Advanced Powder Technol., Vol. 18, No. 6, pp. 813–824 (2007)© VSP and Society of Powder Technology, Japan 2007.Also available online - www.brill.nl/apt

Invited paper

Forced convective heat transfer of nanofluids

YULONG DING 1,∗, HAISHENG CHEN 1,2, YURONG HE 1,ALEXEI LAPKIN 3, MAHBOUBEH YEGANEH 4,LIDIJA ŠILLER 4 and YURIY V. BUTENKO 4

1 Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, UK2 Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, China3 Department of Chemical Engineering, University of Bath, Bath, UK4 School of Chemical Engineering and Advanced Materials, University of Newcastle,

Newcastle upon Tyne, UK

Received 8 April 2007; accepted 14 June 2007

Abstract—Forced convective heat transfer is experimentally investigated using aqueous and ethyleneglycol-based spherical titania nanofluids, and aqueous-based titanate nanotubes, carbon nanotubesand nano-diamond nanofluids. These nanofluids are formulated from dry nanoparticles and purebase liquids to eliminate complications due to unknown solution chemistry. All the formulatednanofluids show a higher effective thermal conductivity than that predicted by the conventionaltheories. Except for the ethylene glycol-based titania nanofluids, all other nanofluids are foundto be non-Newtonian. For aqueous-based titania and carbon and titanate nanotube nanofluids, theconvective heat transfer coefficient enhancement exceeds, by a large margin, the extent of the thermalconduction enhancement. However, deterioration of the convective heat transfer is observed forethylene glycol-based titania nanofluids at low Reynolds numbers and aqueous-based nano-diamondnanofluids. Possible mechanisms for the observed controversy are discussed from both microscopicand macroscopic viewpoints. The competing effects of particle migration on the thermal boundarylayer thickness and that on the effective thermal conductivity are suggested to be responsible for theexperimental observations.

Keywords: Nanofluids; convective heat transfer; thermal conductivity; rheology; mechanisms; heattransfer enhancement.

1. INTRODUCTION

This work is concerned with forced convective heat transfer of nanofluids—heattransfer between a forced flowing nanofluid through a confined region and theconfining walls. Forced convective heat transfer plays a significant role in almostall industrial sectors. Examples include cooling of microelectronics, process

∗To whom correspondence should be addressed. E-mail: y.ding@leeds.ac.uk

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intensification in the chemical industry, heat exchange/waste heat recovery in powerplants and cooling of car engines, to name but a few.Despite the industrial importance, only a small number of studies have been

devoted to convective heat transfer, possibly due to the system being less well-defined. Most of the reported studies show enhancement of convective heat transferby using nanofluids [1–9]. A few studies show inconsistencies, i.e. enhancementunder certain conditions but little enhancement under other conditions [10–12].There are also studies that show little or even a decrease in the convective heattransfer coefficient when nanoparticles are added to the base liquids [13]. Thiswork aims to understand and interpret the controversies through both experimentalwork and simple analyses. Five types of nanofluids were formulated, characterizedfor their thermal and rheological properties, and measured for their convectiveheat transfer coefficient. It will be shown that nanofluids can be Newtonian andnon-Newtonian depending on the properties of the base liquid and nanoparticles,particle concentration, and shear rate. It will also be shown that enhancement ofthermal conduction does not necessarily mean an enhancement in the convectiveheat transfer.

2. MATERIALS AND EXPERIMENTAL TECHNIQUES

Four types of nanomaterials, i.e. titania, titanate nanotubes, carbon nanotubesand nano-diamond particles, were used for nanofluid preparation. Titania nanoflu-ids were formulated by using dry nanoparticles manufactured (using the aerosolprocess) by Degussa (Germany). X-ray diffraction analysis of the nanoparticlesshowed they contained predominantly anatase with a small amount of rutile phase.The primary titania nanoparticles were approximately spherical with an averagediameter of about 20 nm. However, the as-received titania particles were in theform of large agglomerates. Sonication, high shear homogenization and high shearmediummilling were therefore used in series to break the agglomerates. The carbonnanotubes were supplied by Professor F.Wei of Tsinghua University (China) and thedetails of carbon nanotube nanofluid preparation can be found elsewhere [7]. The ti-tanate nanotubes were synthesized in our labs. The primary titanate nanotubes werearound 10 nm (diameter) × 100 nm (length) and their synthesis was based on thealkali hydrothermal transformation [14]. Nano-diamonds were provided by the Fed-eral Research and Production Center ‘Altai’ (Biysk, Russian Federation) and wereadditionally boiled in concentrated nitric acid for 60 min to remove metal impuritiesand non-diamond forms of carbon [15]. The primary nano-diamond particles werearound 2–50 nm in diameter and were produced by the so-called detonation method.Nano-diamond particles and titanate nanotubes were found to be in the form of ag-glomerates so de-agglomeration was performed using the high shear homogenizer.Distilled water was used as the base liquid for formulating most of the nanofluids,

