Accepted Manuscript Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still Saman Rashidi, Shima Akar, Masoud Bovand, Rahmat Ellahi PII:
S0960-1481(17)30817-0
DOI:
10.1016/j.renene.2017.08.059
Reference:
RENE 9157
To appear in:
Renewable Energy
Received Date: 29 May 2017 Revised Date:
18 August 2017
Accepted Date: 23 August 2017
Please cite this article as: Rashidi S, Akar S, Bovand M, Ellahi R, Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still, Renewable Energy (2017), doi: 10.1016/j.renene.2017.08.059. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
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Volume of fluid model to simulate the nanofluid flow and
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entropy generation in a single slope solar still
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Saman Rashidia, Shima Akara, Masoud Bovandb and Rahmat Ellahic,1 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad 91775-1111, Iran b
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Department of Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran c
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a
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Department of Mathematics & Statistics, FBAS, IIUI, Islamabad, Pakistan
Abstract:
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This paper proposes volume of fluid (VOF) model to investigate the potential of Al2O3-
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water nanofluid to improve the productivity of a single slope solar still. Accordingly, VOF
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model is utilized to simulate the evaporation and condensation phenomena in the solar still.
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An entropy generation analysis is used to evaluate the system from the second law of
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thermodynamics viewpoint. The effects of solid volume fraction of nanofluid on the
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productivity and entropy generation in the solar still have been examined. The numerical
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results are compared with the experimental data available in the literature to benchmark the
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accuracy of VOF model. The numerical results showed that the productivity of solar still
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increases with an increase in the solid volume fraction of nanoparticles. The productivity
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increases about 25% as the solid volume fraction increases in the range of 0% to 5%. There
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is about 18% enhancement in the average Nusselt number as the solid volume fraction
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increases in the range of 0% to 5%. Moreover, the maximum values of viscous and thermal
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entropy generations are happened at the regions around the bottom and top surfaces of the
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solar still. Both types of entropy generation increase by increasing the solid volume
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Corresponding author (R. Ellahi) e-mails:
[email protected],
[email protected]
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ACCEPTED MANUSCRIPT fraction of nanoparticles. The viscous and thermal entropy generations increase about 95%
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and 25%, respectively as the solid volume fraction increases in the range of 0% to 5%.
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Keywords: VOF mode; Solar still; Nanofluid; Productivity; Entropy generation
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Nomenclature
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A
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Bc
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C
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df
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dp
nanoparticle diameter (nm)
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E
energy (J/kg)
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F
force (N)
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g
gravitational acceleration (m/s2)
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H
height of solar still (m)
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k
thermal conductivity (W/m.oC)
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lBF
mean free path of water (-)
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L
length of solar still (m)
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mɺ
productivity (Kg/m2)
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Ng
non-dimensional local entropy generation (-)
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Nt
mean entropy generation rate (-)
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Nu
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p
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Pr
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Re
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S ′g′′
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Sh
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surface (m2) Boltzmann constant (-) specific heat (J/kg.oC)
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molecular diameter of base fluid (nm)
Nusselt number (-) Pressure (Pa) Prandtl number (-)
Reynolds number (-) entropy generation rate (W/m3.oC) energy source term (Kg/m.s) 2
Sα
MANUSCRIPT mass source termACCEPTED (Kg/m3.s)
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t
time (s)
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T
temperature (oC)
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u,v
velocity components in horizontal and vertical directions (m/s)
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V
velocity (m/s)
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x,y
rectangular coordinates components (m)
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Subscripts/superscripts
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Ave
average
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b
bottom
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B
Brownian
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eff
effective
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f
base fluid
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g
glass cover
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i
ith phase
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l
left
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p
particle
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r
right
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th
thermal
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v
vapor
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v
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Greek symbols
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α
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δ
distance between particles (nm)
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θ
slope of the glass cover ( )
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µ
dynamic viscosity (kg/m.s)
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viscous
volume/void fraction (-)
o
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ρ
ACCEPTED MANUSCRIPT density of the fluid (kg/m3)
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φ
solid volume fraction of nanoparticles (-)
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Abbreviations
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CFD
Computational fluid dynamics
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VOF
Volume of fluid
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1. Introduction
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Solar stills are recognized as the most efficient desalination technology, which utilize solar
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radiation to desalinate water and generate drinking water. These devices are usually cheap
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and have a simple structure with insignificant maintenance cost. As a matter of fact the
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solar energy is used as a free, stable, and trusty source of energy. However, these devices
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have a low performance. Consequently, there is a necessity to recover the performance of
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solar stills by using active and passive methods. The active methods need external source
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of energy such as applying heat pipe and thermoelectric module [1, 2], put on flat-plate
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solar collector and cooling glass cover [3], using parabolic concentrator [4], by means of
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water sprinkler [5] and via heater [6] are a number of active techniques used to improve the
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efficiency of solar stills. Aside from active method, some researchers used passive methods
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to enhance the efficiency of solar stills. Most common of these methods are installing fins
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[7], blade in solar still [8, 9], porous materials [10, 11], PCM [12], baffles [13] and
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applying vapor adsorbent pipe network [14] and so on.
