Heat transfer performance of ZnO–ethylene glycol and ZnO–ethylene glycol–water nanofluid coolants

Heat transfer performance and transport properties of ZnO–ethylene glycol and ZnO–ethylene glycol–water nanofluidcoolantsK.S.Suganthi,V.Leela Vinodhan,K.S.Rajan ⇑Centre for Nanotechnology &Advanced Biomaterials (CeNTAB),School of Chemical &Biotechnology,SASTRA University,Thanjavur 613401,Indiah i g h l i g h t sHigh thermal conductivity and low-viscous ZnO–ethylene glycol nanofluids prepared. ZnO–ethylene glycol–water nanofluids prepared by hierarchical method.Liquid layering and Brownian motion contribute to thermal conductivity enhancement. Improvement in nanofluid cooling performance inline with thermal conductivity rise.a r t i c l e i n f o Article history:Received 20May 2014Received in revised form 14August 2014Accepted 5September 2014Available online 26September 2014Keywords:ZnO–ethylene glycolZnO–ethylene glycol–water Transient heat transfer NanofluidLiquid layeringHeat transfer rate ratioa b s t r a c tExperiments were carried out on preparation and characterization of ZnO–ethylene glycol (EG)and ZnO–ethylene glycol–water nanofluids and analysis of their performance as coolants.Favorable interactions between ZnO nanoparticles and ethylene glycol molecules ensured superior transport properties of ZnO–EG nanofluids.These interactions were utilized during formulation of ZnO–EG–water nanofluids with preservation of ethylene glycol molecules over ZnO nanoparticles’surface rendering them with bet-ter transport properties.ZnO–EG nanofluids containing 4vol.%nanoparticles showed thermal conductiv-ity enhancement of 33.4%and viscosity reduction of 39.2%at 27°C.Similarly,2vol.%ZnO–EG–water nanofluids showed thermal conductivity enhancement of 17.26%and viscosity reduction of 17.34%at 27°C.Disturbance of hydrogen bonding network of ethylene glycol by ZnO nanoparticles resulted in reduced dispersion viscosity.Empirical models were developed to predict the thermal conductivity enhancement and viscosity reduction of the nanofluids apart from elucidating mechanisms for the same.Transient heat transfer experiments showed that ZnO–EG and ZnO–EG–water nanofluids had better heat absorption characteristics compared to their respective base fluids.The enhancements in heat transfer were proportional to thermal conductivity enhancements,which showed that superior thermal conduc-tivity of nanofluids could be harnessed for cooling applications.Ó2014Elsevier Ltd.All rights reserved.1.IntroductionThermal management and energy storage systems are thrust areas of research in fields such as automobile/industrial cooling,renewable energy utilization as evident from the recent literature [1–11].Maintenance of ideal working temperature by removing the heat dissipated is essential for proper functioning of high speed engines,microprocessors,etc.This has become a great challenge due to increasing thermal loads driven by technological advance-ments.The strategies to improve efficiency of heat transfer sys-tems include active modes (increasing coolant velocity,use of coolants with higher thermal conductivity)and passive modes(use of fins,channels with expansions and constrictions,higher heat transfer area).Thermal conductivity of liquids (0.1<k l <10W/mK)lies between that of insulators and non-metallic sol-ids.It is possible to tailor the thermophysical properties like ther-mal conductivity and viscosity through use of nanoparticle dispersions.Nanofluid,colloidal dispersion of solid nanoparticles in liquid [12]belongs to a new class of coolants on which extensive research has been carried out over the past two decades.Research on nanofluids has been extended towards exploring the influence of different kinds of nanomaterials like metal [13–17],metal oxide [17–27],carbon nanotubes [28–31],graphene [32,33],etc.on the important transport properties:thermal con-ductivity and viscosity.The factors that greatly affect transport properties of nanofluids include morphology of nanomaterials [18,29,34–36],dispersion quality [37–40]and the method of preparation [41–44]./10.1016/j.apenergy.2014.09.0230306-2619/Ó2014Elsevier Ltd.All rights reserved.