whereas a few titania nanofluids were made with ethylene glycol. No stabilizerwas used for titania, and titanate and carbon nanotubes nanofluids. Stabilization

Forced convective heat transfer of nanofluids 815

of aqueous nanofluids was achieved by adjusting pH. Great difficulties wereexperienced in stabilizing nano-diamond nanofluids by using pH control, so asmall amount of SDBS surfactant was employed (10 wt% with respect to particleconcentration). The formulated titania, and titanate and carbon nanotube nanofluidswere found to be stable for a fairly long period of time before any significantsedimentation was visually observed. Despite the use of a small amount of SDBS,significant sedimentation was observed in the nano-diamond nanofluids after a fewhours. The period of stability was sufficient for thermal conductivity and rheologicalmeasurements, and for convective heat transfer experiments.The formulated nanofluids were first characterized for their physical, thermal and

rheological properties. A Malvern nanosizer (Malvern Instrument, UK) was used tomeasure the particle size distribution of nanofluids except for carbon nanotubes,for which scanning and transmission electron microscopy were used [7]. Theresults showed that the average particle (agglomerate) size was around 120 nmalmost independent of particle concentration, indicating that the method used abovewas not able to break the agglomerates into primary nanoparticles. The thermalconductivity of the prepared nanofluids was measured by using a KD2 thermalproperty meter (Labcell, UK), which provided an uncertainty within around 3%.The viscosity of nanofluids was measured by using a Bohlin CVO rheometer with aMooney cell (Malvern Instruments).The experimental system for measuring the convective heat transfer coefficient is

shown schematically in Fig. 1. The details have been reported elsewhere [9]. Inbrief, it consisted of a flow loop, a heating unit, a cooling unit, and a measuring andcontrol unit. The flow loop included a pump with a built-in flowmeter, a nanofluidtank, a collection tank, a test section and various valves. The test section was avertically oriented straight copper tube (1834 mm length, 3.97 mm inner diameterand 6.35 mm outer diameter). The tube was heated by flexible silicon rubber heaters(Watlow, UK) linked to a DC power supply (TTi Ex752m; RS, UK). The powersupply was adjustable and had a maximum power supply rating of 300 W. Therewas a thick thermal isolating layer surrounding the heaters to obtain a constant heatflux condition along the test section. Eight T-type thermocouples were mountedon the test section at the normalized axial positions with respect to the tube innerdiameter of around 50.4 (T1), 151.2 (T2), 201.6 (T3), 252.0 (T4), 302.4 (T5), 352.8(T6), 403.2 (T7) and 453.6 (T8) from the inlet of the test section to measure thewall temperature distribution. Two further T-type thermocouples were inserted intothe flow at the inlet and exit of the test section to measure the bulk temperaturesof nanofluids. In the heat transfer experiments, the pump rotational rate, voltageand current of the DC power supply were recorded, and the temperature readingsfrom the 10 thermocouples were registered by a data requisition system (NationalInstrument, UK). The experimental system gave an uncertainty of nanofluids heattransfer measurements of about 6.5%.

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Figure 1. Experimental system for convective heat transfer experiments.

