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Advances in Mechanical Engineering

Volume 2010 (2010), Article ID 742739, 10 pages

http://dx.doi.org/10.1155/2010/742739

## Experimental Studies of Natural Convection Heat Transfer of Al_{2}O_{3}/DI Water Nanoparticle Suspensions (Nanofluids)

^{1}Department of Mechanical, Industrial, and Manufacturing Engineering, University of Toledo, Toledo, OH 43606, USA^{2}Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0325, USA

Received 5 May 2009; Accepted 4 June 2009

Academic Editor: Oronzio Manca

Copyright © 2010 Calvin H. Li and G. P. Peterson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The natural convection heat transfer characteristics of nanofluids comprised of 47 nm, and water, with volume fractions ranging from 0.5% through 6%, has been investigated through a set of experimental measurements. The temperature of the heated surface and the Nusselt number of different volume fractions of nanofluids natural convection tests clearly demonstrated a deviation from that of pure base fluids (distilled water). In the investigation, a deterioration of the natural convection heat transfer coefficient was observed with increases of the volume fraction of the nanoparticles in the nanofluids. The deterioration phenomenon was further investigated through a visualization study on a 850 nm diameter polystyrene particle/water suspension in a bottom heating rectangular enclosure. The influence of particle movements on the heat transfer and natural flow of the polystyrene particle/DI water suspension were filmed, and the temperature changes on the heating and cooling surfaces were recorded. The results were analyzed in an effort to explain the causes of the natural convection heat transfer deterioration of the 47 nm nanofluids observed in the experiments. The visualization results confirmed the natural convective heat transfer deterioration, and further explained the causes of the deterioration of the nanofluids natural convective heat transfer.

#### 1. Introduction

There is increasing evidence that nanoparticles dispersed in liquid base fluids can have a significant impact on the effective thermal conductivity of nanoparticle/liquid suspensions (nanofluids) [1–18]. For example, nanofluids consisting of 10 nm Cu nanoparticles suspended in ethylene glycol with a volume fraction of 0.3%, have shown a 40% enhancement in the effective thermal conductivity, when compared to that of the base fluid (ethylene glycol) [15]. In addition, 36 nm CuO nanoparticles in distilled water with a volume fraction of 5% have exhibited as much as a 60% increase in the effective thermal conductivity over that of the base fluid (distilled water) at room temperature [16], and 33 nm Al_{2}O_{3 } nanoparticles in distilled water have exhibited a 30% enhancement in the effective thermal conductivity [16]. Moreover, the enhancement of the effective thermal conductivity of these metal oxide nanoparticle nanofluids has been shown to increase with increases in temperature [17].

Recent experiments indicated that water-based nanofluids of 29 nm CuO and 36 nm Al_{2}O_{3} nanoparticles resulted in a range of effective thermal conductivity enhancements from 30% to 52% for CuO/Distilled water nanofluids, and 8% to 30% for Al_{2}O_{3}/Distilled water nanofluids, at volume fractions of 6% and 10%, respectively, and at a bulk temperatures ranging from 27.5°C to 34.7°C [18].

Several mechanisms have been proposed to explain the enhancements described above. Of the two most likely, the first attributed the effective thermal conductivity enhancement to the increased thermal conductivity of the nanoparticles and agglomerations. The second focused on the contribution of the Brownian motion of the nanoparticles. The significance of these two mechanisms are both closely related to the bulk temperature of the nanoparticle suspension, the mean size of the nanoparticles, the volume fraction of nanoparticle in the nanofluids, and the physical properties of base fluid materials.

The increased thermal conductivity of nanoparticle suspensions has been well documented and can be estimated using Maxwell’s equation [19] or the Hamilton and Crosser equation [20]. The Brownian motion mechanism and contribution of the nanoparticles in the base fluid has received a significant amount of attention more recently, and has been extensively explored and/or explained [13, 21–24].

Other heat transfer modes of nanofluids, such as natural and forced convection and boiling heat transfer, have also been investigated by a number of researchers [25–34]. Like the study on the effective thermal conductivity of these nanofluids, several mechanisms and explanations have been proposed. For the natural convection heat transfer of nanofluids, Okada et al. [28, 29] experimentally measured the change of layering and concentration of large soda glass particle/water suspensions in a rectangular cross-section cell, which had a bottom heating surface and five other isothermal walls. The same group of researchers also measured the natural convection heat transfer of 2.97 micron SiO_{2}/water suspension in a rectangular cross-section vessel, which was heated and cooled from two opposing vertical walls and had other four adiabatic walls. Khanafer et al. [30] and Jou and Tzeng [31] conducted numerical studies of the natural convection heat transfer of nanofluids in a two-dimensional enclosure.