⇑Corresponding author.Tel.:+919790377951;fax:+914362264120.E-mail address:ksrajan@ (K.S.Rajan).It is challenging to achieve higher thermal conductivity and lower viscosity simultaneously in nanofluids.Introduction of solid nanoparticles in liquids will eventually increase thermal conductiv-ity[45–47]as well as viscosity and hence higher pumping power [43,45].However,we have recently demonstrated the preparation of metal oxide(MO x)–propylene glycol(PG)nanofluids with lower viscosity and higher thermal conductivity than pure propylene gly-col[24,40,48].Favorable interactions between metal oxide nano-particles and propylene glycol molecules led to lower viscosity of MO x–PG nanofluids.This makes the MO x–PG nanofluids as excel-lent prospects for cooling applications.These researchfindings motivated us to investigate transport properties of ethylene glycol based nanofluids,since ethylene glycol(EG)is chemically similar to propylene glycol having hydrogen bonding networks.The properties of ethylene glycol based nanofluids have been widely studied[39,49–56]due to their use as coolants in automo-biles.Sand–ethylene glycol–water dispersions prepared using stir-red bead milling and ultrasonication showed thermal conductivity enhancement of above20%at a particle concentration of$1.8vol.% [50].Single-walled CNT inclusions were dispersed in ethylene gly-col using bile salt as dispersant and at0.2vol.%of nanotube load-ing,thermal conductivity increased up to14.8%[53].Thermal conductivity of Al2O3–ethylene glycol nanofluids have been stud-ied over a wide temperature range(298–411K)using a liquid metal transient hot wire apparatus[49].Viscosities of CuO–EG–water mixture nanofluids have been studied over a temperature range ofÀ35to50°C[52].The dispersions showed Newtonian flow behavior over the temperature range investigated[52].ZnO–ethylene glycol nanofluids containing5vol.%of nanoparti-cles,prepared by3-h ultrasonication yielded thermal conductivity enhancement of26.5%[51].These nanofluids were non-Newtonian (shear-thinning)at higher concentrations and Newtonian at lower concentrations[51].Kole and Dey[39]prepared ZnO–EG nanofl-uids by extended ultrasonication and the optimum ultrasonication time was found to be60h.Approximately40%enhancement in thermal conductivity of ZnO–EG nanofluids was reported for parti-cle volume concentration of3.75vol.%[39].Understanding the mechanism of interaction between nanoma-terials and basefluid molecules could lead to nanofluid formula-tion methods,which result in well dispersed nanofluids.In our earlier work[44],one such formulation method was reported which resulted in nanofluids with improved transport properties. Surfactant-free ZnO–propylene glycol nanofluids prepared using ultrasonication had higher thermal conductivity[57]and lower viscosity compared to those of propylene glycol[48].Formation of propylene glycol molecular layers over ZnO nanoparticles in ZnO–propylene glycol nanofluids was found to be responsible for higher thermal conductivity,while the disturbance to hydrogen bonding network of propylene glycol contributed to lowering of their viscosity in comparison to that of pure propylene glycol.Thus, a coolant with higher thermal conductivity and lower viscosity was prepared and the underlying mechanisms were understood [48,57].With thesefindings,a new method of formulation of ZnO–PG–water nanofluids was developed in which,water was commixed with ZnO–PG dispersion instead of dispersing ZnO nanoparticles in PG–water mixture using the conventional method.This method aided in preservation of propylene glycol molecular layers over ZnO nanoparticles and foreclosed the inter-action of ZnO nanoparticles and water molecules.The proposed method allowed preparation of ZnO–PG–water nanofluids without any surfactants and with better transport properties[44].How-ever,viscosity reduction of ethylene glycol based nanofluids has not been evidenced in literature thus far.In this work,ZnO–ethylene glycol(EG)nanofluids were prepared using ultrasonication without using any surfactant. ZnO–EG–water nanofluids were prepared using the method similar to that proposed in our earlier work[44].Transport