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Turbulent ow

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the friction factor for nanouids. 2010 Elsevier Ltd. All rights reserved.

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engines through the radiators and in heat exchangers in all typesof industries. In all these applications the uid ow is generallyin the turbulent regime, because higher heat transfer is achievedthrough the turbulent ow.

Therefore, the uid dynamic and heat transfer characteristics ofnanouids under the turbulent ow conditions must be knownaccurately to evaluate their performance. However, only a limited

retical model for heat transfer as follows:

Nu 1 CPef 00h00Rem: 1Here f0 and h0 are the derivatives of the dimensionless velocity andthe dimensionless temperature, respectively. They proposed that C*

was a constant to be determined from the experiment.Following the suggestion of Xuan and Roetzel [6], Xuan and Li

[7] carried out the experiments with copper nanoparticles dis-persed in water to obtain a convective heat transfer equation fornanouids under the turbulent ow condition.

* Corresponding author. Tel.: +1 907 474 6094; fax: +1 907 474 6141.

International Journal of Heat and Mass Transfer 53 (2010) 46074618

Contents lists availab

H

.eE-mail address: dkdas@alaska.edu (D.K. Das).showed that the thermal conductivity and the viscosity of liquidsare altered dramatically by dispersing ultra-ne particles of c-alu-minum oxide (Al2O3), silicon dioxide (SiO2) and titanium dioxide(TiO2). Subsequently, this nding was conclusively establishedfrom experiments of other researchers; notably, Choi [2], Wanget al. [3] and Eastman et al. [4]. For the same Nusselt number ofuid ow in a given ow passage, if the thermal conductivity in-creases then the convective heat transfer also increases in the sameproportion. Nanouids have valuable applications in the area ofheating buildings through the hydronic coils, cooling automotive

the well-known DittusBoelter correlation for the single-phaseuid with slight changes in the constant coefcient and the powerof Prandtl number. Their friction factor and heat transfer measure-ments were limited to particle volumetric concentrations of 2.78%for Al2O3 and 3.16% for TiO2. They also performed viscosity mea-surements up to a volume concentration of 10% and found thatat that concentration level, the viscosity of c-Al2O3 nanouid was200 times greater than that of the base uid. For the TiO2 nano-uid, at the same concentration the viscosity was 3 times greaterthan that of the base uid. Xuan and Roetzel [6] presented a theo-Convection correlationPressure lossFriction factor

1. Introduction

Nanostructured materials can hauids used for the transport of heametallic or non-metallic particles ofwhose dimensions are less than 100tional heat transfer liquids, the effethe resulting medium increases su0017-9310/$ - see front matter 2010 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2010.06.032ajor impact on the liq-eat exchangers. Whenr thermal conductivity,re dispersed in conven-hermal conductivity ofally. Masuda et al. [1]

number of studies appear in the literature on the turbulent charac-teristics of nanouids. Pak and Cho [5] performed the friction fac-tor and convective heat transfer coefcient measurements onc-Al2O3 and TiO2 nanoparticles in water. They determined thatthe Darcy friction factor of the nanouids of volume concentrationranging from 1% to 3% agreed well with the correlation for conven-tional single-phase uid. They presented a new Nusselt numbercorrelation for the turbulent heat transfer, which was similar toNanouidsParticle concentration coefcient correlation from experiments, as a function of these properties and the particle volumetric

concentration. The pressure loss was also measured and a new correlation was developed to representDevelopment of new correlations for conin turbulent regime for nanouids

Ravikanth S. Vajjha, Debendra K. Das *, Devdatta P. KDepartment of Mechanical Engineering, University of Alaska, P.O. Box 755905, Fairbank

a r t i c l e i n f o

Article history:Received 12 February 2009Received in revised form 26 May 2010Accepted 26 May 2010

Keywords:

a b s t r a c t

This paper presents new cfrom the experiments of ndispersed in 60% ethyleneout in the fully developedparticle volumetric concencosity, density, specic heaing particle volume conc

International Journal of

journal homepage: wwwll rights reserved.ctive heat transfer and friction factor

lkarni99775-5905, USA

lations for the convective heat transfer and the friction factor developedparticles comprised of aluminum oxide, copper oxide and silicon dioxideol and 40% water by mass. The experimental measurements were carriedulent regime for the aforementioned three different nanouids at variousions. First, the rheological and the thermophysical properties such as vis-d thermal conductivity were measured at different temperatures for vary-ations. Next, these properties were used to develop the heat transfer

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Their experiment was limited to a 2% particle volumetric concentra-tion. From their pressure loss experimental data, they found thatthe Cuwater nanouid had nearly the same friction factor as water,which they attributed to the dilute concentration. Buongiorno [8]analyzed theoretically the boundary layer in nanouid ow andproposed a Nusselt number correlation for turbulent ow, as a func-tion of the Reynolds number, Prandtl number, friction factor and thelaminar sublayer thickness. He presented an iterative procedure tocalculate the Nusselt number until the nanoparticles volume frac-tion in the laminar sublayer converges to a single value. Nguyenet al. [9] conducted experiments with Al2O3water nanouid. Theytested the nanouid in the range of Reynolds number from 4000 toabout 15,000 and up to a particle volumetric concentration of 6.8%.They found that the heat transfer coefcient increased by 40% overthat of water for a 6.8% volumetric concentration of Al2O3 particle.They did not present a Nusselt number correlation and no pressureloss measurements were reported.

