international journal of heat and mass transfer · 2018. 3. 20. · this allows higher convective...

International Journal of Heat and Mass Transfer 123 (2018) 110–121

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Ferrofluids for heat transfer enhancement under an external magneticfield

https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.1000017-9310/� 2018 Published by Elsevier Ltd.

⇑ Corresponding author.E-mail address: [email protected] (N. Gan Jia Gui).

N. Gan Jia Gui a,⇑, C. Stanley a, N.-T. Nguyen b, G. Rosengarten aa School of Engineering, Aerospace, Mechanical and Manufacturing, RMIT University, Melbourne, VIC 3053, AustraliabQueensland Micro and Nanotechnology Centre, Griffith University, Brisbane, QLD 4111, Australia

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 November 2017Received in revised form 20 February 2018Accepted 22 February 2018

Keywords:FerrofluidMagnetic FieldHeat TransferThermal ConductivityMicrofluidicElectronics Cooling

Overheating of power electronic devices has become a significant issue due to their continued miniatur-ization and increased heat flux that needs to be dissipated. Ferrofluids (magnetic nanofluids) have beenshown to have higher thermal conductivity than their base aqueous or oil based fluids due to the solidmagnetic nanoparticles that make up the ferrofluid. This allows higher convective heat transfer ratesand, importantly, the ability to externally effect the flow using a magnetic field. In this paper, we focuson material characterization of ferrofluids and measurement of heat transfer rates for single-phase fer-rofluidic forced convective flow in microchannels. We show that heat transfer properties of the floware enhanced with the use of ferrofluids and that the material make-up of the ferrofluid affects theseproperties. In this paper, we argue that generally, convective heat transfer rates for ferrofluids areincreased by increasing the solid volume concentration of magnetic particles (�0.2–0.4%).Interestingly, increasing magnetic flux was shown to decrease heat transfer enhancement. This wasdue to a reduction in the thermal conductivity of the bulk fluid caused by magnetic nanoparticles beingdrawn out of the isotropic mixture and becoming pinned to the channel wall in the region of strongestmagnetic field. We show that there is good correlation between both theory and experimental visualiza-tion of this phenomenon.

� 2018 Published by Elsevier Ltd.

1. Introduction

Miniaturization and increased processing capabilities are thetwo technological trends of electronic devices, thus greater energyefficiency is desired whilst reducing their size. However, two majorbarriers to improve performance of such devices are the systeminterconnects and heat removal techniques [1]. System intercon-nect deals with integrating the front-side electronic device andthe back-side cooling system, while heat dissipation techniquesdeal with enhancing heat transfer rates to the cooling system, orimproving heat removal rates of the device [1]. One solution to thisis to integrate cooling into the electronic chips. However, to obtainhigh heat fluxes, integrated liquid cooling typically utilisesmicrochannels for increased surface area to transport fluid volume,which are characterised by very low Reynolds numbers (Re) andhence laminar flow. These characteristics limit the convective heattransfer coefficient to about h � 790 W/cm2 [2]. One way toenhance heat transfer, is to increase the thermal conductivity ofthe working fluid. Nanofluids offer the ability to significantly

enhance heat transfer by embedding nanoparticles of higher ther-mal conductivity than the carrier fluid. The high surface area tovolume ratio inherent with nanoparticles provides excellent con-tact surface area for conductive heat transfer between the fluidand the solid particle, which acts to elevate the effective conductiv-ity of the nanofluid mixture [3]. Ferrofluids are a subclass ofnanofluids made of superparamagnetic nanoparticles that allowthem to be easily manipulated by an external magnetic field [4].Ferrofluids have been commonly used in audio loudspeakers toimprove its audio response, increasing sound amplitude whilereducing distortion. They have also been used in fluid seals fordevices such as rotating shaft seals, where they allow for thealmost complete elimination of frictional losses compared to tradi-tional mechanical seals, or for high-speed computer disk drives toprevent the ingress of dust particles and impurities [4]. Therefore,manufacturing technologies of commercial ferrofluids areadvanced, reliable, and cost effective.

Ferrofluids are essentially made up of three components – solidmagnetic nanoparticles, a surfactant coating which helps preventagglomeration of the particles, and a dispersion fluid medium[5]. Ensuring the particles remain dispersed in the carrier fluid iscritical in achieving higher thermal conductivity compared to

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N. Gan Jia Gui et al. / International Journal of Heat and Mass Transfer 123 (2018) 110–121 111

larger scaled suspensions [4]. The concentration by mass/volume,size and type of magnetic nanoparticle, surfactant, and dispersionmedium, including the method of synthesis dictates the thermo-physical properties of ferrofluids. These in turn influence the trans-port properties and thus, the convective heat transfer rates [4,6–9].

An additional means to enhance heat transfer is introducingmixing in the microfluidic flow. Rapid mixing can be inducedwithin microchannel flow either by active or passive methods[10,11]. Active methods require an external force such as electro-osmosis, magnetism, acoustics, thermocapillary, pulsating flow ormechanical stirring with moving parts [10]. Due to the magneticnature of ferrofluids, rapid mixing can be easily produced by theapplication of an external magnetic field using permanent mag-nets, as has been demonstrated in this work.

In this paper, we aim to explain the behaviour of ferrofluidsunder the effect of an external magnetic field to enhance heattransfer properties of laminar microfluidic channel flow.