properties of ZnO–EG and ZnO–EG–water nanofluids were studied as a function of temperature and nanoparticle volume concentration.Models have been developed to predict the viscosity and thermal conduc-tivity of ZnO–EG nanofluids and ZnO–EG–water nanofluids.These nanofluids have been tested for their cooling performance under transient conditions.2.Materials and methods2.1.MaterialsZinc nitrate hexahydrate,ammonium carbonate,ethylene glycol were procured from Merck,India.All the chemicals were used as procured without any purification.2.2.Synthesis and characterization of ZnO nanoparticlesZnO nanoparticles were synthesized using chemical precipita-tion method using Zinc nitrate hexahydrate as precursor at room temperature[58,59].Ammonium carbonate has been used as reducing agent in the synthesis procedure described in our earlier work[59].Morphology and crystallographic patterns of the synthesized ZnO nanoparticles were examined using scanning electron microscopy(JSM6701F,JEOL,Japan)and powder X-ray diffractometry(D8Focus,Bruker,Germany).2.3.Formulation of nanofluidsZnO–EG nanofluid of concentration4vol.%was prepared by dis-persing the synthesized ZnO nanoparticles in ethylene glycol byNomenclatureSymbol Meaninga,b,c coefficients in Eq.(14)c p specific heat(J/kg K)k thermal conductivity(W/mK)m mass(kg)Q amount of heat transferred(W)T temperature(°C)t time(s)U f uncertainty associated with the measurement of param-eter‘f’U xj uncertainty in the measurement of variable X jx function of nanoparticle concentrationy function of nanoparticle concentration and temperature A,B functions of nanoparticle concentration N number of factors in Eq.(1)Greek symbols/nanoparticle volume concentrationl viscosity(mPa s)q density(kg/m3)Subscriptsbf basefluidnf nanofluidr relative/ratioK.S.Suganthi et al./Applied Energy135(2014)548–559549ultrasonication(Vibracell™,Sonics,USA).20kHz)was carried out until ZnO–EGmum thermal conductivity and minimumthermal conductivity of ZnO–EG dispersionsular intervals of time duringof different volume fractions wereZnO–EG nanofluids with required volumeA hierarchical method demonstrated inhas been utilized for the preparation ofnanofluids by mixing water with4vol.%ofumes.The prepared nanofluids thus had aof50vol.%water and50vol.%ethylenetions of ZnO–EG–water nanofluids wereing2vol.%ZnO–EG–water nanofluids withglycol–water mixture.2.4.Characterization of nanofluidsTransport properties like viscosity andwere studied for the ZnO–EG andfunction of temperature and nanoparticle volume fraction.Thermal conductivity of nanofluids was measured using transient-hot wire method(Decagon devices,USA).KS-1probe has been used for mea-surements.Temperature of the sample was maintained using a cir-culating water bath(TC-502,Brookfield Engineering,USA).Viscosities of nanofluids were measured using a rotational vis-cometer(LVDV-II+Pro,Brookfield Engineering,USA).S18and S64spindles were used for ZnO–EG at higher(27–140°C)and lower temperatures(10–20°C)respectively.S00spindle was used for ZnO–EG–water nanofluids over the entire temperature range investigated.During the viscosity measurements,temperature of the ZnO–EG nanofluids and ZnO–EG–water nanofluids were main-tained using a temperature controller(ThermoselÒ,Brookfield Engineering,USA)and constant temperature bath(TC-502,Brook-field Engineering,USA).Hydrodynamic particle size distribution of ZnO–EG dispersions was measured using dynamic light scattering technique(NanoZS,Malvern instruments,UK)as a function of ultrasonication time.Thermal conductivity,viscosity and hydrodynamic size distribu-tion measurements were repeated at least three times to ascertain the repeatability and reproducibility of measurements.Uncertain-ties in viscosity,thermal conductivity and average hydrodynamic size have been shown in the graphs as standard deviations. Coefficients of variation during thermal conductivity and viscosity measurements for the standards provided by the respective manu-facturer were0.25%and0.77%respectively.Maximum coefficient of variation in thermal conductivity and viscosity measurement of nanofluids and basefluids were0.87%and1.76%respectively.Total