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Research Papers

# Viscosity and Friction Factor of Aluminum Oxide–Water Nanofluid Flow in Circular TubesOPEN ACCESS

[+] Author and Article Information
Clement C. Tang

Mem. ASME
Mechanical Engineering Department,
University of North Dakota,
243 Centennial Drive Stop 8359,
Grand Forks, ND 58202
e-mail: clement.tang@engr.und.edu

Sanjib Tiwari

Mem. ASME
Kiewit Mining Group Inc.,
3555 Farnham Street,
Omaha, NE 68131
e-mail: sanjib.tiwari@kiewit.com

Matthew W. Cox

Mem. ASME
Hutchinson Technology Inc.,
329 North High Drive NW,
Hutchinson, MN 55350
e-mail: Matthew.Cox@hti.htch.com

1Corresponding author.

Manuscript received July 28, 2013; final manuscript received September 23, 2013; published online October 17, 2013. Assoc. Editor: Sushanta K Mitra.

J. Nanotechnol. Eng. Med 4(2), 021004 (Oct 17, 2013) (6 pages) Paper No: NANO-13-1044; doi: 10.1115/1.4025540 History: Received July 28, 2013; Revised September 23, 2013

## Abstract

Experiments have been conducted to characterize the viscosity and friction factor of aluminum oxide (Al2O3) nanoparticle dispersions at 6 vol. % in water. Rheological characterization of the Al2O3 nanofluid has shown that it exhibits a Newtonian fluid behavior for the shear rate range of 6 to 122 s−1 at temperatures between 6 and 75 °C. Friction factor results of the nanofluid flowing through circular tubes of 1 m in length with different inner tube diameters (2.97 and 4.45 mm) were experimentally measured in the laminar and the onset of transition regions. The experimental results from this study indicate that, when the nanofluid properties are properly characterized, the friction factors of the Al2O3 nanofluid are largely in agreement with classical friction factor theory for single-phase flow. An early transition to turbulent flow is observed for the nanofluid flow at a Reynolds number of approximately 1500, when compared with water flow where transition occurs at the textbook Reynolds number of roughly 2300.

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## Introduction

Modern researchers have been in search for more suitable means of efficient heat dissipation for applications with higher operational temperature and more compact designs. The conventional cooling fluids, such as water and air, are becoming inadequate to achieve many of the current needs for heat removal. Several studies have suggested the use of mixtures consisting of suspensions of micrometer-sized particles in base liquid fluids, such as water and oil, to alter the thermal conductivity, thereby achieving higher heat transfer capability [1-3]. Although such mixtures showed improvement in the heat transfer capability, they inherit problems such as clogging and sedimentation. In addition, mixtures with micrometer-sized particles have been found to increase damage in systems due to abrasion. Such mixtures are also found to be inapplicable for miniaturized systems.

In recent years, colloidal dispersion of solid nanoparticles in liquid base fluids (nanofluids) has received significant attention for their potential to be a new class of heat transfer fluids [4,5]. It has been widely documented that adding nanoparticles, such as aluminum oxide or alumina (Al2O3), copper oxide (CuO), and titanium dioxide (TiO2), to a liquid base fluid can enhance the thermal conductivity [6,7]. However, the increase in thermal conductivity does not necessarily mean a beneficial enhancement of heat transfer capability.

Several recent researchers have documented the beneficial enhancements in convective heat transfer using nanofluids [8-10]. However, others have countered that the heat transfer enhancement seen in nanofluids may be offset by the increase of pumping power as a result of increase in the viscous pressure drop. Hence, the cost of higher viscous pressure drop, along with the potential wear on systems, may exceed the benefits from the increase in heat transfer.

Before addressing the tradeoff of heat transfer enhancement with the cost of pressure drop increase in nanofluids, a proper fundamental understanding of the viscous friction factor of nanofluids needs to be established. In this study, Al2O3–water nanofluid properties and the friction factor of nanofluid flow in tubes are measured. The measured nanofluid friction factors are then compared with conventional theory for friction factor of single-phase flow to determine whether or not nanofluid flow behaves as single-phase flow.

