Heat Transfer in Nanofluids A Review

Heat Transfer Engineering, 27(10):3 19, 2006 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630600904593 Heat Transfer in Nanofluids A Review SARIT KUMAR DAS Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India STEPHEN U. S. CHOI Energy Technology Division, Argonne National Laboratory, Argonne, Illinois, USA HRISHIKESH E. PATEL Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India Suspended nanoparticles in conventional fluids, called nanofluids, have been the subject of intensive study worldwide since pioneering researchers recently discovered the anomalous thermal behavior of these fluids. The enhanced thermal conductivity of these fluids with small-particle concentration was surprising and could not be explained by existing theories. Micrometer-sized particle-fluid suspensions exhibit no such dramatic enhancement. This difference has led to studies of other modes of heat transfer and efforts to develop a comprehensive theory. This article presents an exhaustive review of these studies and suggests a direction for future developments. The review and suggestions could be useful because the literature in this area is spread over a wide range of disciplines, including heat transfer, material science, physics, chemical engineering and synthetic chemistry. INTRODUCTION The last few decades of the twentieth century have seen unprecedented growth in electronics, communication, and computing technologies, and it is likely to continue unabated into the present century. The exponential growth of these technologies and their devices through miniaturization and an enhanced rate of operation and storage of data has brought about serious problems in the thermal management of these devices. Another important area that has experienced a similar problem in thermal management is the area of optical devices. Lasers, high-power x- rays, and optical fibers are integral parts of today s computation, scientific measurement, material processing, medicine, material synthesis, and communication devices. The increasing power of these devices with decreasing size also calls for innovative cooling technology. Microscale heat transfer is an area of research This work is supported by the Defence Research and Development Organisation (DRDO), the Department of Science and Technology (DST) of India, and the U.S. Department of Energy, Office of FreedomCar and Vehicle Technologies and Office of Basic Energy Sciences, under contract W-31-109-Eng-38. Address correspondence to Prof. Sarit Kumar Das, Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, IIT Madras, Chennai 600 036, India. E-mail: sarit das@hotmail.com that has been adequately reviewed by texts such as those by Duncan and Peterson [1] and Majumdar et al. [2]. However, all of these texts indicate that the conventional fin-and-microchannel technology [3] appears to be inadequate for the new generation of electronic and optical devices. Choi et al. [4] have shown that power densities of 2000 W/cm 2 can be managed by microchannel heat exchangers that use subcooled liquid nitrogen. An increasing number of studies on microchannel boiling, such as those by Kandlikar and Grande [5], Bergles et al. [6], and Thome et al. [7], also indicates the need for an alternative way to cool micro-size devices. The advent of nanotechnology and Micro-Electro-Mechanical Systems (MEMS) has only intensified this need, asking for a revolution in cooling technology to keep pace with the new revolution in device technology. However, it is important to note that miniaturized devices are not alone in looking for innovative cooling technology. Large devices (such as transportation trucks) and new energy technology (such as fuel cells) also require more efficient cooling systems with greater cooling capacities and decreased sizes. Thus, big or small, new and enhanced cooling technology is the need of the hour. This need must be met in two ways: introducing new designs for cooling devices, such as microchannels and miniature cryodevices, and enhancing the heat transfer 3

4 S. K.DASET AL. capability of the fluid itself. The present review deals with the second option. The suspension of nanoparticles in conventional fluids are usually called nanofluids. Before going into the details of nanofluids and their potential in cooling technology, it is worth first examining the rationale behind the idea of nanofluids. THE RATIONALE BEHIND NANOFLUIDS It is obvious from a survey of thermal properties that all liquid coolants used today as heat transfer fluids exhibit extremely poor thermal conductivity (with the exception of liquid metal, which cannot be used at most of the pertinent useful temperature ranges). For example, water is roughly three orders of magnitude poorer in heat conduction than copper as is the case with engine coolants, lubricants, and organic coolants. It goes without saying that all of the efforts to increase heat transfer by creating turbulence, increasing area, etc., will be limited by the inherent restriction of the thermal conductivity of the fluid. Thus, it is logical that efforts will be made to increase the thermal conduction behavior of cooling fluids. Using the suspension of solids is an option that came to mind more than a century ago. Maxwell [8] was a pioneer in this area who presented a theoretical basis for calculating the effective thermal conductivity of suspension. His efforts were followed by numerous theoretical and experimental studies, such as those by Hamilton-Crosser [9] and Wasp [10]. These models work very well in predicting the thermal conductivity of slurries. However, all of these studies were limited to the suspension of micro- to macro-sized particles, and such suspensions bear the following major disadvantages. 