1.1. Thermal conductivity

Table A1 in the appendix compiles past experimental results offerrofluid thermal conductivity. Generally, the published resultsdemonstrate that thermal conductivity increases with an increasein solid volume fraction (/) and magnetic flux (B), and thermalconductivity decreases with an increase in temperature of the fer-rofluid. Philip et al. [12,13] found that enhancement in thermalconductivity compared to the base fluid occurs when solid volumefraction is more than 1.7%. The maximum thermal conductivityenhancement observed was 300% when / = 6.3% at a magnetic fluxof 8.2 mT, at 25 �C, where the magnetic field was applied parallel tothe temperature gradient for a kerosene-based ferrofluid. The teamobserved that the maximum enhancement occurred when thevalue of magnetic flux matched the value of saturation magnetiza-tion of the ferrofluid. Past this value, thermal conductivitydecreases with increasing magnetic flux. They attribute this tothe cross-linking of the chains and subsequent distortion in thenematic-like order [12].

Gavili et al. [14] recorded a maximum thermal conductivityenhancement of 65.5% when / = 5% at a magnetic flux of 60 mT,at 25 �C, where the magnetic field was applied perpendicular tothe measurement apparatus for a water-based ferrofluid. It mustbe noted that for both Gavili et al. [14] and Philip et al. [13] the testarea used for measurements might be too small to record accurateresults according to the manufacturer’s specifications – a mini-mum of 15 mm of material parallel to the sensor in all directionsis necessary for accurate measurements. Altan et al. [15,16]observed that thermal conductivity decreases with increasing solidmass concentration (which translates to an increase in solid vol-ume concentration). Jiang et al. [9] and Pastoriza-Gallego et al.[17] recorded an increase in thermal conductivity with an increasein temperature. However, Jiang et al. [9] prepared the water-basedferrofluid using thermal decomposition with phase transfermethod as compared to co-precipitation adopted by otherresearchers who report a decrease in thermal conductivity withan increase in temperature, and Pastoriza-Gallego et al. [17] pre-pared ethylene glycol-based ferrofluids. As explained earlier, thedifference in method of synthesis and dispersion fluid mediumalters thermophysical characteristics of the ferrofluid. Hence, wecannot directly compare these two studies. Furthermore, this high-lights the need for each ferrofluid type to have its properties care-fully measured.

1.2. Viscosity

Minimising viscosity is important in minimising the pumpingpower required for the system.

Table A2 in the appendix compiles past experimental results forferrofluid viscosity. Past experimental results have agreed that vis-cosity increases with an increasing solid volume concentration andmagnetic flux strength, and viscosity decreases with increasingtemperature [8,18–21]. Li et al. [18] andWang et al. [19] found thatthe rate of increase in viscosity is reduced with increasing solidvolume concentration, magnetic flux strength and temperature.However, Li et al. [18] uses solid magnetic nanoparticles that aregreater than 16 nm – the prescribed theoretical size limit for mag-netite (Fe3O4) nanoparticles to remain superparamagnetic [4].

As explained above, an increase in viscosity is unfavourable forthe cost of pumping. However, while an increase in solid volumeconcentration and magnetic flux increases viscosity, and thus pres-sure drop, it also increases the thermal conductivity of the fer-rofluid. Hence, an optimal solid volume concentration percentageand magnetic flux strength should be found to enhance heat trans-fer of the magnetofluidic flow whilst limiting the increase in vis-cosity; the aim being to increase the ratio of Nu/DP.

2. Materials and experimental methods

2.1. Material characterization

Commercial water-based ferrofluids (Domain Detection Kit,Ferrotec), containing fluid types EMG308, EMG408, EMG707,EMG708 and EMG807, were used to make diluted samples of 5%and 10% ferrofluid content for each EMG series, with de-ionizedwater (DIW). The initial properties given by the supplier are shownin Table 1. This gives a volume ratio of ferrofluid:DIW as 0.05:0.95for 5% dilution, and 0.10:0.90 for 10% dilution. Thermophysicalproperties of the diluted samples were measured and compiledin Table 2.

Density of the diluted samples was measured at room temper-ature (RTP) (�22 �C) using a density bottle, also known as a pyc-nometer (Calibrated 25.102 cm3, BLAUBRAND�). DIW was usedas the calibration standard. Measurements were repeated threetimes and averaged.

Contact angle of the diluted ferrofluid samples on a flat poly-dimethylsiloxane (PDMS) surface (the material of the microchan-nel) was captured using a Canon EOS 700 digital single-lensreflex (DSLR) camera at RTP, then evaluated using ImageJ software.

2.1.1. Particle sizingIt is well known that the size, shape, and composition of the

magnetic nanoparticles strongly influence the thermophysical pro-file of the ferrofluid, and thus, their transport and flow properties.Since all the diluted samples contain Fe3O4 magnetic nanoparticles,the only variable is size. Depolarized dynamic light scattering(DDLS) and transmission electron microscopy (TEM) wereemployed to size the particles. Size distribution of the magneticnanoparticles was obtained using DDLS, performed on an ALV-5022F spectrometer. Four measurements of 2-min duration wereperformed, and the average of the data sets were taken. Morphol-ogy of the diluted samples were observed on a JEOL 1010 TEM(100 kV) equipped with a CCD camera (Orius SC600A, Gatan).

2.1.2. Transport propertiesViscosity and thermal conductivity are dependent on the type

and concentration of magnetic nanoparticles, and surfactantmake-up of the ferrofluid. The type and strength of external mag-netic field applied also affects these properties.

2.1.2.1. Viscosity. Kinematic viscosity of the diluted ferrofluidsamples was measured at 25 �C using a capillary viscometer(Micro-Ubbelohde 531 10, SCHOTT) along with a viscosity

Table 1Supplier given properties – domain detection kit.