## Background

###### Friction Factor.

The friction factor for internal flow in a circular tube can be determined from the pressure drop using the Darcy–Weisbach equationDisplay Formula

(1)$Δp=fLDρU22$

The average flow velocity (U) can be determined experimentally from the measured mass flow rate ($m·=ρUA$). Thus, the friction factor in Eq. (1) can be expressed in terms of mass flow rate asDisplay Formula

(2)$f=18ρm·2ΔpLπ2D5$

For laminar fully developed flow, the conventional theory for friction factor is simply f = 64/Re. When the flow is turbulent, the friction factor can be determined from several correlations available in the literature. One of the most ubiquitous ones is the correlation from Blasius [11] for 4000 ≤ Re ≤ 105Display Formula

(3)$f=0.316Re-0.25$

About two decades after Blasius [11], the following correlation for 4000 ≤ Re ≤ 5 × 106 was introduced by Drew et al. [12]Display Formula

(4)$f=0.0056+0.5Re-0.32$

Churchill [13] presented an elaborate correlation that spans the laminar-to-turbulent regimesDisplay Formula

(5)$f=8[(8Re)12+1(A1+B1)1.5]1/12$

where

$A1={2.457ln[1(7/Re)0.9 + 0.27(ε/D)]}16$

and

$B1=(37530Re)16$

In this study, the effect of tube roughness (ε) needed for A1 is considered negligible. Later, Bhatti and Shah [14] proposed a correlation for 4000 ≤ Re ≤ 107Display Formula

(6)$f=0.00512+0.4572Re-0.311$

Investigations of nanofluid flow friction factor in tubes have been conducted during the last few years. Xuan and Li [15] investigated the convective heat transfer and the flow features of Cu–water nanofluids in a 10-mm inner diameter tube. The experimental results from their study, in the turbulent region, showed that the friction factors of the nanofluids, between 1 and 2 vol. % fractions, are roughly the same as those of water flow.

Williams et al. [16] experimentally investigated the turbulent flow of alumina–water and zirconia–water nanofluids in tubes. They found that existing correlations for single-phase flow can adequately predict nanofluid flow convective heat transfer and pressure drop. Rea et al. [17] conducted a study on the laminar convective heat transfer and pressure drop of alumina–water and zirconia–water nanofluids in a tube with 4.5-mm inner diameter. Their findings showed that, with properly measured nanofluid properties, there is no deviation in convective heat transfer and pressure drop of nanofluid flow from conventional single-phase flow theory.

Yu et al. [18] conducted an experimental study on the laminar convective heat transfer of Al2O3–polyalphaolefin nanofluids containing spherical- and rod-like particles. The results from their study showed that conventional single-phase flow theory provides satisfactory prediction of the friction factor for nanofluids containing spherical particles. However, predictions from the conventional single-phase flow theory do not agree well with nanofluids containing nonspherical particles.

A recent investigation performed by Meyer et al. [19] used aqueous suspensions of multiwalled carbon nanotubes to flow through a straight tube. The results from the study showed that, in the turbulent region, pressure drop does not change with concentration (0.33 vol. % and 0.75 vol. %) at the same average flow velocity and is 3% higher than that of water flow. In the laminar region, the pressure drop of 0.33 vol. % concentration is 10% higher than that of water flow, and for 0.75 vol. % concentration, the pressure drop is 20% higher than that of water flow.

###### Dynamic Viscosity.

Particle-to-particle interaction and hydrodynamic interaction of particles with the base liquid affect the viscosity of the nanofluids. Viscosity, in turn, influences the thermal transport behavior of nanofluids. The flow behavior is affected when nanoparticles alter the viscosity of nanofluids that influences the pumping power. The earliest theoretical model for viscosity of solid particle suspension in liquid base fluids was introduced by Einstein for spherical particles at relatively low volume fraction (ϕ ≈ 0.01) [20]. When the solid particle loading in a base fluid increases, the effect of particle-to-particle interaction at closer proximity becomes more significant and could render the mixture to exhibit non-Newtonian behavior. Non-Newtonian behaviors in nanofluids have been observed by several investigators [15,21-24]. The literature contains many correlations for calculating the viscosities of particle dispersions in fluids. In a recent review, Mukesh Kumar et al. [25] have cataloged over 30 correlations that may be applicable for predicting nanofluid viscosities.