1. The particles settle rapidly, forming a layer on the surface and reducing the heat transfer capacity of the fluid. 2. If the circulation rate of the fluid is increased, sedimentation is reduced, but the erosion of the heat transfer devices, pipelines, etc., increases rapidly. 3. The large size of the particles tends to clog the flow channels, particularly if the cooling channels are narrow. 4. The pressure drop in the fluid increases considerably. 5. Finally, conductivity enhancement based on particle concentration is achieved (i.e., the greater the particle volume fraction is, the greater the enhancement and greater the problems, as indicated in 1 4 above). Thus, the route of suspending particles in liquid was a wellknown but rejected option for heat transfer applications. However, the emergence of nanofluids helped stimulate the reexamination of this option. Modern materials technology provided the opportunity to produce nanometer-sized particles which are quite different from the parent material in mechanical, thermal, electrical, and optical properties. Thus, nanofluid technology coupled with new heat-transfer-related studies on microchannel flow [11] has provided a new option of revisiting suspensions of nanoparticles. The first proposition in this area was from Argonne National Laboratory (ANL) through the seminal work of Choi [12], who designated the nanoparticle suspension a nanofluid. From a purist s point of view, this designation may not be acceptable every fluid is nano because of its molecular chains but the term has been accepted and become popular in the scientific community. It must be kept in mind that biologists have been using the term nanofluid for different types of particles, such as DNA, RNA, proteins, or fluids contained in nanopores [13 15]. The attractive features which made nanoparticles probable candidates for suspension in fluids are a large surface area, less particle momentum, and high mobility. With respect to conductivity enhancement, starting from copper, one can go up to multi-walled carbon nanotubes (MWCNTs), which at room temperature exhibit 20,000 times greater conductivity than engine oil [16]. When the particles are properly dispersed, these features of nanofluids are expected to give the following benefits: 1. Higher heat conduction. The large surface area of nanoparticles allows for more heat transfer. Particles finer than 20 nm carry 20% of their atoms on their surface, making them instantaneously available for thermal interaction. Another advantage is the mobility of the particles, attributable to the tiny size, which may bring about micro-convection of fluid and hence increased heat transfer. The micro-convection and increased heat transfer may also increase dispersion of heat in the fluid at a faster rate. It is already found that the thermal conductivity of nanofluids increases significantly with a rise in temperature [17], which may be attributed to the above reasons. 2. Stability. Because the particles are small, they weigh less, and the chances of sedimentation are also less. This reduced sedimentation can overcome one of the major drawbacks of suspensions, the settling of particles, and make the nanofluids more stable. 3. Microchannel cooling without clogging. Nanofluids will not only be a better medium for heat transfer in general, but they will also be ideal for microchannel applications where high heat loads are encountered. The combination of microchannels and nanofluids will provide both highly conducting fluids and a large heat transfer area. This cannot be attained with meso- or micro-particles because they clog microchannels. Nanoparticles, which are only a few hundreds or thousands of atoms, are orders of magnitude smaller than the microchannels. 4. Reduced chances of erosion. Nanoparticles are very small, and the momentum they can impart to a solid wall is much smaller. This reduced momentum reduces the chances of erosion of components, such as heat exchangers, pipelines and pumps. 5. Reduction in pumping power.to increase the heat transfer of conventional fluid by a factor of two, pumping power must usually be increased by a factor of ten. It can be shown that