uncertainty in the measurement of a parameter was calculated taking into account of the random error only,as the sys-tematic error was negligible compared to random error.Uncertain-ties in relative viscosity,thermal conductivity ratio and heat transfer ratio were calculated using the following formula[60] and have been expressed as standard deviation.U f¼ÆX Nj¼1U xj@f@x j 2"#0:5ð1Þ2.5.Heat transfer experimentsIn order to compare the performance of nanofluids as coolants in relation to their basefluids,transient heat transfer experiments were carried out using nanofluids and basefluids.The experimen-tal setup(Fig.1)comprised a stainless steel sample reservoir, electrical heating coil connected to AC power supply and a temperature sensor connected to data logger.In order to maintain constant heatflux boundary condition,test section was heated by supplying constant AC power through the heatingfilament wound over the test section,which was subsequently insulated.In a typ-ical experiment,the test section wasfilled with a constant volume of testfluid.A constant voltage of10V was supplied.Temperature increase of testfluid was measured as a function of time for about 10–20min.The testfluids studied were:1.5vol.%ZnO–EG,1vol.% ZnO–EG,0.25vol.%ZnO–EG,and EG and2vol.%ZnO–EG–water, 1.5vol.%ZnO–EG–water,0.5vol.%ZnO–EG–water and EG–water.3.Results and discussionZnO nanoparticles used in this study had uniform spherical morphology with a size range of25–40nm(Fig.2a).Highly crystal-line nature of the ZnO nanoparticles synthesized through chemical precipitation method was evident from the X-ray diffraction pat-tern(Fig.2b),which are in accordance with those for hexagonal wurtzite phase(JCPDS No.89-1397).As evident from the scanning electron micrograph,synthesized ZnO nanoparticles prevail in slightly agglomerated state.Nanofl-uids with high dispersion quality are known to have superior transport properties[55,61,62].The advantages of well dispersed nanofluids to be used as coolants are(i)higher surface area for heat transfer,(ii)lower viscosity and lesser pumping power,and(iii) good colloidal stability due to the smaller size of aggregates[46].Ultrasonication plays a critical role in the formulation of nano-fluids by assisting in breakage of aggregates resulting in high qual-ity dispersions.However,there exists an optimum ultrasonication time in the preparation of nanofluids[24,40,48,61,62].In case of extending ultrasonication beyond the optimum ultrasonication time,re-aggregation may occur leading to formation of larger aggregates resulting in instability of the nanofluids[59].Other than the physical and chemical properties of the dispersed phase of nanofluids,dispersion characteristics have significant influence on thermal conductivity,viscosity and stability of nanofluids. Hence,it is pertinent to determine optimum ultrasonication energy(or)time required to prepare nanofluids with superior dis-persion characteristics,evidenced in terms of increased thermal conductivity and reduced viscosity.Fig.3a shows the influence of ultrasonication time on thermal conductivity and viscosity of4vol.%ZnO–EG nanofluid.Thermal conductivity of ZnO–EG nanofluid(4vol.%)gradually increased with increasing ultrasonication time and saturated at about30h. Also,viscosity of the dispersion decreased with increasing Fig.1.Schematic representation of the experimental setup used for heat transfer experiments.550sonication time.Fig.3b shows the influence of ultrasonication time on the average hydrodynamic diameter of the ZnO–EG dispersion, from which it is evident that the average hydrodynamic diameter decreased with ultrasonication time.As ultrasonication time increased,larger aggregates of ZnO nanoparticles had been broken up into smaller aggregates (Fig.3b).Formation of smaller aggregates resulted in increase in the fraction of heat conducting paths and decrease in the fraction of continuous phase with relatively higher thermal resistance.In other words,size reduction of aggregates or dispersion of nanopar-ticles resulted in increased surface area which resulted in increase in thermal conductivity.As ZnO–EG dispersion was ultrasonicated, larger