3. EXPERIMENTAL RESULTS AND DISCUSSION

3.1. Thermal conductivity of nanofluids

Thermal conductivity measurements were carried out for all nanofluids formulated.The following observations are obtained. (i) For a given type of nanofluid, the effec-tive thermal conductivity increases with increasing nanoparticle concentration andthe increase is generally a non-linear function of concentration. (ii) The thermalconductivity increases with increasing temperature and the enhancement is a non-linear function of temperature. (iii) Given particle concentration, the measured ther-mal conductivities in the descending order are water–carbon nanotube nanofluids,water–diamond nanofluids, water–titanate nanofluids, water–titania nanofluids andethylene glycol–titania nanofluids. For example for 0.1 wt% nanofluids at 30◦C,the enhancements of these nanofluids are 18%, 8%, 4%, 3 and 2%, respectively.This indicates strong effects of particle shape and material properties, althoughthis comparison is rather crude (as solution chemistry and particle size, etc., arenot taken into account). Note that the last two figures (3 and 2%) are also withinthe uncertainty of the measurements, although each data point is an average overat least five measurements. (iv) The conventional Hamilton–Crosser model withshape factor correction does not provide an adequate prediction of the experimentsin two aspects, i.e. the predicted thermal conductivity is lower than the measuredvalues, and prediction shows linear concentration and temperature dependence. Itis important to note that current method of comparing the effective thermal con-ductivity of different nanofluids in terms of particle concentration and/or tempera-

Forced convective heat transfer of nanofluids 817

ture can be misleading because the effective thermal conductivity of nanofluids isalso likely to be a function of primary particle size, particle shape and aggregatesize (often controlled by the solution chemistry and nanofluid formulation process),apart from temperature and concentration. In this sense, collaborations betweencolloid chemists and thermophysicists would be a good way to attack the prob-lem.

3.2. Rheological behavior of nanofluids

Rheological measurements were performed on all nanofluids. The results reveal thefollowing. (i) Nanofluids can exhibit either or both Newtonian and non-Newtonianbehavior depending on particle size, particle shape, base liquid properties, solutionchemistry, particle concentration, shear rate, etc. (ii) Aqueous-based nanofluids ofcarbon nanotubes, titania, titanate and nano-diamond are non-Newtonian, whereasthe ethylene glycol based titania nanofluids are Newtonian. (iii) Aqueous-basednanofluids of carbon nanotubes, titania and titanate show the shear thinning behav-ior, whereas the aqueous-based nano-diamond nanofluids exhibit shear thinning atlow shear rates, Newtonian or weak shear thickening behavior at medium shear ratesand shear thickening at high shear rates (Fig. 2). As will be seen later, such unusualbehavior has an implication for its convective heat transfer behavior although themechanism remains a subject of further investigation. (iv) Given the shear rate, theshear viscosity decreases with increasing temperature, decreasing particle concen-tration or decreasing particle size. (v) Given other conditions, the shear viscosity of

Figure 2. Rheological behavior of nano-diamond nanofluids at six temperatures (0.1 wt%, 0.01%SDBS surfactant). This figure is published in color on http://www.ingenta.com

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nanofluids containing non-spherical particles is higher than those containing spher-ical nanoparticles.As the viscosity of nanofluids at low shear rates reflects the structuring of

nanoparticles in the base liquid, it also affects the effective thermal conductivity.It may be possible to establishing a relationship between the low shear viscosityand the effective thermal conductivity. Work is underway to address this.

3.3. Convective heat transfer of nanofluids

Experiments on convective heat transfer were carried out on all the nanofluidsformulated under various flow conditions. Pure base liquids were tested first as thebase for comparison before nanofluids were tested. The results can be summarizedas follows.

(i) The convective heat transfer coefficient of nanofluids has the highest valueat the entrance, but decreases with axial distance and reaches a constant value inthe fully developed region. The entrance length depends on the properties andbehavior of nanofluids. For a given nanofluid, the entrance length at low flow rates,e.g. laminar flow for Newtonian fluids, is longer than that at high flow rates, e.g.turbulent flow for Newtonian fluids.(ii) Given particle concentration and flow conditions, aqueous-based carbon

nanotube nanofluids give the highest enhancement of convective heat transfercoefficient, followed by (in descending order) aqueous-based titanate nanofluids andaqueous-based titania nanofluids. The ethylene glycol-based titania nanofluids andaqueous-based nano-diamond nanofluids are found to give virtually no enhancement(Figs 3 and 4).(iii) For aqueous based titania, and titanate and carbon nanotube nanofluids,

the convective heat transfer coefficient generally increases with increasing flowrate or increasing particle concentration and the enhancement exceeds by a largemargin the extent of the thermal conduction enhancement, indicating that differentmechanisms are operating. However, if one takes into account the enhancement ofthe thermal conductivity, deterioration of the convective heat transfer is apparentfor the ethylene glycol-based titania and aquesous-based nano-diamond nanofluids.The exact reasons for this are a subject of our current investigation. However, foraqueous-based nano-diamond nanofluids, the use of SDBS surfactant creates somefoam. The foam could migrate to the wall region due to its surface activity, thusprevents effective heat transfer [16]. Another reason for the convective heat transferdeterioration of nano-diamond nanofluids is their shear rheological behavior asmentioned above. Quantitative understanding of these is currently underway andthe results will be reported later. The deterioration of ethylene glycol-based titaniananofluids is very interesting. It is believed to be associated with the high viscosityof the base liquid (see below for more discussion). Another possible reason isthat the enhancement is within the error bars of the measurement system as thethermal conductivity enhancement is small and the relatively large uncertainty of