Based on the assumptions used in these simulations, such as the thermal and flow equilibrium between the fluid phase and nanoparticles, the uniform shape and size for nanoparticles, and most importantly, the enhancement in the effective thermal conductivity of the nanofluids due to the thermal dispersion, the two numerical investigations resulted in the same conclusion, that the natural convection heat transfer of nanofluids had been greatly increased at various flow parameters. Putra et al. [32] experimentally evaluated Al_{2}O_{3} and CuO nanoparticle/water nanofluids in a horizontal cylindrical unit, heated on one vertical side and cooled on the other vertical side in a horizontal direction. It was found that a systematic and definite deterioration in natural convection heat transfer had occurred in both of these types of nanofluids. Similar natural convection heat transfer deterioration results were also reported in the investigation at various volume fractions of TiO_{2}/water nanofluids [33]. Discussion of those two reports focused on several possible parameters, which could lead to this deterioration, such as the thermophysical properties, particle concentration, the pH value, and the particle/water surface interaction.

To determine the effect of nanoparticle concentration, a visualization study of the natural convection of 57 micron diameter glass particle suspensions under intermittent heating was conducted [34]. A transient change of flow patterns was observed and a particle-free layer at the top of convection cell was observed. When compared to tests on pure liquid, a peculiar sedimentation driven two-layer convection was found.

Based on the previous studies of the effective thermal conductivity and the viscosity of Al_{2}O_{3}/distilled water nanofluids, the current investigation was focused on the experimental measurement of natural convection heat transfer of Al_{2}O_{3} nanofluids. The particle movement influences on the natural convection heat transfer deterioration was also analyzed by visually studying the heat transfer process of an 850 nm polystyrene particle/DI water suspension in a rectangular enclosure. The two components were integrated in an effort to explain the causes of the new phenomena of nanofluids natural convective heat transfer deterioration. In Al_{2}O_{3} nanofluids test, there is no surfactant involved to avoid the hydrophobic to hydrophilic aqueous interfaces effect introduced by surfactants [35, 36], rather the samples were kept in original pH value around 7 and ultrasonic bath was used to make sure a good dispersion in a reasonably time period of 24 hours. As pointed by [37], the tested effective thermal conductivities of the nanoparticle suspensions were repeatable with negligible changes in this time period.

#### 2. Experimental Test Facility and Results

##### 2.1. The Experimental Measurement of Natural Convection Heat Transfer of Al_{2}O_{3} Nanofluids

In the current investigation, the natural convection heat transfer of Al_{2}O_{3} nanofluids was studied using the test facility shown in Figure 1. This system was thermally insulated and consisted of a support rig, two copper bars, one rubber o-ring and the thermal insulation materials. The copper bars have a diameter of 25.4 mm (1 inch), and a length of 254 mm (10 inches). The o-ring had a diameter of 2.5 mm and formed a circle with 25.4 mm outer diameter, which was used to form a test cell along with the two 25.4 mm diameter cross-section copper bars. Starting at the surfaces, eighteen k-type thermocouples (Omega, USA) were inserted at the center of both copper bars 25.4 mm apart along the axis. Temperatures at each insertion point were measured simultaneously using a 40-channel thermocouple amplifier HP 34970A data acquisition system at a DAQ rate of 100 fps. The heat flux was determined through a one-dimensional conduction equation. The lower copper bar was connected to a heater to heat up the bottom of test cell, and the upper copper bar was connected to a heat pipe heat dissipater, which rejected heat to the environment. The whole system was calibrated with pure water and the uncertain was estimated to be less than 5%.

The Al_{2}O_{3} nanofluids were produced by dispersing Al_{2}O_{3} nanoparticles into the base fluid, distilled water (DI water). The Al_{2}O_{3} nanoparticles were purchased from Nanophase Technologies Corporation, USA, and had a spherical shape with a mean diameter of 47 nm as shown in Figure 2. Prior to each test, the Al_{2}O_{3 } nanofluids were processed in an ultrasonic bath for 90 minutes to break any possible aggregations of Al_{2}O_{3} nanoparticles and to keep the nanofluids uniformly dispersed. The dispersing method could ensure that the nanofluids were stable for more than 24 hours without any visible sedimentations and agglomerations. After the Al_{2}O_{3 } nanofluid samples were prepared, they were charged into the test cell for the natural convection heat transfer tests.