aggregates were broken up progressively and hence the per-sistent increase in thermal conductivity.At about$30h,saturation in thermal conductivity increase was observed showing that nano-particles/clusters were well dispersed.Aggregate sizes in solid–liquid dispersions have profound influ-ence on their viscosity.Greater the ratio of aggregate size to pri-mary particle size,higher is the resistance tofluidflow[59,63] and hence higher viscosity.As ultrasonic processing progressed, viscosity decreased(Fig.3a)probably due to the reduction in the size of the aggregates.3.1.Viscosity of dispersions3.1.1.Influence of nanoparticle concentration on viscosity3.1.1.1.ZnO–EG dispersions.Viscosities of ZnO–EG nanofluids were independent of shear rate over a range of66–238sÀ1(Fig.4a)for the concentration range investigated(0.25–4vol.%).This reveals that dispersion of ZnO nanoparticles did not alter theflow behavior significantly and nanofluids remained to be Newtonian.Relative viscosity(l r=l nf/l b)–ZnO nanoparticle volume con-centration relationship of ZnO–EG nanofluids(Fig.4b)shows that relative viscosity of ZnO–EG dispersions(averaged over shear rates in the range66–238sÀ1)decreased with increasing nanoparticle loading.Viscosities and relative viscosities of ZnO–EG nanofluids showed a contradictive behavior with those reported for other nanofluid systems as well as ZnO–EG nanofluids in literature.Gal-lego et al.[64]reported increasing viscosity of ZnO–EG nanofluids with increasing nanoparticle concentration.However,those nano-fluids were prepared by ultrasonication for a time period of16min only,which was much lower compared to the ultrasonication time used in this study.Yu et al.[51]dispersed ZnO nanoparticles of size 10–20nm in ethylene glycol using ultrasonic processing for3h. ZnO–EG dispersions thus prepared had higher viscosities($100% increase)than basefluid and showed shear thinning characteristics at particle concentrations P3vol.%.Moosavi et al.[65]observed $26%enhancement in viscosity of ZnO–EG nanofluids for a very low particle concentration of0.6vol.%,while using ammonium cit-rate as dispersant.From the nanofluid viscosity-ZnO nanoparticle concentration data of the above[51,64]and the shear-thinning nature of nanofluids in the work of Mossavi et al.[65],it appears that those nanoparticles exhibited high degree of aggregation. ZnO–EG nanofluids prepared by Kole and Dey[39]were ultrasoni-cated for an optimum ultrasonication time of60h and viscosities of ZnO–EG nanofluids(63.5vol.%)were very close to that of base fluid.This was attributed to the well-dispersed nature of ZnO nanoparticles in ethylene glycol.Hence the disparity observed inFig.2.(a)Scanning electron micrograph of synthesized ZnO nanoparticles and(b) X-ray diffraction pattern of ZnO nanoparticles.Fig.3.Influence of ultrasonication time on(a)thermal conductivity and viscosity vol.%ZnO–EG nanofluids at27°C and(b)average hydrodynamic diameter of ZnO nanoparticles in ZnO–EG nanofluids.the viscosities of ZnO–EG nanofluids mightbe due to the differ-ences in nanofluid formulation method (ultrasonication time/use of surfactant),morphological characteristics of ZnO nanopowder used,etc.which ultimately resulted in different aggregate size distributions.Intermolecular as well as intramolecular hydrogen bonding per-sists in ethylene glycol.Metal oxide nanoparticles are known have hydroxyl groups on their surface when dispersed in polar liq-uids [66].Hydroxyl groups engaged in intramolecular and intermo-lecular hydrogen bonding between ethylene glycol molecules are likely to form hydrogen bonds with hydroxyl groups on nanoparti-cles’surface.Hence,the hydrogen bonding network of ethylene glycol is reorganized.At higher nanoparticle concentration,the number of ZnO nano-particles interacting with ethylene glycol molecules was higher and hence,perturbations to the hydrogen bonding network of eth-ylene glycol were enhanced leading to decrease in viscosity with increasing nanoparticle concentration.In our recent studies of propylene glycol based nanofluids [24,40,48,67],rheological behavior similar to that of ZnO–EG nanofluids of the current study was