¼ U gaE ðhEW þ U gaW ÞAgE AgW E01 ¼ U gaW hEW þ h1f ;E 2AgE

Appendix B


 Ac F Rc U L;c ðAF R ðasÞÞ1 ¼ Ac F Rc ðasÞc;eff þ PF 2 ðasÞm;eff Am F Rm 1  m_ f C f ðAF R U L Þ1 ¼ ðAc F Rc ÞU L;c þ ðAm F Rm ÞU L;m ð1 

Ac F Rc U L;c ðAF R U L Þ1 Þ;K k ¼ 1  m_ f C f m_ f C f


 m_ f C f F 0 Ac U L;c 1  exp  ; U L;c m_ f C f 
0  m_ f C f F Ac U L;m ¼ 1  exp  U L;m m_ f C f

Ac F Rc ¼ Am F Rm

ðasÞc;eff ¼ PF c ðap sg Þ; ðasÞm;eff ¼ ½ðasÞ2;eff þ PF 1 ðasÞ1;eff  ðasÞ1;eff ¼ ac sg b  gc sg b; ðasÞ2;eff ¼ ap ð1  bÞs2g ; PF 1 ¼

hpf U tc;p ; PF 2 ¼ U tc;p þ U tc;a hpf þ U L2

hpf hpf U L2 ; U L;m ¼ 0 ; U L2 ¼ U L1 þ U tp;a ; F 0 hpf þ U tp;a F hpf þ U L2 hpf U tp;a ¼ 0 ; F hpf þ U tp;a

PF c ¼ U L;c

U L1 ¼

 1  1 U tc;a U tc;p 1 Lg 1 Lg ; U tc;a ¼ þ ; U tc;p ¼ þ ; ho K g hi K g U tc;a þ U tc;p

ho ¼ 5:7 þ 3:8V; hi ¼ 2:8 þ 3V z¼

2pr 11 UL m_ f C f

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