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Common liquids such as water have almost small value of thermal conductivity and thus
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cannot achieve acceptable heat transfer rates in thermal systems. A method to overcome
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this defect is adding nanoparticles in such liquids in order to enhance their thermal
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conductivity. Some researchers used this technique in different solar systems, for instance
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Mahian et al. [15] evaluated the applications of them in solar systems in a review paper.
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They reported that applyingACCEPTED nanofluids inMANUSCRIPT solar collectors has some economic and
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environmental advantages as they cause a decrease in CO2 pollution and fuel savings.
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Some investigators have used nanoparticles inside the solar still as a passive technique to
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improve the performance of this device. Kabeel et al. [16] used the nanofluid in a solar still
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integrated with external condenser. The productivity of their solar still was increased about
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116% and 53.2% by using the nanofluids and external condenser, respectively. Kabeel et
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al. [17] applied nanofluids and vacuum simultaneously in an experimental work to enhance
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the efficiency of a solar still. Their results showed that these techniques enhance
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considerably the evaporation and condensation rates and accordingly, cause a more
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productivity. Sahota and Tiwari [18] examined the influence of nanofluids on the
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efficiency of a double slope solar still. They observed the higher thermal energy efficiency
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and thermal exergy for nanofluids in comparison with the case of pure water. Elango et al.
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[19] inspected experimentally the effects of various water nanofluids containing Al2O3,
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ZnO, Fe2O3, and SnO2 on the efficiency of a single slope solar still. They concluded that
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Al2O3-water nanofluid, with 29.95% higher productivity in comparison to the water, has
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the maximum productivity among all nanoparticles considered in this research. Sahota and
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Tiwari [20] studied the influence of Al2O3 nanoparticles on the efficiency of a passive
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double slope solar still. They observed about 12.2% enhancement of yield for 35 kg
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basefluid by adding Al2O3 nanoparticles with 0.12% concentration. Sahota and Tiwari [21]
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used Al2O3, CuO, and TiO2-water nanofluids in a double slope solar still. They concluded
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that the optimization of concentration of nanoparticles depends on the climatic conditions
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containing the ambient temperature and solar intensity. El-Said et al. [22] coupled a hybrid
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desalination system with Al2O3-water nanofluids solar heater. They reported that the solar
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water heater efficiency is about 49.4%. Sharshir et al. [23] used nanofluids and glass cover
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cooling simultaneously in an experimental research to improve the efficiency of a solar
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still. They used copper oxideACCEPTED and graphite MANUSCRIPT as the nanoparticles. They reported a daily
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efficiency of 30% for the non-modified still. They recorded 46% and 49% for the daily
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efficiencies of the still by applying copper oxide and graphite particles with glass cooling,
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respectively. Kabeel et al. [24] reported both theoretically and experimentally the effects of
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nanofluids and external condenser on the performance of a solar still. They used aluminium
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oxide and cuprous oxide as the nanoparticles. They concluded that the daily efficiency of
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the modified still is 84.16% and 73.85% when applying cuprous oxide and aluminium
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oxide nanoparticles, respectively, with operating the fan. Additionally, the daily efficiency
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of their conventional still was about 34%. Sahota et al. [25] analytically investigated the
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influences of Al2O3, CuO, and TiO2-water nanofluids on the efficiencies of the active solar
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distillation systems. They coupled the double slope solar still with photovoltaic thermal flat
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plate collectors and helical heat exchanger. They observed a higher productivity by using
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CuO-water nanofluid in comparison with Al2O3 and TiO2-water nanofluids. Sahota et al.