Sample Supplier given properties

Components (% by Volume) Density (kg/m3) Sat Magnetization (mT)

Magnetite Surfactant Carrier

EMG308 0.4–1.1 0.5–1.5 97.4–99.1 1060 6.6EMG408 0.4–1.1 0.5–1.5 97.4–99.1 1070 6.6EMG707 1–4 7–27 69–92 1100 11EMG708 1–4 7–27 69–92 1080 6.6EMG807 1–8 6–60 32–93 1100 11

Table 2Measured properties of diluted ferrofluid samples.

Sample Magnetite content (% by volume) Measured properties

q (kg/m3) m (mPa�s) Contact angle (�) j (W/(m�K))EMG308 5% 0.02–0.055 1006.0 1.025 90 0.646EMG308 10% 0.04–0.11 1008.1 1.046 110 0.644EMG408 5% 0.02–0.055 1004.6 1.029 113 0.636EMG408 10% 0.04–0.11 1006.2 1.040 114 0.626EMG707 5% 0.05–0.2 1012.9 1.078 80 0.642EMG707 10% 0.1–0.4 1021.0 1.103 106 0.645EMG707 20% 0.2–0.8 1022.5 1.129 80 0.655EMG708 5% 0.05–0.2 1005.9 1.029 109 0.682EMG708 10% 0.1–0.4 1009.8 1.060 105 0.684EMG807 5% 0.05–0.4 1006.7 1.040 100 0.644EMG807 10% 0.1–0.8 1009.7 1.050 84 0.651DIW – 1000.0 1.000 115 0.610

112 N. Gan Jia Gui et al. / International Journal of Heat and Mass Transfer 123 (2018) 110–121

measuring system (ViscoSystem� AVS350, SCHOTT). This measure-ment was taken three times, and the final reading is the average ofthe three. DIW was used as the calibration standard.

Grade N42 neodymium permanent magnets (40 � 15 � 8 mm,Aussie Magnets) were used to apply an external magnetic field tothe ferrofluid. Magnetic flux was tuned by varying the offset dis-tance between the capillary tube and the magnets.


Thermal conductivity of the diluted samples was measured at25 �C using the KD2 Pro Thermal Property Analyzer (DecagonDevices Inc.), which is based on the transient hot-wire method.The KS-1 single needle sensor with 1.3 mm diameter and 60 mm

Fig. 1. Custom 3D printed aluminium box dimensions.

length was used. The fluid sample was held in a custom 3D printedaluminium box (see Fig. 1) connected to a water bath (MB-5,Julabo), to keep the sample at a controllable constant temperature.The test sample containment area had a diameter of 31.3 mm, anda height of 75 mm because a minimum of 15 mm of material par-allel to the sensor in all directions is necessary for accurate mea-surements. Like the viscosity experiment, permanent magnetswere used to apply an external magnetic field to the ferrofluidsand magnetic flux was varied by varying the offset distancebetween the aluminium box and the magnets.

2.3. Microchannel fabrication

To fabricate the microchannel, we adopted the method pro-posed by Saggiomo and Velders [22]. The design of the sacrificialmicrochannel mould (see Fig. 2) was first 3D printed out in acry-lonitrile butadiene styrene (ABS) with a layer thickness of 0.254mm. The microchannel mould was then vapour smoothed usingacetone. Following this process, optical profiling was performedusing the Olympus LEXT OLS4100 3D Measuring Laser Microscopeto obtain both 2D (planar) and 3D (areal) surface roughness of theuntreated and treated microchannel sacrificial moulds. Resultsindicated that the treated sacrificial moulds were about four timessmoother than the untreated moulds (refer to Table 3) and that thecross section became circular.

Fig. 2. Microchannel sacrificial mould dimensions.

Table 3Surface roughness results.

Sample 2D surface roughness(lm)

3D surface roughness(lm)

Top Bottom Top Bottom

Sample 1 8.12 33.35 9.02 47.53Sample 2 9.04 28.48 7.41 36.31Sample 3 10.32 11.82 13.97 15.52Sample 4 5.43 10.09 15.29 14.26

Fig. 3. 3D casted PDMS microchannel with embedded nichrome heater.


The bottom surface of the sacrificial mould, which was in directcontact with the rough support structure during the 3D printingprocess, decreased in roughness by a factor of 2–4 after treatment.However, the top surface, free from contact, becomes about 0.5–0.8times rougher after treatment. This was due to the arbitrary vapoursmoothing process. Overall, it was observed that surface roughnesswas improved after performing vapour smoothing with acetonewith an approximate roughness to channel diameter ratio of 1/100.

A nichrome heater coil (wire gauge 28, JayCar) was carefullywrapped around the treated sacrificial mould over a section ofthe straight length (see Fig. 2). Thermocouples were positionednear the microchannel walls using additional scarification ABSstems held perpendicular to the microchannel with an ABS guidestructure (thermocouple adapter). Degassed PDMS at a mixtureratio of 10:1 was then poured into the pre-prepared glass mouldover the sacrificial mould. The PDMS was left to cure in the ovenat 75 �C for 2–3 h. The thermocouple adapter and PDMS mouldwas removed, and the desired cured thermocouple-embeddedmicrochannel PDMS was soaked in acetone for at least 48 h toallow the acetone to soften the sacrificial mould. Acetone was then

Fig. 4. Embedded thermocoup

pushed through the inlet/outlet ports of the PDMS mould using aneedleless syringe until all the sacrificial mould was fully dissolvedand flushed out, creating a cavity. Finally, DIWwas flushed throughthe cavity to clear any remaining solid particles, producing thedesired microchannel (see Fig. 3).