## Experimental Approach

###### Experimental Setup.

The experimental setup used in this study was designed for the measurement of internal flow friction factor for tubes of various diameters. The schematic of the entire experimental setup for the present study is shown in Fig. 1.

The working fluid is stored in a 3-gal medium density polyethylene reservoir. The working fluid is then pumped from the reservoir, by a Liquiflo gear pump (model 35 F), through a shell-and-tube heat exchanger. The purpose of the heat exchanger is to remove heat added to the working fluid during an experiment run. In addition, it functions to maintain a consistent inlet temperature during the course of an experiment run.

From the heat exchanger, the working fluid flows through a metering valve, which is used for regulating its flow rate. The working fluid then flows through a Micro Motion Coriolis mass flow meter (model CMFS010M) that is connected to a digital transmitter (model 1700 R). The Coriolis mass flow meter has a ± 0.1% accuracy for 1–50 g/s. The flow rate signal of the working fluid is conditioned by the digital transmitter for the data acquisition system. From the Coriolis mass flow meter, the working fluid then flows into the test section.

The test section assembly contains the instruments necessary for measuring the bulk inlet and outlet fluid temperatures and pressure drop across the test section. The bulk inlet and outlet fluid temperatures were measured with T-type thermocouples from Omega (model TMQSS-020U-6), inserted at the upstream and downstream of the test section. Pressure drop across the test section was measured by three Rosemount pressure transmitters (model 3051) that correspond to different pressure ranges (62, 248, and 2070 kPa, with an accuracy of ± 0.15%). The accuracy of the pressure transmitters were verified using Dwyer digital pressure gages (models DPG-104 and DPG-107). All output signals from the instrumentations are recorded by an Agilent 34972 A data acquisition unit.

The test section assembly was designed to incorporate tubes with various diameters. In this study, AISI 304 stainless steel tubes with inner diameters of 2.97 and 4.45 mm were used as test sections. Both tubes used as test sections have the same length of 1 m. Six small segments from each tubes were cut so that the inner diameters can be verified with a laser scanning microscope (Zeiss LSM 5 Pascal). Analysis from laser scanning microscopy found that, using Student t distribution at 95% confidence level, the uncertainty of both inner diameters is about ±1%.

###### Nanofluid Properties.

The nanofluid used in this study is a colloidal dispersion of aluminum oxide or alumina (Al2O3) at 20% by weight (6 vol. %) in liquid water. The nanofluid was purchased from Alfa Aesar®, with Al2O3 particle size of 50 nm specified by the vendor. Nanofluids are often described in terms of volume fraction (ϕ), thus the density, weight, and volume fractions can be expressed asDisplay Formula

(7)$ρnf=(1-φ)ρbf+φρp$

(8)$φ=χρbfχρbf+(1-χ)ρp$

The bulk density of Al2O3 is 3965 kg/m3, as specified by the vendor, and compares within ±1% of the value reported in Ref. [26]. The bulk density of the Al2O3 nanofluid was also measured using a digital balance with a readability of 0.01 g. When comparing the measured nanofluid density with the density determined from Eqs. (7) and (8), where ρp = 3965 kg/m3 and ρbf = 1000 kg/m3, the agreement is within ±1.5%.

The dynamic viscosity of the nanofluid was measured by a Brookfield viscometer (model DV-II+ Pro EXTRA) with an accuracy of ±1%. The nanofluid dynamic viscosity was measured for temperature between 6 and 75 °C. The temperature of the nanofluid was maintained using a Brookfield temperature bath (model TC-550MX). In addition, the effect of shear rate on the shear stress of the nanofluid was measured to determine whether its rheological behavior is Newtonian or non-Newtonian.