The heat flux in the copper bars was determined by measuring the temperatures at different locations inside the upper and lower copper bars to obtain temperature profiles and was then computed with one-dimensional heat conduction equation as follows:

After the heat flux was obtained, the heat transfer coefficient, *h*, was calculated by

The Nusselt number (Nu) and the Rayleigh number (Ra) were calculated based on the temperature difference between the upper and bottom surfaces and heat transfer coefficient, as shown in (4). The effective thermal conductivity and viscosity of Al_{2}O_{3} nanofluids were obtained from the previous work [18, 38]. The mean heat flux of this experiment was found to be 120 W/m^{2}, and the distance between two surfaces of the test cell was 2.5 mm:

##### 2.2. Experimental Results of Natural Convection Heat Transfer of Al_{2}O_{3}/DI Water Nanofluids

For the experimental measurements of natural convective heat transfer, temperature changes against time were recorded and are presented in Figures 3 and 4. As indicated, the temperature differences between each pair of different volume fraction nanofluids were approximately 1°C. The highest heating surface temperature occurred at the 6% volume fraction nanofluid, and the lowest heating surface temperature occurred for pure water. The cooling surface temperatures of different volume fraction Al_{2}O_{3}/DI water nanofluids had virtually no difference due to the excellent heat transfer performance of heat pipe heat dissipater.

It was interesting to note that, within the first 200 seconds, the heating surface temperatures of Al_{2}O_{3}/DI water nanofluids at all volume fractions underwent an evolving process whereby the heating surface temperature of 6% volume fraction nanofluid moved up to be the highest and the heating surface temperature of pure water changed to be the lowest among all the heating surface temperatures, which originally were at the same value. After the first 200 seconds, the temperature of the heating surface for the pure water case was still the lowest, with the next lowest being the 0.5% volume fraction nanofluid, followed by the 2% volume fraction nanofluid, the 4% volume fraction nanofluid, and finally the highest heating surface temperature occurred for the 6% volume fraction nanofluid. After the first 400 seconds, the heating surface temperature differences of all the different volume fraction tests were reduced but still had the same order that heating surface of the 6% volume fraction had the highest value, followed by the 4% volume fraction, and next by 2% volume fraction, then by 0.5% volume fraction, and finally by pure water, as shown in Figure 4.

The relationships between the Nu and Ra numbers for each volume fraction of the Al_{2}O_{3}/DI water nanofluid and pure water are presented in Figure 5, which demonstrates that the pure water had the highest Nu number at a given Ra number, followed by the 0.5% volume fraction Al_{2}O_{3}/DI water nanofluid, 2% volume fraction Al_{2}O_{3}/DI water nanofluid, 4% volume fraction Al_{2}O_{3}/DI water nanofluid, and finally the 6% volume fraction Al_{2}O_{3}/DI water nanofluid. This decreasing trend of Nu number with the increase of volume fraction has also been previously reported by other investigators [32, 33], which clearly illustrated a deterioration of natural convection heat transfer against the increase of volume fraction of Al_{2}O_{3}/DI water nanofluids with the experimental data of pure water and Al_{2}O_{3}/DI water nanofluids.

This deterioration of natural convection heat transfer against the increase of volume fraction of Al_{2}O_{3}/DI water nanofluids is directly opposite to the enhanced effective thermal conductivity of Al_{2}O_{3}/DI water nanofluids with the increase of volume fraction, which is shown in Figure 6(a). This can be partially explained by the enhanced viscosity of the Al_{2}O_{3}/DI water nanofluids as shown in Figure 6(b), which matched the prediction of Einstein’s equation of [39] as demonstrated in Figure 7. However, many experimental and theoretical studies on the forced convection heat transfer of nanofluids demonstrated that the forced convection heat transfer would be enhanced by the nanofluids compared to that of pure base fluid under the same enhanced viscosity conditions [21, 40–43]. Henceforth, the increase of viscosity could not explain the deterioration of natural convection heat transfer of nanofluids alone. It was proposed that the kinetics of particles in flowing were the reason for the change of heat transport in laminar flow of polystyrene suspensions by [44, 45] and the double-layering of particle concentration for the natural convection of 57 micron diameter glass particle suspensions by [34]. Therefore, visualization investigations on particle kinetics, more specifically, the bulk migrating movement of Al_{2}O_{3 } nanoparticles in the nanofluids and the rotational and translational Brownian movements of individual Al_{2}O_{3 } nanoparticles, are very necessary. Currently, the experimental observation methods of the nanometer scale particle movements are very limited. In order to conduct the nanoparticle kinetics observation investigation, a 850 nm polystyrene particle/DI water suspension has been employed for the visualization study under the optical microscope.