2.4. Single phase flow heat transfer

Eight T-type thermocouples (Teflon-insulated twisted pair solid1/0.2 mm) were embedded in the PDMS; two thermocouplesembedded into the microchannel flow – one at the inlet heatedarea, and the other at the outlet heated area (see Fig. 4). The othersix thermocouples were along the microchannel length (seeFig. 4a). Small diameter thermocouple wires were used to min-imise conduction losses. Temperatures were recorded using a tem-perature data logger (TC-08, Pico Technology). The temperaturemeasurement system was calibrated against a traceable platinumresistance thermometer (PRT) (P795, Dostmann).

2.4.1. Nusselt number calculationNusselt number, Nu, is expressed as

Nu ¼ hDhj

ð1Þ

where Dh represents the hydraulic diameter, and j is the thermalconductivity of the fluid. The average convective heat transfer coef-ficient of the flow, h, is expressed as

h ¼ qfðTw;avg � Tf ;avgÞ ð2Þ

where qf is the heat flux in W/m2, Tw,avg is the average wall temper-ature difference (Tw,out + Twin)/2 and Tavg is the average fluid tem-perature difference (Tout + Tin)/2 across the heater. Here, qf can becalculated as

qf ¼_QqcpðTout � TinÞ

Að3Þ

where _Q is the volumetric flow rate, q is density of the fluid, cp isthe specific heat capacity of the fluid, (Tout � Tin) is the average fluidtemperature difference, and A is the area in contact with the fluid.

As the solid volume fraction of magnetic nanoparticles is esti-mated to have an average of 0.03–0.4% depending on the sample,and cp for ferrofluid was assumed to have the same value as thecarrier fluid (DIW).

2.5. Flow visualization

Flow visualization was conducted for EMG707 20% mixed witha fluorescein solution (Rhodamine 123:Ethanol = 2 mg:10 mL)with a volume ratio of 5:1. Magnetic flux strength of 200 mT per-

les in microchannel flow.


pendicular to the direction of flow was provided by grade N42cuboid permanent magnet(s) with a base, width, and height of3.2 mm (B222, K&J Magnetics Inc.). A PDMS microfluidic chip fab-ricated using soft lithography bonded onto a 1 mm thick micro-scope glass slide (Prosciteh) with a channel width of 500 mm andheight of 200 lm was used. Magnetic particle build-up wasvisualized using confocal microscopy (Eclipse Ti, Nikon). Single-phase ferrofluid flow was introduced to the microfluidic chip usinga precision syringe pump (PHD ULTRATM, Harvard Apparatus) via agastight glass syringe (50 mL luer lock, SGE Analytical Science).

2.6. Experimental uncertainty analysis

Uncertainty estimations of measured parameters are based onthe method outlined in Coleman & Steele [23], using the examplesshown in Stanley [24] as a guideline. The estimated uncertainty forNusselt number determination is 39% which comprised of a bias(systematic) error and a precision (random) error [24].

Fig. 6. EMG807 TEM results.

3. Results

3.1. Material characterization

3.1.1. Particle sizing3.1.1.1. Depolarized dynamic light scattering (DDLS). As the undi-luted ferrofluid comes from the same stock, only 5% dilution fer-rofluid samples were used for DDLS and TEM.

For DDLS, due to the opaqueness of the diluted ferrofluid sam-ples, it was necessary to further dilute the samples to prevent thescattering of light. A dilution factor of 500 with DIW was per-formed on the 5% dilution ferrofluid samples. Intensity weightedgraphs represents the amount of light intensity absorbed by theparticles (see Fig. 5). The larger the particle size, the more intensityit absorbs, thus, showing a higher peak. However, if a smaller sizedparticle can be observed compared to a larger particle, it meansthat there should be a lot of smaller particles observed in compar-ison to the larger particles. Number weighted graphs representsthe predicted concentration of particles in the solution (seeFig. 6). As seen in all measured samples, the number weightedgraphs indicate that most of the sample is made up of smaller par-ticles compared to larger ones. The reliability of these results wasverified by performing TEM on the samples.

Fig. 5. DDLS results for EMG707 ferrofluid – number weighted vs intensityweighted graphs.

3.1.1.2. Transmission electron microscopy (TEM). From TEM, it wasobserved that the ferrofluids were fabricated using the co-precipitation method, reflected by the polydisperse magneticnanoparticles [25]. The particle sizes obtained from TEM areslightly larger than those obtained from DDLS (see Fig. 6). This isdue to the evaporation under ambient atmosphere of the solutionduring sample preparation, where the nanoparticles are depositedonto strong carbon grids (GSCu200C-50), spurring the nanoparti-cles towards further aggregation due to the elevating free energyat the grain boundary [9]. However, it can be concluded that thenumber weighted graphs are reliable when compared to the TEMresults (refer to Tables 4 and 5).

3.1.2. Transport properties3.1.2.1. Viscosity. It was observed that viscosity increases linearlywith density (see Fig. 7), and that both viscosity and density ofthe diluted ferrofluid samples are greater than that of the base fluid– DIW. The magnetic nanoparticles are considerably denser thanthe base fluid (qFe3O4 = 5170.0 kg/m3). It was also observed thatviscosity increases linearly with magnetic flux (see Fig. 8). The lar-gest increase in viscosity is about 5% for EMG308 10% under a mag-netic flux of 50 mT compared to 0 mT at RTP (�22 �C). The increasein viscosity can be attributed to the alignment and clustering ofmagnetic nanoparticles in the direction of the applied magneticfield, which is perpendicular to the flow. These chains increasethe resistance to the flow, thereby increasing viscosity. This is con-sistent with previous studies [8,18–21].