###### Experimental Uncertainty.

The friction factor, Eq. (2), can be determined by measuring the pressure drop (Δp) across the test section, the density of the working fluid (ρ), the test section inner diameter (D), the pressure drop length of the test section (L), and the mass flow rate ($m·$). Each of these measurands is accompanied with quantifiable uncertainty, Table 1. Using the description of Kline and McClintock [27] to express experimental uncertainty, and the procedure described by Moffat [28], the uncertainties associated with the measured friction factor results were estimated to be between ±5.5 and ±8.5%. Among the five measurands listed in Table 1, the uncertainty of the tube inside diameter contributed the most to the uncertainty of the friction factor. This is due to the friction factor that is expressed with the inner diameter (D) being raised to the fifth power, Eq. (2).

## Experimental Results

###### Nanofluid Viscosity.

The dynamic viscosity of the Al2O3 nanofluid was measured at different temperatures. The measured nanofluid viscosity is needed to determine the Reynolds number of nanofluid flow. Figure 2 shows the influence of temperature on the viscosity of nanofluid in comparison with the viscosity of water as the base fluid. At 6 °C, the nanofluid viscosity is at 12.3 cP. As the temperature increases to 75 °C, the nanofluid viscosity decreases to 3.45 cP, representing a 72% decrease in viscosity over 6 to 75 °C. Over the same temperature range, the nanofluid viscosity is 8.3 to 9.2 times more viscous than water, as shown in the viscosity ratio curve in Fig. 2.

The rheological behavior of the Al2O3 nanofluid, whether Newtonian or non-Newtonian, was determined by subjecting the colloid to shear rate ranging from 6 to 122 s−1. Figure 3 shows the shear stress results of the nanofluid measured at different temperatures with varying shear rate. The results indicate that the Al2O3 nanofluid behaves as a Newtonian fluid (within the measurement conditions), with the shear stress being proportional to the shear rate. As the temperature increases from 6 to 75 °C, the proportionality constant of the shear stress versus shear rate curve (or viscosity) decreases from 12.3 to 3.45 cP.

###### Friction Factor of Water Flow.

Before conducting measurements for nanofluid flow, the reliability of the experimental setup and procedures were checked and validated by making several water flow runs. Friction factor measurements for water flow were conducted for a Reynolds number range of approximately 480 to 8800. Measurements for both inner tube diameters of 2.97 and 4.45 mm were conducted.

The water flow friction factor results that were obtained experimentally are compared with the friction factors calculated from correlations that are available in the literature, Eqs. (3) to (6). When compared with the correlations of Blasius [11], Drew et al. [12], and Bhatti and Shah [14], Eqs. (3), (4), and (6), respectively, the measured friction factor results of water flow in the turbulent region are all within ±5% agreement (Fig. 4). When compared with the Churchill [13] correlation, the measured water flow friction factor results are within ±5% agreement in the laminar and turbulent regions and within ±8% agreement in the transition region (Figs. 4 and 5).

With the exception of the transition region, the measured water flow friction factor results are within ±5% agreement with the correlations considered. The discrepancies between the measured and the calculated results are within the experimental uncertainties. The results for water flow show that the experimental setup and measurement procedures used in this study are able to acquire data that agreed with established friction factor correlations.

###### Friction Factor of Nanofluid Flow.

The friction factor results for the Al2O3 nanofluid were measured for two different tubes with inner diameters of 2.97 and 4.45 mm. Due to the higher viscosity of the nanofluid, the friction factor measurements were conducted at lower Reynolds number range (80 < Re < 2400). Thus, the nanofluid flow measurements are in the fully developed laminar flow regime and the onset of transition flow.

Measured friction factor results for 2.97 - and 4.45-mm inner diameter tubes are compared with the theoretical f = 64/Re equation. Figure 6 shows the measured friction factors for the nanofluid flow in the 2.97-mm inner diameter tube. Between the Reynolds number of approximately 80 and 1500, the measured friction factor results are within ±5% agreement with the theoretical friction factor. Likewise, Fig. 7 illustrates that the measured nanofluid flow friction factor results for the 4.45-mm inner diameter tube agree with the theoretical friction factor for 80 < Re < 1500. Both Figs. 6 and 7 also show that, at the Reynolds number below 1500, nanofluid flow friction factors agree with that of water flow.