##### 2.3. Visual Study of Submicron Particle Suspension Transient Natural Convection

To complement the experimental measurements of natural convection heat transfer of Al_{2}O_{3}/DI water nanofluids and to study the influences of local and bulk nanoparticles movements in the natural convection heat transfer of Al_{2}O_{3}/DI water nanofluids, a series of visualization investigations of the natural convection heat transfer of 850 nm polystyrene/DI water suspensions were conducted to analyze and predict the relationship between the movement of the particles and flow pattern and the resulting heat transfer coefficient deterioration found in the foregoing experiments on Al_{2}O_{3}/DI water nanofluids.

A rectangular enclosure was fabricated to provide a bottom heating geometry as illustrated in Figure 8, and a diluted 850 nm diameter polystyrene/DI water suspension was charged into the rectangular enclosure. A platinum ribbon was placed on the bottom of the rectangular enclosure to provide the heating surface for the visualization experiments. The original 2.5% volume fraction suspension was purchased from Seradyn, Inc., and the platinum ribbon (99.9% pure) was obtained from Scientific Instrument Services, Inc.

The platinum ribbon heater was first calibrated under the range of temperatures in the natural convection heat transfer measurements of nanofluids, and the relationship between temperature and platinum ribbon electric resistance was obtained. The repeatability and stability of the relationship were verified by a number of repeats of the calibration tests. The relationship between the temperature and the platinum electric resistance at the corresponding temperature is

The coefficient was obtained in the calibration setup in which the platinum ribbon was sandwiched between two thick layers of insulation material and was attached with three evenly placed thermocouples along its length. The entire calibration system was covered with a flexible insulation material in an environmental chamber. By carefully adjusting the temperature of the environmental chamber, the temperature differences between the three thermal couples were observed to be C at a steady-state, and the electrical resistance and temperature were simultaneously recorded by a digital data logger. A linear curve fit was obtained from the data recorded, and the coefficient was identified as shown in Figure 9. The electric resistance and temperature relationship for the 2.5 mm width platinum ribbon is shown as follows:

This relationship can be expressed in the form of (1) as

In this expression, the coefficient, , is approximately equal to 0.00752 for the 2.5 mm width platinum ribbon.

This bottom heating rectangular enclosure unit was first fabricated on a glass slide using a Microelectromechanical System (MEMS) technique to create a 2.5 mm wide, 0.5 mm deep rectangular channel. And a 0.05 mm thick, 2.5 mm wide platinum ribbon was placed on the bottom of the channel. Then a 0.1 mm thick glass slide was used to cover the channel and to finish the enclosure. Inside the rectangular enclosure test unit, it was charged with the 0.1% volume fraction 850 nm diameter polystyrene/water suspension diluted from the original 2.5% volume fraction suspension.

The sample charged test unit for the bottom heating natural convection visualization is shown in Figure 10. The electric power, electric resistance measurement device and thermocouples were all connected to the test unit under the optical microscope as represented in Figure 11. The temperature of the upper surface of the test cell was measured directly with thermocouples and the bottom heating surface temperature was calculated through the relationship between the temperature and electrical resistance as described in (7). Both surface temperatures were used later to calculate the Ra number of the 0.1% volume fraction 850 nm diameter polystyrene/water suspensions.

The simultaneous temperature and electric resistance data collection was started when a heating power of 2.7 W was applied to the platinum ribbon. During the entire bottom heating natural convection heat transfer visualization process, the particle movements were filmed using an optical microscope mounted with a high speed visualization system. The optical microscope was equipped with a 50X objective lens. The mounted charge-coupled device (CCD) imaging system had a maximum magnification of 500 frames per second (fps) rate and a maximum recording rate of 2000 fps with a reduced magnification. The movements of the 850 nm diameter polystyrene particles were synchronized with the temperature data recorded through the HP 34970A data logger to explore the effects of particle movements on the natural convection heat transfer in the bottom heating rectangular enclosure.