Thermal conductivity measurements show that all the dilutedferrofluid samples have a slightly higher thermal conductivityvalue at 25 �C compared to DIW (see Fig. 9).

The thermal conductivity increases exponentially with theapplication of an external magnetic field (see Fig. 10). The highestenhancement is about 100% for EMG708 10% compared to DIW.The increment of thermal conductivity can be attributed to thealignment of the magnetic nanoparticles with the application ofan external magnetic field [26,27]. Due to the superparamagnetic

Table 4Summary of DDLS measurement results.

Sample Particle size (nm)

Run 1 Run 2 Run 3 Run 4 Avg Max

EMG308 2.13 4.07 8.17 8.56 5.73 46EMG408 2.81 4.9 7.11 7.11 5.48 55EMG707 3.38 3.89 6.48 10.3 6.01 110EMG708 4.26 6.19 8.18 8.18 6.70 121EMG807 3.89 3.89 5.64 8.96 5.60 80

Table 5Summary of TEM results.

Sample Measured particle size (nm)

Reading 1 Reading 2 Reading 3 Reading 4 Avg

EMG308 6.93 7.73 8.64 13.64 9.23EMG408 7.58 9.09 11.36 15.15 10.80EMG707 4.51 6.77 9.77 15.04 9.02EMG708 7.58 11.36 13.64 16.67 12.31EMG807 7.58 9.09 9.85 15.15 10.42

Fig. 7. Dynamic viscosity vs density of diluted commercial ferrofluid solutions @RTP.

Fig. 8. Viscosity experimental results with magnetic field @ RTP.


nature of the magnetic nanoparticles, the solid nanoparticles willalign themselves in the direction of the applied magnetic field.These solid nanoparticles cluster to form more efficient conductionpathways which enhances conductive heat transfer.

3.3. Single phase flow heat transfer

3.3.1. Diluted ferrofluid samples (without a magnetic field)Generally, we found that there is minimal to no enhancement of

heat transfer without an external magnetic field (see Fig. 11).

3.3.2. Diluted ferrofluid samples (with a magnetic field)Magnetic field strengths of 10, 20, 30, 40 and 50 mT were

applied to the fluid flow along the heated section. Generally, itwas observed that Nu decreases with increasing magnetic fieldstrength for all diluted ferrofluid samples (see Fig. 12). It can alsobe observed that at a lower magnetic flux of 10 mT, for certain fer-rofluid samples (EMG707 10%, EMG708 10%, EMG807 5%) heattransfer rate is higher compared to 0 mT, and that Nu decreasessignificantly when the magnetic flux is 30 mT and above (see

Fig. 9. Measured thermal conductivity ratio (jFF/jDIW) without magnetic field@ 25 �C.

Fig. 10. Measured thermal conductivity ratio (jFF/jDIW) with magnetic field @ 25�C.

Fig. 11. Measured Nu ratio (NuFF/NuDIW) without magnetic field @ Re = 11.6.

Fig. 12. Nu ratio vs magnetic flux density of EMG807 5% @ Re = 11.6.

Fig. 13. Nu ratio vs magnetic flux density @ Re = 11.6.


Fig. 13). This could be attributed to the solid magnetic nanoparti-cles getting attracted to, and at high enough fluxes, pinned in placeagainst the wall of the channel under the action of the magneticfield. The removal of the nanoparticles from the carrier fluidreduces the effective thermal conductivity of the mixture. This inturn is detrimental to heat transfer at the area where magnetic fluxis applied. This particle trapping behaviour is explained by Heja-zian and Nguyen [28]. They explain how the solid magneticnanoparticle escapes, focuses into a line, until they reach a maxi-mum field zone and become almost stationary being trapped atits centre. Hatami et al. [29] also found that heat transfer decreaseswith the application of an external magnetic field.

Fig. 14 shows a schematic of how the effective thermal conduc-tivity is decreased due to the magnetic field during the flow. Wefound that a thermal conductivity ratio of jeff/jDIW for EMG70720% was 1.07 (see Fig. 10).

To calculate the effective thermal conductivity in the presenceof a magnetic field (j0eff ), we assume that the solid magneticnanoparticles get stacked in the region of highest magnetic fluxas a complete solid, and take the average thickness of the solidnanoparticle layer (hFF) such that the thickness layer ratio

(hFF/hDIW) reflects upon the effective thermal conductivity ratio(hFF:hDIW = jeff:jDIW). Hence, j0eff is expressed as

j0eff ¼hDIWh

� �jDIW þ hFFh

� �jeff ð4Þ

where jeff’ represents the effective thermal conductivity of the fer-rofluid in the presence of a magnetic field in W/(m�K), hDIW and hFFare the thickness layers of DIW and the solid magnetic nanoparticle(Fe3O4) respectively in m, h is the total thickness of the channel inm, jDIW and jeff are the thermal conductivities of DIW and Fe3O4respectively in W/(m�K). Using this approach, we calculated theeffective thermal conductivity value of j0eff = 0.559W/(m�K) forEMG707 10% at a flow rate of 2 mL/h and a magnetic flux of 200mT. This value is lower than compared to the effective thermal con-ductivity obtained when the magnetic particles were in suspensionwithout the effect of an external magnetic field (i.e. jeff/jDIW = 1.07W/(m�K) vs jeff’ /jDIW = 0.916 W/(m�K)).

However, it was also observed that the obtained Nu for zeromagnetic flux was lower than the first round of measurements.This can be attributed to the samples themselves becoming unsta-ble due to oxidization from other testing, thus affecting the results.