observed.CuO–PG,ZnO–PG,Fe 2O 3–PG,sand–PG,Mn 0.43Fe 2.57O 4–PG nanofluids had viscosities lesser than propylene glycol and perturbations hydrogen bonding network was identified as the rationale behind the unusual rheological behavior of propylene glycol based nanofluids.3.1.1.2.ZnO–EG–water nanofluids.The influence of nanoparticle concentration on relative viscosity of ZnO–EG–water nanofluids (Fig.5)shows decreased viscosities at higher particle concentra-tion.It may be recalled that the ZnO–EG–water nanofluids were prepared by addition of water to ZnO–ethylene glycol dispersion,which had lower viscosity than ethylene glycol due to disturbance in hydrogen bonding network.By adding water to ZnO–EG disper-sion,viscosity reduction has been maintained by preserving ethyl-ene glycol molecular layers over ZnO nanoparticles and thus avoiding the direct contact of ZnO nanoparticles and water mole-cules.It is known that the direct contact of surfactant-free ZnO nanoparticles with water molecules promote their aggregation [44,59,68]and increase dispersion viscosity.Hence,through pre-vention of direct contact between surfactant-free ZnO nanoparti-cles and water and preservation of ZnO nanoparticles–ethylene glycol interactions,17.34%reduction in viscosity has been obtained for 2vol.%ZnO–EG–water nanofluid.The percentage reduction in viscosity of 2vol.%ZnO–EG–water nanofluids (17%)is comparable to that of 2vol.%ZnO–EG nanofluid ($20%).3.1.2.Influence of temperature on viscosity3.1.2.1.ZnO–EG nanofluids.As coolants,nanofluids will be sub-jected to temperature variations.Hence,it becomes pertinent to investigate rheological behavior of nanofluids under thermal loads.Influence of temperature on viscosity of ZnO–EG nanofluids has been studied over a wide temperature range of 10–140°C (Fig.6a and b).Viscosity of ZnO–EG nanofluids decreased in an asymptotic manner with increasing temperature similar to that of ethylene glycol,the base fluid (Fig.6a).Viscosity variation of nanofluids and the base fluid with temperature could be fitted into power law as followsl ¼AT ÀBð2ÞValue of ‘B ’signifies the temperature dependency of viscosity of the fluids.‘B ’value decreased with increasing concentration with pure ethylene glycol having the highest ‘B ’value.This shows that the addition of nanoparticles had reduced the temperature depen-Fig.4.(a)Influence of shear rate on viscosity of ZnO–EG nanofluids of different concentrations and ethylene glycol and (b)influence of nanoparticle volume concentration on relative viscosity of ZnO–EG nanofluids.Fig.5.Influence of nanoparticle volume concentration on relative viscosity of ZnO–EG–water nanofluids.Energy 135(2014)548–559nanoparticles to increased viscous dissipation is temperature-inde-pendent.Hence,viscosity of ZnO–EG nanofluid shows lower tem-perature dependence than pure ethylene glycol,with lowest temperature dependence observed at the highest nanoparticle con-centration(4vol.%)investigated.In order to further evaluate the effect of addition of nanoparti-cles on nanofluid viscosity,the relative viscosity of nanofluids was calculated as follows:l r ¼l nanofluid l base fluid¼A nf TÀB nfA bf TÀB bfðFig.7shows the relationship between relative viscosity andtemperature at different nanoparticle concentrations.From Fig.it can be observed that relative viscosity increases with increasing temperature,which implies that decrease in viscosity of nanofluids with temperature is lower than that of basefluid.Highest reduc-tion in viscosity of ZnO–EG nanofluids has been observed at the lowest temperature investigated.For instance,reduction in viscos-ity of4and2vol.%ZnO–EG nanofluids at10°C are66%and45% respectively.At lower temperatures,movement of liquid mole-cules is dominated by intermolecular forces,which have higher influence over liquid viscosities at lower temperatures.At higher temperatures,intermolecular forces between molecules begin diminish and the movement of liquid molecules is controlled by their translational energy.Since the addition of ZnO nanoparticles brings out reduction of dispersion viscosity by disturbing hydrogen bonding network,viscosity reduction is more pronounced at lower temperatures at which liquid viscosities depend on intermolecular forces than that at higher temperatures at which influence of inter-molecular forces on liquid viscosity is negligible.Another striking observation from viscosity measurements that relative viscosities of ZnO–EG nanofluids were lower than unity up to temperature of110°C.This shows that pumping power required to circulate ZnO–EG nanofluids will be lower than that required for pure ethylene glycol up to110°C.As long as the tem-perature is below110°C,relative viscosity of4vol.