Williams et al. [10] conducted experiments with alumina and

Nomenclature

Cp specic heat (J/kg K)d inside diameter of tube (m)dp nanoparticle diameter (m)f Darcy friction coefcienth heat transfer coefcient, h = q0 0/(Tw Tb), (W/m2 K)k thermal conductivity (W/m K)L length of the tube (m)_m mass ow rate (kg/s)Nu Nusselt number, Nu = (hd/K)Pr Prandtl number, Pr = (lCp/k)_q rate of heat transfer (W)q00 heat ux (W/m2)Re Reynolds number, Re = (qVd/l)R2 coefcient of determinationT temperature (K)T0 reference temperature, 273 KV velocity (m/s)

4608 R.S. Vajjha et al. / International Journal of Hzirconia nanouids in water. The alumina concentration testedwas up to 3.6% and the zirconia up to 0.9%. They found that the vis-cous pressure losses were within 20% of the theory of Blasius andMcAdams which are for the single phase liquid. They did not pres-ent a Nusselt number correlation.

The objective of this study was to use more nanouids andhigher concentrations tested by prior researchers and developthe friction factor and Nusselt number correlations, so that theywill be more general. The correlation of Xuan and Li [7] is basedon the experiment on only one nanouid. Pak and Cho [5] devel-oped their correlation from two nanouids. Furthermore, the par-ticle volumetric concentrations tested thus far were low (lessthan 3.6%). Therefore, in the present study three nanoparticles,Al2O3, copper oxide (CuO) and SiO2 (two metallic and one non-metallic) were selected for the experiments because of their goodthermal properties and easy availability. The base uid was chosento be 60% ethylene glycol and 40% water mixture by mass (60:40EG/W), which is widely used as the heat transfer uid in the coldregions of the world in building heating and in automobile radia-tors. First the thermophysical properties of these nanouids weremeasured and correlations were developed. Then these propertiescorrelations were used to develop the friction factor and heattransfer relations. The experiments revealed that the convectiveheat transfer and pressure loss of nanouids are higher than thebase uid. The physical and mechanistic explanation for thisenhancement may be due to multiple effects; higher thermal con-ductivity, Brownian motion, thermophoresis, transport mecha-nisms of nanoparticles and uid properties variation in the near-wall region. All these effects should be examined in the futureresearch.

2. Determination of thermophysical properties

Three types of nanouids, Al2O3, CuO and SiO2 were tested inthis study. The nanouids were procured from Alfa Aesar [11] ata particle mass concentration of 50% in water. Then properly calcu-lated mass of 60:40 EG/W mixture was added to the concentratednanouid and careful mass measurement of the resulting uid in aprecise electronic mass balance was conducted to arrive at the de-sired particle volumetric concentration of nanouids of 1%, 2%, 4%,6%, 8%, and 10%. Before using any nanouid sample for measure-ments, it was subjected to ultra-sonication for several hours in abath type sonicator to ensure proper dispersion of the nanoparti-cles. The characteristics of nanoparticles used in this study are

Greek symbolsDP differential pressure loss (Pa)DT temperature difference (K)j Boltzmann constant, 1.381 1023 (J/K)l viscosity (mPa s)q density (kg/m3)s shear stress (Pa)/ particle volumetric concentration (%)

Subscriptsb bulkbf base uidf uidnf nanouidp nanoparticlew wall

and Mass Transfer 53 (2010) 46074618summarized in Table 1 below.

2.1. Viscosity

Measurements of viscosity of copper oxide nanoparticlesdispersed in 60:40 EG/Wwere conductedusing the LVDV-II+ Brook-eld viscometer [15] with a Julabo computer controlled tempera-ture bath to set the nanouids temperature at different values.Namburu et al. [16] carried out the measurements and presentedthe following correlation for the viscosity of CuOnanouid as a func-tion of concentration and temperature.

loglnf AeBT; 3where A and B are second order polynomial functions of particlevolumetric concentration /. This correlation was based on volumet-ric concentration of 0 6 / 6 0.06 and between a temperature rangeof 35 C < T < 50 C for their application in cold regions.

Namburu et al. [17] further conducted similar measurementson SiO2 nanouids and developed a correlation similar to Eq. (3),but the curve-t coefcients A and Bwere different. The coefcientA was a third order polynomial and B was a second order polyno-mial function of particle volumetric concentration /. Sahoo et al.[18] measured the rheological properties of Al2O3 nanouids withthe same experimental setup that was used by Namburu et al. They

rived. It is observed that lbf (i.e., the viscosity of the base uid)takes care of the temperature effect on viscosity in Eq. (5) so thatno additional term involving T is necessary. The above correlationis applicable in the temperature range of 273 K(0 C) < T