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[26] presented the influences of Al2O3, CuO, and TiO2-water nanofluids on the exergy of a
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double slope solar still. They found that the exergy of the solar still increases by using the
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nanofluid. Mahian et al. [27] investigated the influences of nanofluids on the evaporation
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rate in a solar still equipped with a heat exchanger. They used Cu and SiO2-water
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nanofluids. They reported that at high temperatures, employing SiO2-water nanofluid,
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which has a lower effective thermal conductivity in comparison with Cu-water nanofluid,
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causes the higher performance. Sahota and Tiwari [28] performed exergoeconomic and
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enviroeconomic analyses for a hybrid double slope solar still. Their analyses were
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performed for three cases containing hybrid solar still operating without heat exchanger
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(case A), hybrid solar still operating with helically coiled heat exchanger (case B), and
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conventional solar still (case C). They used Al2O3 and CuO-water nanofluids. They
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observed that CuO-water nanofluid has better annual performance and exergoeconomic
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ACCEPTED MANUSCRIPT and enviroeconomic for the cases A and B, while, Al2O3-water nanofluid has better results
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for the case C. Chen et al. [29] studied stability, optical characteristics, and thermal
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conductivity of SiC-saline water nanofluids used in a solar distillation system. Their
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results showed that enhancing the salt concentration have some negative influences on the
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stability and thermal conductivity of nanofluid used in a solar distillation system.
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There are many experimental works to investigate the potential of nanoparticles for
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enhancing the productivity in solar stills. Usually, experimental techniques are expensive
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and time consuming. Accordingly, it is essential to consider a low cost and quick technique
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to investigate the interesting phenomena in solar stills. Computational fluid dynamics as a
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worthy method can be used in this regard. Some researcher applied this method for the
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conventional solar stills [30-32]. Rahbar and Esfahani [31] used CFD method to obtain the
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productivity and convective heat transfer coefficient of a single slope solar still. They
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found that the accuracy of the CFD technique to obtain the convective heat transfer
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coefficient is superior in comparison with the productivity prediction. Rahbar et al. [32]
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repeated this problem for a tubular solar still. They reported about 200% enhancement in
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the productivity as the glass temperature reduces only 50 C. Lately, Rashidi et al. [9] used
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numerically a blade in a single slope solar still. They concluded that using a blade inside
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the still creates a higher number of vortices with smaller sizes. Smaller vortices create
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enough pathways to transfer the thermal energy between the glass and water surfaces and
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enhance the still productivity.
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All numerical researches performed for solar still used the moist air model. In this model,
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evaporation and condensation phenomena are not simulated in solar still and fluid is only
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supposed as a moist air. However, an actual two-phase flow with a vapor-liquid phase
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change process is occurred in a solar still. This is the main darkness of the moist air model
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for modelling a solar still.
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ACCEPTED MANUSCRIPT Volume of fluid based CFD has a capability to overcome this darkness for solar stills and
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models the vapor-liquid phase change. This model can be used to follow the interface
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between liquid and vapor phases. It has an ability to simulate mass and heat transports
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through interface. This model has been used for various two-phase problems. Ganapathy et
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al. [33] applied this technique to model the condensation heat transfer in the microchannel.
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They compared the results obtained by VOF method with some available universal
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predictive correlations. They found a good agreement between these results. Ding et al.
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[34] used a VOF technique to model the vapor-liquid phase change with numerical
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oscillation suppression. They used the energy source donor-acceptor procedure to suppress
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the numerical oscillation. They found that there is a good matching between the results for
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phase change obtained by VOF model and theoretical methods for higher values of mass
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transfer coefficient. Arunkumar et al. [35] determined air-water two-phase flow regimes by
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utilizing infrared sensor and VOF methods. They utilized high-speed videography to
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perform a comparison between the results of infrared sensor and VOF method. They found
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a good matching between two results. Some relevant studies on the topic of nanoparticles
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can be found in [36-39] and several references therein.
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The literature review indicated that researchers used mostly moist air model in solar stills.
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Moreover, most of researchers investigated experimentally the potential of nanoparticles
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for improving the performance of solar stills and the numerical activities are rarely
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presented for this topic. Determination of local entropy generation in a thermal system
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such as a solar still is essential to detect the regions with high values of irreversibilities.
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This paper tries to cover above points and uses the volume of fluid model to simulate the
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nanofluid flow and entropy generation in a single slope solar still.
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ACCEPTED MANUSCRIPT 2. Description of the problem
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The solar still under simulation is disclosed schematically in figure 1. As disclosed in this
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figure, a solar still with the height of the left side (Hl=0.1m), the height of the right side
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(Hr=0.47m) and the length (L=0.98m) is modeled. A glass cover with angle (θ=20o) and
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temperature of Tg=30°C is placed as top side. Furthermore, the bottom surface has a
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constant temperature of Tb=40°C and two sidewalls are adiabatic. At initial time, the water
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depth is 2cm. It should be stated that the solar irradiance spreads inside the still after
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absorbing and reflecting by the glass cover. After that, this irradiance is absorbed by water
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in the still. Finally, it is supposed that the flow to be two dimensional, two phase, laminar,
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and time dependent.