Fig. 14. Effective thermal conductivity phenomenon.


To obtain more accurate results, in future work we will fabricationferrofluids in-house.

3.4. Flow visualization

Magnetic particle build-up was visualized to explain the phe-nomenon of effective thermal conductivity. Magnetic particlesbuild up against the channel wall if the magnetic flux strength isgreater than the hydrodynamic force on the particles. At a flow rateof 2 mL/h (see Fig. 15a), and a magnetic flux of 200 mT, weobserved that the rate of growth of the deposited layer was0.283 lm/s. However, for a flow rate of 5 mL/h (see Fig. 15b), nobuild-up of magnetic particles was observed. This effect can beseen in the sequence of images shown in Fig. 15.

To understand the trajectory of the magnetic nanoparticles asthey come out from a polydisperse solution due to an externalmagnetic field. We modelled the balance of hydrodynamic andmagnetic forces as follows. We assume that there are only twoforces acting on the particle. The first is the external magneticforce, FB expressed as

FB ¼ l0H2d2 ¼B2

l0d2 ð5Þ

where l0 is the permeability of vacuum in free space in m�kg/s2A2,H is the magnetic field strength in A/m, B is the magnetic flux den-sity in T, q is density of the particle in kg/m3, and d is the diameterof the particle in m.

Fig. 15. Magnetic particle build up @ (a) Q

The other force present is drag force, FD acting against themotion of the particle, which can be expressed as

FD ¼ �3plvyd ð6Þwhere l is the viscosity of the ferrofluid in kg/(s�m), and vy is thevelocity of the particle in the y component in m/s.

The critical value of vy is when FB = FD which can be expressedas

vy;critical ¼ B2d

l0ð�3plÞð7Þ

Taking upwards as positive (see Fig. 15), the sum of forces acting inthe y-direction is;

�FB þ FD ¼ mdvydt ð8Þ

where m is the mass of the particle in kg, dvy/dt is the rate of changeof velocity of the particle in the y-direction in m/s.

Assuming that magnetic field is constant throughout the thick-ness of the channel, Eq. (9) can be integrated as such

Zm

�3plvyd� FB dvy ¼Z

dt:

Hence,

t ¼ � m3pld

lnj � 3plvyd� FBj þ C ð9Þ

_= 2 mL/h, (b) Q_= 5 mL/h B = 200 mT.

Fig. 16. Magnetic particle trajectory and velocity profile for rectangular channel @0.5 mL/h (Re = 0.36).

100 μm

Moving Magne�c Par�cles

Sta�onary Magne�c Par�cles

Fig. 17. Flow visualization stitch of magnetic particle trajectory for Dt = 8 s @ 0.5mL/h (Re = 0.36).


We assume vy = 0 m/s at t = 0 s, therefore,

C ¼ m3pld

lnj � FBj ð10Þ

Therefore, we can express vy as

vy ¼FB 1þ e�3pldtm� ��3pld ð11Þ

where vy is the velocity of the particle in the y-component.To find the y-position of the particle, we integrate vy as such

y ¼ y0 þFB

�3pldZ

1þ e�3pldtm� �

dt

¼ y0 þFB

�3pld tþme

�3pldtm

�3pld

!ð12Þ

where y is the y-position of the particle in m, y0 is the initialy-position of the particle in m, FB is the magnetic force actingon a particle in N, l is the viscosity of the fluid in Pa�s, d is thediameter of the particle in m, m is mass of the particle in kg,and t is time in s.

For laminar flow in a rectangular channel, the velocity profile vxis expressed as

vx ¼ vðy; zÞ ¼ 16a3

lp3�dPdx

� � X1i¼1;3;5;...

ð�1Þi�12 1� coshipz2a

� �cosh ipb2a

� � !

�cos ipy2a� �i3

¼ dxdt

ð13Þ

where v(y, z) = vx = dx/dt which is the x-component of velocity inm/s, �a � y � a is the width of the channel in m, (�dP/dx) is thepressure gradient in Pa/m, and �b � z � b is the height of the chan-nel in m [30].

To enable simple integration, we approximate the solution of vxin the channel miplane by a fourth order polynomial. For a flow

rate of _Q = 0.5 mL/h, we obtain the equation as

vx ¼ �6Eþ 11y4 þ 223394y3 � 7232:7y2 � 0:0104yþ 0:0026ð14Þ

Substituting Eq. (7) into Eq. (9), and neglecting the exponential termas it is very small, we obtain the following expression

vx ¼dxdt ¼ �6Eþ 11 y0 þFB

�3pld t� �4

þ 223394 y0 þFB

�3pld t� �3

� 7232:7 y0 þFB

�3pld t� �2

� 0:0104 y0 þFB

�3pld t� �

þ 0:0026:

ð15ÞIntegrating, we obtain the following expression for x-position

with respect to time

x ¼ x0 þ�6Eþ 11ðy0 þ FB�3pld tÞ

5ð�3pldÞ5FB

þ223394 y0 þ FB�3pld t

� �4ð�3pldÞ

4FB

�7232:7 y0 þ FB�3pld t

� �3ð�3pldÞ

3FB

�0:0104 y0 þ FB�3pld t

� �2ð�3pldÞ

2FBþ 0:0026t: ð16Þ

where x is the x-position of the particle in m, x0 is the initial x-position of the particle in m, FB is the magnetic force acting on a par-ticle in N, l is the viscosity of the fluid in Pa�s, d is the diameter ofthe particle in m, and t is time in s.