%nanofluid lower than that of2vol.%whereas at140°C,the relative viscosity 4vol.%is higher than that of2vol.%.To get better understanding,variation of relative viscosity with nanoparticle concentration at different temperatures has been plotted in Fig.8.The slope of the curve gradually changes from negative to positive as the temperature is increased from10 140°C.3.1.2.2.Viscosity model.The abundance of suspensions and disper-sions in practical applications puts forward the demand for devel-opment of models to predict viscosity.Einstein[71]derived an expression to determine viscosity of dispersions of spherical, non-interacting particles in a dilute suspension.Mooney[72]pro-posed a model for prediction of relative viscosity of concentrated suspensions(/>0.05)in which empirical constants were used.Fig.6.Influence of temperature on viscosity of ZnO–EG nanofluids and ethylene glycol(a)27–140°C and(b)10–20°C.Fig.7.Influence of temperature on relative viscosity of ZnO–EG nanofluids different concentrations.Fig.8.Influence of nanoparticle volume concentration on relative viscosities ZnO–EG nanofluids at different temperatures.semi-empirical equation for proposed by Krieger andcle concentrations.Taking particle et al.[74]proposed a modified tion that predicted viscosity aggregation well.All these enhancement in viscosity of Since viscosity reduction has uids,these models cannot beA new empirical model isZnO–EG nanofluids over aof0–4vol.%and27–140°C account increase in viscosity due viscosity due to disturbance in particle addition and the effect of lr¼xÀywhere‘x’is increase in relative‘y’is decrease in relative viscosity ular forces.While‘x’is a function ‘y’is a function of nanoparticle To determine the expression nanofluid viscosity withcosity of nanofluid at140°C was centration,as the influence ofon viscosity at this temperature (l r)-nanoparticle volumewas found to be l r=1+5.9765/. predict the increase in viscosity Therefore,Eq.(4)becomeslr¼1þ5:9765/ÀfðT;/ÞTaking into account of the fact particle concentration(Fig.8),the‘y’in Eq.(4)isticle concentration andUsing the relative viscosity27–140°C,the following empirical Minitab16with a regressionlr¼1þ5:9765/À518:979/TÀ0:The developed empirical model ZnO–EG dispersions well,as comparison between predicted viscosities.3.1.2.3.ZnO–EG–water nanofluids. temperature on viscosity of water(basefluid)over aof ZnO–EG–water nanofluidsture exponentially and could be nanofluids(Eq.(2)).‘B’values(from Eq.(2))of2vol.%ZnO–EG–water were found respectively.Similar to ZnO–EG with increasing nanoparticleis an indication of dependency ofature.Viscosity of ethylene glycol–water mixture,the basefluid showed higher temperature dependency compared to nanofluids, which might be due to the higher magnitude of intermolecular forces that existed in the basefluid.Relative viscosities of ZnO–EG–water nanofluids have been cal-culated using Eq.(3)and have been plotted against temperature (Fig.10b).Relative viscosities were less than one over the entire temperature range investigated(10–55°C).Relative viscosity of 2vol.%nanofluid was lower than that of1vol.%nanofluids at all temperatures.The relative viscosity may be related to temperature and nanoparticle concentration using the form Eq.(5)with expres-sion for f(T,/)specifically derived for ZnO–EG–water system as follows:fðT;/Þ¼5TÀ0:1802/0:5455ð7Þparison between experimental and predicted relative viscosities ZnO–EG nanofluids.Fig.10.(a)Influence of temperature on viscosity of ZnO–EG nanofluids and ethylene glycol and(b)influence of temperature on relative viscosity of ZnO–EG nanofluids at different concentrations.554。