if one can multiply the conductivity by a factor of three, the heat transfer in the same apparatus doubles [12]. The required increase in the pumping power will be very moderate unless there is a sharp increase in fluid viscosity. Thus, a very large savings in pumping power can be achieved if a large thermal conductivity increase can be brought about with a small volume fraction of particles. Often, nature proves to be more exciting than imagination. Henry Becquerel thought uranium ore absorbs sunlight and then radiates it back until discovering radioactivity, which radiates without any absorption of sunlight. Similarly, the first test with nanofluids gave more encouraging features [18] than they were thought to possess. The four unique features observed are listed below. 1. Abnormal enhancement of thermal conductivity. The most important feature observed in nanofluids was an abnormal rise in thermal conductivity, far beyond expectations and much higher than any theory could predict. 2. Stability. Nanofluids have been reported to be stable over months using a stabilizing agent [18, 19]. 3. Small concentration and Newtonian behavior. Large enhancement of conductivity was achieved with a very small concentration of particles that completely maintained the Newtonian behavior of the fluid. The rise in viscosity was nominal; hence, pressure drop was increased only marginally. 4. Particles size dependence. Unlike the situation with microslurries, the enhancement of conductivity was found to depend not only on particle concentration but also on particle size. Ingeneral, with decreasing particle size, an increase in enhancement was observed. The above potentials provided the thrust necessary to begin research in nanofluids, with the expectation that these fluids will play an important role in developing the next generation of cooling technology. The result can be a highly conducting and stable nanofluid with exciting newer applications in the future. Before exploring how many of these dreams have been attained by the early results, it is necessary to say that this field of research is interdisciplinary, with inputs from chemistry, mechanical and chemical engineering, physics, and material science; hence, it is worth going into the details of not only applications but also synthesis and characterization. SYNTHESIS AND PREPARATION OF NANOPARTICLES Various methods have been tried to produce different kinds of nanoparticles and nanosuspensions. Gleiter [20] provides a good overview of the synthesis methods. The first materials tried for nanofluids were oxide particles, primarily because they were easy to produce and chemically stable in solution. Various investigators have produced Al 2 O 3 and CuO nanopowder by an S. K. DAS ET AL. 5 inert-gas condensation (IGC) process [18, 21] that produced 2 200 nm-sized particles. The major problem with this method is its tendency to form agglomerates and its unsuitability to produce pure metallic nanopowders. The problem of agglomeration can be reduced to a good extent by using a direct evaporation condensation (DEC) method. The DEC method is a modification of the IGC process that has been adopted at ANL [22 24]. Even though this method has limitations of low vapor-pressure fluids and oxidation of pure metals, it provides excellent control over particle size and produces particles for stable nanofluids without surfactant or electrostatic stabilizers. Another method is the LASER vapor deposition technique used to produce SiC nanoparticles from SiH 4 and C 2 H 4 [25]. Recently, carbon nanotubes were used to produce nanofluids. The multi-walled carbon nanotubes (MWCNTs) used for this purpose can be produced through the chemical vapor deposition technique by using xylene as a carbon source and ferrocene as the catalyst [26]. Pure chemical synthesis is another option for producing nanoparticles known as metal clusters. Two of the methods by which nanofluids are made directly are described by Patel et al. [27]. Recently, Zhu et al. [28] prepared nanofluids of metallic Cu nanoparticles dispersed in ethylene glycol by a one-step chemical method. Thus, a variety of physical, chemical, and LASER-based methods are available for the production of the nanoparticles required for nanofluids. However, the task to characterize and disperse them in fluid remains. To achieve a stable nanofluid that exhibits true nano behavior, the particles should be dispersed with no or very little agglomeration. This can be done through various methods, including electrical, physical, or chemical. In the literature, the commonly used dispersion techniques use an ultrasonic or stator rotor method [17]. In some cases [19, 22], stabilizing agents are also used during dispersion. However, the best way to produce them may be by a single-step method where, instead of nanoparticles, nanofluids are produced directly, thus reducing the chance of agglomeration. THERMAL CONDUCTIVITY ENHANCEMENT IN NANOFLUIDS The thermal conductivity of nanofluids is much improved when compared with usual suspensions. The enhancement of the thermal conductivity of nanofluids over that of the base fluid is often a few times better than what would have been given by micrometer-sized suspensions. So far, the base fluids used include water, ethylene glycol, transformer oil, and toluene. The nanoparticles that are used can be broadly divided into three groups: ceramic particles, pure metallic particles, and carbon nanotubes (CNTs). Different combinations of the above particles and fluids give different nanofluids. This study, however, will classify them mainly by the type of particles.