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Insert figure 1 here
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3. Mathematical modelling
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3.1.
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In current paper, the volume of fluid model presented by Hirt and Nichols [40] is employed
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to model the condensation and evaporation phenomena in the solar still. Commonly, this
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model is employed to model a two-phase flow where the alteration of joint surface between
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two phases is serious as the vapor-liquid interface can be followed by employing volume
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of fluid model. In this model, it is necessary to obtain the volume fraction in any cell of
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domain. The sum of the volume fraction for liquid or vapor phase in a cell should be unity
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as follows: nphase
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∑α i =1
i
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Governing equations
=1
(1)
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where α indicates the volume fraction and i shows the ith phase. The viscosity of a vapor-
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liquid two-phase flow in any cell is obtained by employing the mean values of the vapor
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MANUSCRIPT and liquid phases, weighted byACCEPTED their relevant volume fractions. As a result, the viscosity of
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a vapor-liquid two-phase flow can be given by [41]:
222
µ = α v µ v + (1 − α v )µ eff
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where µ denotes the viscosity. The subscripts v and eff in this equation denote the
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properties of vapor phase and nanofluid as liquid phase, respectively. A single phase
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approach is used to determine the properties of nanofluid. These properties are presented at
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the appendix section. The identical trend can be utilized to obtain the density or thermal
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conductivity of a vapor-liquid two-phase flow. The tracking of the interface between two
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phases is performed by solving a continuity equation for the volume fraction of two
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phases. This equation is presented as follows:
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(2)
∂α i S + V∇.α i = αi ∂t ρi
(3)
where ρi is the density of the ith phase. Moreover, V and t are the velocity and temperature,
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respectively. Mass transport between vapour and liquid phases for the condensation and
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evaporation phenomena in the solar still is considered by applying Sαi as the source term in
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Eq. 3. A single momentum equation is considered for all over the computational domain,
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and the resulting speed field is shared among the phases. The momentum equation is given
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by:
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∂ ∂t (ρV ) + ∇.(ρVV ) = −∇p + ∇. µ eff (∇V + ∇V ′) + ρg + F
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(4)
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where F denotes the surface tension forces at the joint surface between two phases [42].
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Moreover, p is the pressure. These forces create due to exist of the attractive forces
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between molecules in a fluid. They act for balancing the radially inward inter-molecular
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attractive force with the radially outward pressure gradient force through the interface. It
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should be stated that the gravity term (ρg) in above equation has a capability for making
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the natural gravitational drag to condense vapor into pure water to drop out. The energy 10
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ACCEPTED equation is shared among the phases. TheMANUSCRIPT energy equation can be presented in the
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following form:
∂ (ρE ) + ∇.[V (ρE + p )] = ∇.( k∇T ) + S h ∂t
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(5)
where k is the thermal conductivity. In above equation, the energy E and temperature T are
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used as mass-averaged parameters:
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n phase
E=
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∑α ρ E i =1 nphase
i
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(6)
∑α ρ i
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Note that the source term Sh is used in the energy equation to model the heat exchange
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during the phase change process (evaporation or condensation processes).
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3.2.
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The following boundary conditions are employed for this case:
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•
Boundary conditions
u = v = 0, T = Tg = 300 C
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Along the glass cover:
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where the subscript g denotes the glass cover.
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•
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∂T =0 ∂x
(8)
Along the bottom wall:
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Along the side surfaces: u = v = 0,
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(7)
u = v = 0, T = Tb = 40 0 C
(9)
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where the subscript b denotes the bottom surface of the solar still.
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3.3.
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The average Nusselt number:
Parameter definition
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H ave L ∂T Nuave = − L(Tw − Tg ) ∫0 ∂n
ACCEPTED MANUSCRIPT dx
(10)
water
where n is normal direction to the water surface. L is the length of the still. Moreover, Heve
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is the mean height of the still ((Hr+Hl)/2).
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The local volumetric viscous entropy generation:
268
2 2 2 µ ∂u ∂v ∂u ∂v S g′′′,v = 2 + + + T ∂x ∂y ∂y ∂x
(11)
where u and v are the velocity components in x and y directions.
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The local volumetric thermal entropy generation:
272
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(12)
The dimensionless local entropy generation:
Ng =
2 S g′′′H ave
k
where k is the thermal conductivity.