The friction factor results for both tube inner diameters, shown in Figs. 6 and 7, indicated that the tube size does not influence the friction factor of laminar nanofluid flow. Any deviation between the measured results and the theoretical f = 64/Re equation can be attributed to experimental uncertainties. The nanofluid flow friction factor results for both 2.97 - and 4.45-mm inner diameter tubes show departure from the theoretical f = 64/Re curve at the Reynolds number of about 1500. This suggests that the onset of transition flow Reynolds number for the nanofluid is approximately at 1500.

When plotting the Poiseuille number (fRe) with the variation of Reynolds number, the departure of the friction factor from fRe = 64 can be seen clearer. Figures 8 and 9 show the Poiseuille number plotted against the Reynolds number for 2.97 - and 4.45-mm inner diameter tubes. For both tubes, the Poiseuille number for the nanofluid flow is observed to be above 5% of fRe = 64 at approximately the Reynolds number of 1500, Figs. 8 and 9. When comparing with the Poiseuille number for water flow, the measured results indicate that the onset of transition flow is at a Reynolds number of approximately 2300, which agrees with the textbook value. By comparing the two results of nanofluid and water flow, the nanofluid flow is observed to be experiencing early transition. The complete picture of the mechanisms that causes early transition, as observed in the nanofluid results, is still unclear. Further study needs to be done to properly understand the presence of nanoparticles in a base fluid that could lead to flow instabilities and hence early transition to turbulent flow.

## Summary

When the properties, such as density and viscosity, of Al2O3 (6 vol. %) nanofluid are properly characterized and used in the evaluations of Reynolds number and friction factor, the flow behavior of the nanofluid can then be predicted using classical single-phase theory. Rheological measurements have shown that, for shear rate ranging from 6 to 122 s−1 and temperature between 6 and 75 °C, the nanofluid behaves as a Newtonian fluid.

For 80 < Re < 1500, the deviations in the nanofluid friction factor results from fRe = 64 are within ± 5%, which may be attributed to experimental uncertainties. When the tube inner diameter is decreased from 4.45 to 2.97 mm, the experimental results show no indication that the nanofluid flow would deviate from conventional theory for friction factor. The measured friction factor results have shown that the nanofluid flow in tubes of different inner diameters (2.97 and 4.45 mm) begin to enter into transition flow at a Reynolds number of approximately 1500.

The experimental study conducted by Rea et al. [17], using alumina–water and zirconia–water nanofluids in a tube with 4.5-mm inner diameter, showed that pressure drop of nanofluid in laminar flow can be predicted using conventional single-phase flow theory. The agreement of the nanofluid pressure drop results with the conventional theory can be achieved after having properly characterized the nanofluid properties. The results from this study also agree with them.

Viscosity of nanofluids is an important parameter for determining the friction factor of nanofluid flow in tubes, since the proper values of this parameter are necessary when using conventional theory to estimate friction factor. Viscosity correlations for nanofluid, such as those compiled by Mukesh Kumar et al. [25], would need to be validated with experimental data to determine the conditions of their applicability.

Further studies on the critical Reynolds number of nanofluid flow in tubes are of interest as well. The influence of nanoparticles on the transition from laminar to turbulent flow is still rather ambiguous. In addition, the entrance effect of nanofluid flow from developing to fully developed, as a result from the impact of nanoparticles, is still unclear.

## Acknowledgements

The authors would like to acknowledge John Roche and Emerson Rosemount for generously donating the pressure transmitters utilized in this study. Part of this work is sponsored by funds from the NSF North Dakota EPSCoR and the Mechanical Engineering Department at University of North Dakota. The views expressed in this article are those of the authors and do not reflect the official policy or position of the National Science Foundation.