Fig. 16 below shows the trajectory of magnetic particles withdifferent initial positions within the channel, y0, at a relative x-position of x0 = 0. Also shown is the centreline velocity profile ofthe flow for a flow rate of 0.5 mL/h. Along each path line, the timestep between data points is Dt = 1 s. The results here indicate theattraction of the particles towards the wall as they advect withthe flow under the influence of the magnetic force. Flow visualiza-tion further supports this effect. Fig. 17 shows representative par-ticle trajectories at the same flow conditions via digitallyoverlaying 100 frames of a sequence of images. To prevent oversat-uration, the images’ greyscale was inverted, hence, moving mag-

Max

imum

thermal

condu

ctivityratio( j

f/jb)

B(//),/

=5%

;1.16

B(∟

),(/

=5%

);1.45

/=1.71

%;2.15

B=12

mT,

/=6.3%

;3.25

/=1.71

%;2.25

B(//)=40

mT,

/=6.3%

;4.0

B(∟

)=60

mT,

/=5%

;1.67

B(∟

)=10

0mT,

/=5%

;3.0

/=2%

;2.8

/=4.8%

;1.25

/=4.8%

;1.22

(con

tinu

edon

next

page)


netic particles appear white in the image. A number of slow mov-ing particles can be seen to be drawn towards the bottom wall ofthe channel, creating piecewise streak lines on a diagonal to thedirection of flow. Larger particles moving at higher velocities inthe centre of the channel do not experience the same gradientand so appear as a number of individual white blotches separatedby much larger distanced. As an artefact of the processing stepsused, the stationary magnetic particles remain dark as shown atthe bottom of the image.

netic

particle

Mag

netic

nan

oparticlesize

(nm)

Fabricationmethod

Mea

suremen

tmethod

Mag

netic

field

26DirectMixing

Tran

sien

thot-w

ire–tw

owirestyle

method

//mag

netic

field–indu

ced

byso

lenoid(90mT)

∟mag

netic

field–

perm

anen

tmag

net

(25

mT)

46.7

Unkn

own

KD2Pro(transien

thot-w

ire)

Solenoid-like

electrom

agnet

(50mT)

Vial(d

=24

mm;mightbe

toosm

allfor

accu

rate

mea

suremen

ts)

46.7

Unkn

own

KD2Pro(transien

thot-w

ire)

Solenoid-like

electrom

agnet

(50mT)

Vial(d

=24

mm;mightbe

toosm

allfor

accu

rate

mea

suremen

ts)

410

±3

Co-precipitation

KD2Pro(transien

thot-w

ire)

Helmholtz

coils

Test

area

(d=10

mm;mightbe

too

smallforaccu

rate

mea

suremen

ts)

4Unkn

own

Unkn

own

Tran

sien

thot-w

ire

Non

e3

9Co-precipitation

KD2Pro(transien

thot-w

ire)

∟mag

netic

field–Iron

CoreElectrom

agnet

48.4–

10.9

Co-precipitation

KD2Pro(transien

thot-w

ire)

Non

e

4. Conclusions and recommendations

We have investigated the effect of various commercialwater-based ferrofluid types with a dilution factor of 5% and10%, on the heat transfer properties under the application ofan external magnetic field. We have shown the importanceof characterizing the ferrofluid material to better understandthe heat transfer enhancement effect. We found that generally,a higher solid volume concentration of magnetic nanoparticlesenhances heat transfer rates. We recorded about a 100%enhancement in thermal conductivity for EMG708 10% undera magnetic flux of 50 mT at RTP compared to DIW, and abouta 116% enhancement in heat transfer for EMG708 5% withouta magnetic field. However, we observed that heat transfer ratewas diminished with increasing magnetic field strength whichmay be attributed to the solid magnetic nanoparticles becom-ing trapped against the channel wall in the magnetized area.We also showed experimentally and numerically that the effec-tive thermal conductivity of the ferrofluid is reduced due tothe trapping of the magnetic particles. The balance of forcesbetween magnetic and hydrodynamic is what determines mag-netic particle trapping, which also allowed us to predict parti-cle trajectory.

It was also observed that viscosity increases with an increasein magnetic flux, but only to a small extent. The largest incre-ment of viscosity was for EMG308 10%, with an increment of5% at a magnetic flux of 50 mT, compared to the viscosity at 0mT. It was difficult to associate the enhanced heat transfer phe-nomenon to a material characteristic of the ferrofluid due to thecommercial nature of the substance. Therefore, we will be self-fabricating ferrofluids for future experiments. Future works alsoinclude two-phase liquid-liquid ferrofluidic plug flow, and pres-sure drop experiments. Mixing can also be enhanced by usinga non-uniform magnetic field which will also be investigatedfor future studies.

offerrofl

uids

. Mag

nan

o

fonate

Fe

.5nm)

Fe3O

.5nm)

Fe3O

teFe

3O

Fe3O

mon

ium

H)

Fe2O

Fe3O

Conflict of interest

None.

alresu

ltsforthermal

cond

uctivity

Basefluid

Surfactanttype

Water

Sodium

Dod

ecylbe

nesul

(activator)

Keros

ene

Oleic

Acid(t=1

Keros

ene

Oleic

Acid(t=1

Water

Tri-so

dium-citra

Hyd

rocarbon

Oleic

Acid

Water

Tetram

ethyl

amhyd

roxide

(TMA

Water

TMAH

Acknowledgements

We thank David Dunstan and RMIT’s MNRF, RMMF and AMP forassistance, Mark Greaves from the CSIRO Manufacturing ElectronMicroscopy, Digital Imaging and Surface Analysis Facility withinthe Characterisation Group for his contribution to the optical pro-filing experiment, and the Australian Research Council for fundingthis research (linkage project ID LP150100153).