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The average entropy generation rate:
1 ∫ ( N g )dA A A
(13)
(14)
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∂T 2 ∂T 2 + ∂x ∂y
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k S g′′′,th = 2 T
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where A is the surface of the still.
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4. Numerical method
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A numerical method based on finite volume technique is considered for solving the
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mentioned equations. Staggered mesh arrangement is employed for storing the velocity and
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pressure terms at the cell faces and cell center, respectively. Furthermore, the SIMPLE
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algorithm presented by Patankar [43] is employed to couple the pressure and velocity
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terms. Second-Order Upwind technique is considered to discretize all equations. The
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convergence criteria are acceptable when the summation of residuals to be smaller than 10-
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ACCEPTED for all equations. All simulations in this MANUSCRIPT paper are developed employing the Ansys-
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Fluent.
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4.1.
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The mesh generated within the modeled solar still is disclosed in figure 2. It can be seen
289
that a two-dimensional square grid with non-uniform distribution is considered for this
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problem. This mesh is refined near the regions with large values of gradients such as near
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the walls and interface between two phases. A mesh independent test is performed here to
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guarantee that the results are independent of grid size. Four mesh numbers containing
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10000, 20000, 40000, and 80000 are considered to perform this test. The relevant water
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productivity for each mesh number and the percentage difference between them are
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presented in Table 1. As presented in this table, the difference in water productivity
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between the mesh numbers of 40000 and 80000 is only 0.3%. As a result, the mesh number
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of 40000 is considered for the rest modeling.
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Mesh independent test and validation
Insert figure 2 here
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Insert table 1 here
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To evaluate the accuracy of the volume of fluid model, the results achieved by this model
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are compared with the experimental data of Rashidi et al. [44]. The validation is performed
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for a conventional solar still without applying nanofluid. The results of this comparison are
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presented in Table 2. It can be seen that the results achieved by volume of fluid model have
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a good agreement with experimental data with maximum error of 16%. There is always a
305
discrepancy between the numerical and experimental results. This error is created due to
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the following reasons:
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•
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The discrepancy is created by some experimental factors containing calibrating
308
equipment for lab measurements, experiment accuracy, human errors, missing out
309
some processes, etc.
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•
ACCEPTED MANUSCRIPT The discrepancy is created by some numerical errors. These numerical errors are created by considering some simplification assumptions such as two dimensional
312
modelling. Moreover, it is assumed that the side walls of the solar still are adiabatic in
313
this numerical modelling. However, they were not completely adiabatic in the
314
experiments. Insert table 2 here
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5. Results and discussion
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In this section, the results of this study are presented to investigate the potential of Al2O3-
318
water nanofluid to improve the productivity of a single slope solar still.
319
Figure 3 shows the contours of water vapor fraction during time for conventional and
320
modified stills by using Al2O3-water nanofluid at φ=5%. The red and blue colours in these
321
contours denote the liquid and vapor phases, respectively. It can be seen that the contours
322
have a stable level for liquid fraction at the bottom region of two stills at the start time (See
323
contours for first row). Phase change is happened and vapor creates during time as the
324
volume fraction of the vapor phase is increasing during time. This phase change is
325
happened due to rise in the water temperature within two stills. The vapor arises from the
326
water surface and transfers toward the glass cover due to the free convection and buoyancy
327
force generated in the still. The vapor contacts with the glass cover and due to the low
328
temperature of this surface, the condensation is occurred and distilled water can be
329
generated. It should be stated that the amounts of the evaporation and condensation heat
330
transfers are improved by adding the Al2O3 nanoparticles in the still as the volume fraction
331
of liquid phase is more in comparison with the conventional still (φ=0%). Note that the
332
thermal conductivity of the fluid enhances by adding the nanoparticles. This leads to
333
increase in the convective and evaporative heat transfers in the still. Moreover, the
334
fluctuating movements of the nanoparticles in the water enhance the heat transfer rate.
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ACCEPTED MANUSCRIPT Insert figure 3 here
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Figure 4 shows the variations of productivity with solid volume fraction of nanoparticles
337
for two values of temperature difference between surfaces of water and glass cover (e.g.
338
4°C and 10°C). Using all numerical data, the following empirical equation was derived for
339
the productivity:
340
0.21 0.7486 mɺ = 0.8176+ 0.0391× (Tb − Tg ) × (ϕ)
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336
(15)
Note that for obtaining this equation, the simulations are performed for four values of
342
temperature difference containing 4oC, 6oC, 8oC, and 10oC at 1%