Nomenclature
• A =

cross-sectional area, m2

• A1 =

expression in Churchill correlation, Eq. (5)

• B1 =

expression in Churchill correlation, Eq. (5)

• D =

inside diameter, m

• f =

Darcy friction factor

• fRe =

Poiseuille number

• L =

length of pressure drop, m

• $m·$ =

mass flow rate, kg/s

• Re =

Reynolds number (= ρUD/μ)

• U =

average flow velocity, m/s

Greek Symbols
• Δp =

pressure drop, Pa

• ε =

tube wall roughness, m

• μ =

dynamic viscosity, Pa·s or cP

• ρ =

density, kg/m3

• ϕ =

particle volume fraction

• χ =

particle weight fraction

Subscripts
• bf =

base fluid (liquid)

• nf =

nanofluid

• p =

particle

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## References

Hamilton, R. L., and Crosser, O. K., 1962, “Thermal Conductivity of Heterogeneous Two Component Systems,” Ind. Eng. Chem. Fundam., 1(3), pp. 187–191.
Ahuja, A. S., 1975, “Augmentation of Heat Transport in Laminar Flow of Polystyrene Suspensions. I. Experiments and Results,” J. Appl. Phys., 46(8), pp. 3408–3416.
Ahuja, A. S., 1975, “Measurement of Thermal Conductivity of (Neutrally and Nonneutrally Buoyant) Stationary Suspensions by the Unsteady-State Method,” J. Appl. Phys., 46(2), pp. 747–755.
Masuda, H., Ebata, A., Teramea, K., and Hishinuma, N., 1993, “Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles,” Netsu Bussei, 7(4), pp. 227–233.
Choi, S. U. S., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, D. A.Siginer and H. P.Wang, eds., Fluids Engineering Division, San Francisco, CA, 231, pp. 99–105.
Prasher, R., Bhattacharya, P., and Phelan, P. E., 2005, “Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluids),” Phys. Rev. Lett., 94(2), p. 025901. [PubMed]
Wang, X.-Q., and Mujumdar, A. S., 2007, “Heat Transfer Characteristics of Nanofluids: A Review,” Int. J. Therm. Sci., 46(1), pp. 1–19.
Yang, Y., Zhang, Z. G., Grulke, E. A., Anderson, W. B., and Wu, G., 2005, “Heat Transfer Properties of Nanoparticle-in-Fluid Dispersions (Nanofluids) in Laminar Flow,” Int. J. Heat Mass Transfer, 48(6), pp. 1107–1116.
Fotukian, S. M., and Nasr Esfahany, M., 2010, “Experimental Investigation of Turbulent Convective Heat Transfer of Dilute γ-Al2O3/Water Nanofluid Inside a Circular Tube,” Int. J. Heat Fluid Flow, 31(4), pp. 606–612.
Heyhat, M. M., Kowsary, F., Rashidi, A. M., Momenpour, M. H., and Amrollahi, A., 2013, “Experimental Investigation of Laminar Convective Heat Transfer and Pressure Drop of Water-Based Al2O3 Nanofluids in Fully Developed Flow Regime,” Exp. Therm. Fluid Sci., 44, pp. 483–489.
Blasius, H., 1913, “Das Ähnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten,” Forsch. Geb. Ingenieurwes., 131, pp. 1–40.
Drew, T. B., Koo, E. C., and McAdams, W. H., 1932, “The Friction Factor for Clean Round Pipes,” Trans. AIChE, 28, pp. 56–72.
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## Figures

Fig. 1

Schematic representation of the experimental setup for pressure drop measurements

Fig. 6

Al2O3–water (6 vol. %) nanofluid flow friction factors, in comparison with water flow, in a 2.97-mm inner diameter tube (L/D = 337)

Fig. 7

Al2O3–water (6 vol. %) nanofluid flow friction factors, in comparison with water flow, in a 4.45-mm inner diameter tube (L/D = 225)

Fig. 8

Poiseuille numbers (fRe) of the Al2O3–water (6 vol. %) nanofluid flow, in comparison with water flow, in a 2.97-mm inner diameter tube

Fig. 9

Poiseuille numbers (fRe) of the Al2O3–water (6 vol. %) nanofluid flow, in comparison with water flow, in a 4.45-mm inner diameter tube

Fig. 2

Viscosity of Al2O3–water (6 vol. %) nanofluid with variation of temperature

Fig. 3

Rheological behavior of the Al2O3–water (6 vol. %) nanofluid

Fig. 4

Measured friction factors of water flow in comparison with various friction factor correlations in the turbulent region

Fig. 5

Measured friction factors of water flow in comparison with various friction factor correlations from laminar to turbulent region

## Tables

Table 1 Summary of experimental uncertainties

## Discussions

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