##### 2.4. Results of Visualization Study on 850 nm Diameter Polystyrene/Water Suspensions

The visualization results of both bulk movement and individual particle movement of the 850 nm polystyrene particles were quite interesting. As shown in Figure 12 the individual particle movements, the rotational and translational Brownian motions of the particles, were found to be quite strong all the time. Before power was applied to the platinum ribbon heater, the individual particle Brownian motion was the only phenomena that were observed, as shown in Figure 12(a). Particles were moving in random patterns around each original position in the suspension. Immediately following the initiation of power to the platinum ribbon heater, in addition to Brownian motions, the particles began to slowly migrate from the bottom to the top. More interestingly, the random Brownian motion and the migrating movement appear independent to each other. More often than not, the displacement Brownian motion of particles will move in the direction against the bulk migrating movement. This stage of particle movements was captured in Figure 12(b). In a relatively long time period after the heating was turned on, the migrating movements of particles maintained roughly at the same order of magnitude as the displacement Brownian motion had, and the Brownian motions of particles were still very distinguishable, as shown in Figure 12(c). At the moment approximately 210 seconds after the platinum ribbon heating power was turned on, Strong bulk migrating movement was observed, which was several orders greater than that of the individual particles Brownian motions. The Brownian motions were not to be distinguished any more. From then on, the 850 nm diameter polystyrene/water suspension experienced a natural convection inside the rectangular enclosure. As demonstrated in Figure 13, a vertical layer of concentrated particles was visualized in the middle region of the enclosure and was represented by the red arrows in Figure 13(a). This phenomenon is similar to what was previously reported by [20] except that it was believed that, in the current experiment, the concentration layer was caused by natural convection cycles rather than the double diffusive convection resulting from temperature and concentration gradients in [20]. Figure 13(b) presented one recorded image of particle bulk movement at the top of the middle region in the enclosure. The temperatures of both the bottom heating surface and the upper cooling surface were recorded simultaneously with the images as shown in Figure 14. In the time period right after the heating power was turned on, the temperature of the bottom heating surface increased relatively sharply first. Then the bottom heating surface temperature increase became more gradually. At the moment of around 207 seconds after the heating power on the platinum ribbon was turned on, the bottom heating surface temperature dropped around 5°C abruptly and then climbed back to the previous value in a time period of several tens seconds. This sudden drop of bottom heating surface temperature corresponded to the visualization of a sudden augmentation of bulk migrating movement at the same time. After this period of temperature recovering, the bottom heating surface temperature kept at relatively stable value with a minor increase comparing to the temperature changing manner prior to the moment of the sudden drop. With the temperature information of both surfaces, it was found out that the Ra number was greater than the critical Ra number of 1708 for the onset of natural convection in an enclosure [46]. It implied that the onset of internal natural convection of 850 nm diameter polystyrene/water suspension was delayed, with the evidence of a larger critical Ra number.

#### 3. Discussions and Conclusions

From the experimental measurements of Al_{2}O_{3}/DI water nanoparticle suspension natural convection heat transfer, the natural convective heat transfer of 47 nm Al_{2}O_{3}/DI water nanofluids demonstrated a deterioration with the increase of volume fraction of Al_{2}O_{3} nanoparticle, as reported in previous experiments [27, 33]. The experimental results were directly against the simulation results that the nanofluids could enhance the heat transfer coefficient in natural convection heat transfer by [30, 31].

For visualization experiments on the 850 nm diameter polystyrene/water suspension, the results indicated that the Brownian motions and thermophoresis movements were the key reasons for the heat transfer before the onset of natural convection heat transfer. Those particle movements delayed the onset of the natural convection heat transfer and might still play a role in the heat transfer deterioration after the onset. The Brownian motions and bulk migrating (thermophoresis) movement were not proposed in the previous experimental nanofluids natural convection heat transfer study [32, 33]. More recently, the combined influence of the Brownian motions and thermophoresis movement on the natural convection heat transfer found in current research echoes a recent theoretical study on nanofluids natural convection heat transfer by [47], which theoretically confirmed the influence from Brownian motions and thermophoresis movement of nanoparticles to the nanofluid natural convection heat transfer. However, its conclusion of the nanoparticle movement effect supported the previous simulation results that nanofluids would have a higher natural convective heat transfer coefficient of nanofluids than that of pure water [30, 31].