TableA1

Past

expe

rimen

t

Inve

stigators

[18]

[12]

[13]

[14]

[31]

[32]

[6]

Appendix A

See Tables A1 and A2.

Table A1 (continued)

Investigators Base fluid Surfactant type Magneticnanoparticle

Magneticnanoparticle size(nm)

Fabrication method Measurement method Magnetic field Maximum thermalconductivity ratio (jf/jb)

[33] Kerosene Oleic Acid Fe3O4 15 One-Step PhaseTransfer

Short hot-wire None / = 3%; 1.11

155 (DLS)[26] Water Ammonium Citrate Fe3O4 9.8–10 Co-precipitation Transient hot-wire None / = 1%; 1.34[16] Water Oleic Acid (activator);

Citric Acid (surfactant)Fe3O4 6 Thermal

DecompositionFlucon GmBH Lambda (transient hot-wire)

None / = 5%; 1.4

Water Citric Acid or Capric Acid 10 Co-precipitation / = 1.2%; 0.89[15] Water Capric Acid Fe3O4 10 Co-precipitation Flucon GmBH Lambda (transient hot-

wire)Solenoid-likeelectromagnet

/ = 7%; 1.048

B(∟) = 200 mT, / = 1.28%;1.028

[17] EthyleneGlycol

Unknown Fe3O4 15 ± 4 Co-precipitation KD2 Pro (transient hot-wire) None / = 6.6%; 1.16

EthyleneGlycol

Unknown Fe2O3 29 ± 18 One-Step PhaseTransfer

/ = 6.6%; 1.12

[34] Kerosene Oleic Acid Fe3O4 9.9 Co-precipitation Flucon GmBH Lambda (transient hot-wire)

Solenoid-likeelectromagnet (100 mT)

B(∟), / = 4.7%; 1.23

[9] Toluene Oleic Acid Fe3O4 4–12 ThermalDecomposition

KD2 Pro (transient hot-wire) None Unknown

Water Poly (acrylic acid) (PAA) 4–12 ThermalDecomposition + PhaseTransfer

Unknown

[35] Water Unknown Fe3O4 �10 Unknown Transient hot-wire Current-carrying wire (I =0.5 A)

B(∟), / = 2%; 1.09

Table A2Past experimental results for viscosity of ferrofluids.

Investigators Base fluid Surfactant type Magneticnanoparticle

Magneticnanoparticle size(nm)

Fabrication method Measurement method Magnetic field Maximumviscosity(mPa�s)

[18] Water Oleic Acid Fe3O4 20 Co-precipitation Capillary Tube Viscometer ∟ magnetic field –permanent magnet (25 mT)

/ = 2.83%; 25

Water SodiumDodecylbenesulfonate

Fe 26 Direct Mixing // magnetic field – inducedby solenoid (90 mT)

/ = 4%; 1.4

[19] Water Unknown Fe3O4 7.5 Co-precipitation Sine-Wave Vibro Viscometer (SV-10) ∟ magnetic field –permanent magnet (30 mT)

/ = 5%; 1.78

[36] Water Oleic Acid (activator);PEG-4000 (surfactant)

Fe3O4 �9–10; 23 Co-precipitation Capillary Tube Viscometer (= Capillary Rheometer) andRotating Rheometer (Brookfield LVDV III+)

None Unknown

Oleic Acid (activator); PEGpowder (surfactant)

ChemicalPrecipitation + BallMilling

None Unknown

[20] Methanol Tetramethyl ammoniumhydroxide (TMAH)

Fe3O4 5 ± 0.2 Co-precipitation Dial reading viscometer (Brookfield, M/00–151) ∟ magnetic field Unknown

Oleic Acid Unknown[8] Kerosene Oleic Acid Fe3O4 6–20; mean 10.6 Co-precipitation MCR300 Rheometer (Physica Anton Paar GmbH) using

plate-plate spindle (PP25-MRD)// magnetic field – fromrheometer (electromagnet)

Unknown

[21] SyntheticEster Oil

APGW05 (Ferrotec) Fe3O4 + c-Fe2O3

Unknown Unknown Parallel plate Rheometer ∟ magnetic field –permanent magnet

Unknown

SyntheticEster Oil

APGW010 (Ferrotec) Fe3O4 + c-Fe2O3

Unknown Unknown Unknown

120N.G

anJia

Gui

etal./International

Journalof

Heat

andMass

Transfer123

(2018)110–

121


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Ferrofluids for heat transfer enhancement under an external magnetic field1 Introduction1.1 Thermal conductivity1.2 Viscosity

2 Materials and experimental methods2.1 Material characterization2.1.1 Particle sizing2.1.2 Transport properties2.1.2.1 Viscosity

2.2 Thermal conductivity2.3 Microchannel fabrication2.4 Single phase flow heat transfer2.4.1 Nusselt number calculation

2.5 Flow visualization2.6 Experimental uncertainty analysis

3 Results3.1 Material characterization3.1.1 Particle sizing3.1.1.1 Depolarized dynamic light scattering (DDLS)3.1.1.2 Transmission electron microscopy (TEM)

3.1.2 Transport properties3.1.2.1 Viscosity

3.2 Thermal conductivity3.3 Single phase flow heat transfer3.3.1 Diluted ferrofluid samples (without a magnetic field)3.3.2 Diluted ferrofluid samples (with a magnetic field)

3.4 Flow visualization

4 Conclusions and recommendationsConflict of interestAcknowledgementsAppendix AReferences

international journal of heat and mass transfer · 2018. 3. 20. · this allows higher convective...

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