Forced convective heat transfer of nanofluids 819

Figure 3. Convective heat transfer coefficient of nano-diamond-based nanofluids (0.1 wt%).

Figure 4. Ethylene-based titania nanofluids (Reynolds number = 135).

the convective heat transfer measurements. It is noted that the work on ethyleneglycol nanofluids was only carried out at low Reynolds numbers. The results thusobtained may not apply to other conditions.(iv) The data for the aqueous-based titania and titanate nanofluids seem to in-

dicate that particle shape plays an important role in the convective heat transferenhancement given other conditions, i.e. large aspect ratios give a higher enhance-

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ment. This is also supported by comparing the results of this work on carbon nan-otube nanofluids with those by Yang et al. [13] on disk-like graphite nanofluids.(v) There seems to be a relationship between the rheological behavior and

convective heat transfer behavior. For example, for aqueous-based carbon nanotubenanofluids, a drastic increase in the convective heat transfer coefficient occurs ata flow rate corresponding to a shear rate where shear viscosity is close to thelowest [7].

4. MECHANISMS OF ENHANCEMENT OF CONVECTIVE HEAT TRANSFER

The mechanisms of the enhanced convective heat transfer can be looked at fromboth macroscopic and microscopic aspects. Considering a flow with uniformvelocity and temperature distributions through a pipe, the flow has a differenttemperature from the wall temperature (Fig. 5). Due to friction between the fluidand the pipe wall, a hydrodynamic boundary layer will form at the wall regionin which the flow velocity increases from zero at the wall to maximum in aradial position depending on the axial position from the entrance. At a certainaxial position from the entrance, the thickness of the boundary layer approachesa constant value and the flow is regarded as fully developed. Similarly, dueto the different temperature of the fluid from the pipe wall, a thermal boundarylayer is developed, although its thickness and the entrance length can be different.Macroscopically, the forced convective heat transfer coefficient, h, is given byh = k/δt, where δt is the local thickness of the thermal boundary layer and k is thelocal effective thermal conductivity of nanofluids adjacent to the wall surface. Thissimple expression indicates that either or both of an increase in k and a decrease in δtcould result in an increase in the convective heat transfer coefficient. This explainswhy the entrance region gives a higher convective heat transfer coefficient. Asnanofluids have a higher thermal conductivity in comparison with the base liquid,the simple expression also partially explains the enhanced convective heat transfer

Figure 5. Boundary layer development in a pipe flow in the laminar flow regime; for turbulent flow,the entrance region is much shorter and the boundary layer thickness is thinner.

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coefficient. The expression, however, cannot provide an adequate explanationto the experimental observations that, in some cases the convective heat transfercoefficient enhancement is much higher than the thermal conduction enhancement,while in other cases, there is no convective heat transfer enhancement despiteconsiderable thermal conduction enhancement. Before a detailed discussion onthe apparent controversy, a point is made below on the view of nanofluids beinghomogeneous. There are a number of publications stating that nanofluids arehomogenous and can be considered as single-phase fluid; as a result, a numberof people even model nanofluids based on this statement (e.g. Ref. [17]). Letus first accept the statement, then the convective heat transfer coefficient for afully developed pipe flow under constant wall heat flux conditions should take thefollowing form:

h = 4.26k/D, (1)

where D is the pipe diameter. Given D, (1) suggests that h is only a functionof k. This is in disagreement with experimental observations; see Section 2 andRefs [3, 5, 13]. Let us look more closely at the entrance region. If nanofluidswere homogeneous, the entrance region length should follow the expression forthe flow of single-phase flows. This is again in contradiction to the experimentalobservations [5, 7, 9, 12]. For homogenous fluids flowing through a pipe with aconstant wall heat flux, the heat transfer coefficient for fully developed turbulentflows is give by:

h = 0.023

(ρ0.8U 0.8C0.33

p

D0.2

)(k0.67

μ0.47

), (2)

where U is the average flow velocity, Cp is the heat capacity, ρ is the fluid densityand μ is the fluid viscosity. Due to low particle concentrations of nanofluids, theheat capacity and density of nanofluids are expected to be similar to those of the baseliquids. If nanofluids were homogenous, then the convective heat transfer coefficientwould be proportional to (k0.67/μ0.47). This implies that the enhancement under theturbulent flow conditions is much lower than that under the laminar flow conditions.This again disagrees with the experimental observations [4, 9]. These argumentssuggest that nanofluids are likely to be inhomogeneous during flow at least in somecases. In the following, possible reasons for the inhomogeneity and the implicationsfor convective heat transfer are discussed.Microscopically, there are at least two possible reasons for the inhomogeneity.

One is the presence of agglomerates in nanofluids, which can be associated witheither sintering during nanoparticle manufacturing or solution chemistry duringnanofluid formulation. The former is often seen in processes involving elevatedtemperatures, e.g. aerosol reactors. The resulting agglomerates are very strong, andare difficult to break down to primary nanoparticles even with prolonged high shearprocessing and ultrasonication. The latter is due to attraction between nanoparticles,e.g. van der Waals attractive force, and depletion phenomena. The agglomerates

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(aggregates) can be controlled by adjusting solution chemistry and applying shear.At this point, a revised definition of nanofluids is proposed here as dilute liquidsuspensions of particles with at least one critical dimension smaller than around100 nm. This definition includes suspensions containing nanoparticle agglomerateswhich have been shown both theoretically and experimentally to be responsiblefor the observed thermal conduction enhancement [18, 19]. The second reason isparticle migration due to viscosity and velocity gradients. Experimental evidenceof particle migration is the longer entrance length of nanofluids as discussed in theSection 2 and in a recent experimental study by Merhi et al. [20]. There are alsoplenty of theoretical studies on particle migration (e.g. Refs [21–23]). If particlesare very small, Brownian motion is dominant and the effect of the above-mentionedparticle migration is negligible. If particles are large, e.g. aggregates of hundredsof nanometers, the contribution of the Brownian motion is small and a particledepletion region may exist at the wall, which gives non-uniform distributions ofparticle concentration, viscosity and thermal conductivity. The direct results ofparticle migration are lower particle concentration at the wall region and a thinnerboundary thickness due to disturbance by the moving particles. This, according toh = k/δt, can lead to three possible results: (i) h is enhanced if the decrease in δtexceeds the decrease in k, (ii) h does not change if the decrease in δt is equal to thedecrease in k and (iii) h is reduced if the decrease in δt is lower than the decreasein k. This qualitatively explains the experimental results. However, quantitativeexplanation requires understanding of how nanoparticles behave under shear, andhow they interact with each other and with fluid in the boundary layer.

5. CONCLUDING REMARKS

Nanofluids are defined as dilute suspensions of particles with at least one criticaldimension smaller than around 100 nm. A considerable amount of effort has beenput in to understanding the enhancement of thermal conductivity of nanofluidsover the past decade, which has led to a conclusion that nanoparticle clustering(structuring) is likely to be the dominant mechanism [19]. However, less effort hasbeen put in to the other aspects of nanofluids such as natural and forced convectiveheat transfer and boiling heat transfer, although the number of publications on theseaspects is on the increase.This work is concerned with forced convective heat transfer, which is much

more complicated than thermal conduction in microscopically static conditionsdue to the involvement of fluid hydrodynamics, macroscopic motion of particlesand nanofluid–wall interactions. The complication is demonstrated experimentallyin this work; nanofluids with an enhanced thermal conductivity do not guaranteean enhancement in the convective heat transfer. The exact reason for this is notfully clear, but particle migration could be a major factor responsible for theexperimental observations. Such a hypothesis requires validation, which can be

Forced convective heat transfer of nanofluids 823

done experimentally, theoretically or even through mathematical modeling. Workis underway to address this aspect.

Acknowledgments

The work is supported financially by UK EPSRC under grants EP/D000645/1 andEP/EP/E00041X/1. H. C. wishes to thank the Chinese Academy of Sciences fora visiting fellowship. Y. V. B. is grateful to the European Community’s SixthFramework Programme for a Marie Curie Incoming International Fellowship undergrant MIF1-CT-2005-021528.

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