Based on the observations of the 850 nm diameter polystyrene/water suspension natural convection heat transfer and the previous reports, it is reasonable to anticipate that nanometer size particles will have an even stronger Brownian motions and thermophoresis movement, which will greatly influence the nanofluids natural convection heat transfer process by delaying the onset of natural convective flow and heat transfer. This delayed onset of natural convection heat transfer may be directly caused by the enhanced effective thermal conductivity and enhanced effective viscosity of the nanofluids as the results of the mixing and stirring effects of the nanoparticle Brownian motions, as shown in Figure 6. This mixing and stirring effect was extensively demonstrated by [13]. It is believed that the enhanced effective thermal conductivity will reduce the temperature gradient and the enhanced effective viscosity will damp out the hydrodynamic perturbation, and in turn, will delay the onset of natural convection heat transfer. After the natural convection heat transfer is developed, both enhanced effective thermal conductivity and effective viscosity will still play a role in slowing down the bulk movement of the nanofluids in natural convection by reducing the temperature gradient and advection momentum. If taking into account the size effect, it should be reasonable to expect that the nanoscale particle should have stronger Brownian motion and thermophoresis activities, and the natural convection onset should be even further slowed down.

In summary, a combined experimental investigation of natural convection heat transfer characteristics of 47 nm Al_{2}O_{3} nanofluids at various volumetric fractions and a 850 nm diameter polystyrene/water suspension has been conducted. The visual observation study on the 850 nm diameter polystyrene/water suspension served as a virtual reference to interpret the deterioration of nanofluids natural convection heat transfer. The results of current investigation were compared with the previously reported results to offer new experimental evidence for the unclarified phenomena. The controversy resulted from simulation study and experimental study is still not clear, but it might be caused by the simulation assumption of uniform nanoparticle size distribution, constant properties, lack of gravity effect on nanoparticles, and the interaction among nanoparticles. To nail down the exact reasons, an extensive comparison study on the results with different assumption in simulation is needed.

The reasons drawn in current study for the natural convection heat transfer deterioration are summarized as follows:

(1)the higher viscosity of the nanofluids,(2)the temperature gradient smoothing and perturbation damping effects in the body of nanofluids by the mixing and stirring effect of the Brownian motions, which might cause the delayed onset of natural convection,(3)the influence on the flow field and temperature field from the Brownian motions and thermophoresis movements after the natural convection was developed.Although care has been taken to eliminate other influences from the nanofluid and polystyrene/water suspension samples, it is still possible that other factors might have played a role, such as the slow aggregation of individual particles, the sedimentation of the particles and/or aggregations, and the influence of the nonuniform size of the particles.

#### Nomenclature

: | Cross-sectional area of the copper bar |

: | Cross-sectional area of the test cell |

: | o-ring contact area with the copper bar surface |

: | Constant |

: | Distance of gap |

: | Heat transfer coefficient |

: | Effective thermal conductivity of the fluid suspension |

: | Thermal conductivity of the rubber o-ring |

: | Thermal conductivity of the copper bar |

: | Thermal conductivity of the base fluid |

: | Constant |

: | Heat flux |

: | Resistance of platinum ribbon at temperature T |

: | Resistance of platinum ribbon at the reference temperature T_{o} |

: | Temperature difference between surface of the upper and lower copper bars |

: | Temperature difference between two adjacent thermocouples along the axis of the copper bars |

x: | The coordinate on the axis of copper bars |

: | The distance between two adjacent thermocouples along the axis of the copper bars |

: | Thickness of the test cell |

: | Absolute temperature |

: | Thermal diffusivity of fluid/ratio of the nanoparticle and base fluid thermal conductivity |

: | Electric resistance-temperature coefficient of the platinum ribbon |

: | Volume expansion coefficient of the fluid |

: | Volume fraction of the nanoparticle suspension |

: | The viscosity of the base fluid |

: | Viscosity |

: | Kinematic viscosity of the fluid. |

#### Acknowledgments

The authors would like to acknowledge the support of the Office of Naval Research through Grant ONR N000140010454, the National Science Foundation through grant CTS-0312848, and The University of Toledo through the startup grant.

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