6 S. K.DASET AL. Ceramic Nanofluids Ceramic nanofluids were the first type of nanofluid investigated by the ANL group. The first major publication in this area [18] presented conductivity measurements on fluids that contained Al 2 O 3 and CuO nanoparticles in water and ethylene glycol. Conductivity was measured by the traditional transient hot-wire (THW) method. The results clearly indicated that the thermal conductivity enhancement of the Al 2 O 3 and CuO nanofluids were high. They used volume fractions of only 1 5%. The enhancement was higher when ethylene glycol was the base fluid. An enhancement of 20% was observed at 4% volume fraction of CuO. The enhancement when water was the base fluid was lower but still substantial, with 12% enhancement at 3.5% CuO, and 10% enhancement with 4% Al 2 O 3. (Figure 1 shows the original publication s measurements [18].) These results were high when compared with the model for suspensions proposed by Maxwell [8], which was improved in 1962 [9] to include the effect of particle shape. These models predict the effective thermal conductivity as essentially a weighted average of solid and liquid conductivity derived from a point source method. The original Maxwell model reads as follows: k eff 3(k p /k f 1) φ = 1 + (1) k f (k p /k f + 2) (k p /k f 1)φ whereas the Hamilton-Crosser [9] model reads as k eff = k p + (n 1)k f (n 1)φ(k f k p ) (2) k f k p + (n 1)k f + φ(k f k p ) In both models, k eff = effective thermal conductivity of suspension, k f = thermal conductivity of liquid, k p = thermal conductivity of solid particles, n = shape factor (for sphere = 3, for cylinder = 6), and φ = volume fraction of nanoparticles. Figures 2a and 2b show the measurements of Lee et al. [18] and those predicted by the Hamilton-Crosser [9] model for Al 2 O 3 water and CuO water nanofluids, respectively. Wang et al. [21] also measured the thermal conductivity of CuO water and Al 2 O 3 water nanofluids, but their particle size was smaller (23 nm for CuO and 28 nm for Al 2 O 3 ). They also Figure 1 Enhanced thermal conductivity of oxide nanofluids systems as measured by Lee et al. [18]. k/k o denotes the ratio of thermal conductivity of nanofluid to that of the base fluid. Figure 2 Increase of the thermal conductivity ratio obtained by Lee et al. and predicted by the Hamilton-Crosser model for (a) Al 2 O 3 /water nanofluids and (b) CuO/water nanofluids [18]. k/k o denotes the ratio of thermal conductivity of nanofluid to that of the base fluid.

measured the nanofluids with ethylene glycol and engine oil (Pennzoil 10W-30) as the base fluids. The measurements showed a clear effect of the particle size and method of dispersion. Xie et al. [29] measured the thermal conductivity of aqueous Al 2 O 3 nanofluids with even smaller particles (1.2 302 nm). They also observed the effect of particle size in addition to the effect of the base solution. Thus, it has been generally found that oxide ceramic particles, which themselves do not exhibit very high thermal conductivity, can enhance the thermal conductivity of fluids in nanosuspensions. The main reason for the many studies on oxide particle-based nanofluids is the availability of oxide nanoparticles. Murshed et al. [30], who measured the thermal conductivity of aqueous solutions of spherical and cylindrically shaped TiO 2 nanoparticles, found that 15 nm-sized spherical particles show slightly less enhancement than 10 40 nm rods, which showed an enhancement of 33% for a volume fraction of 5%. However, the enhancement was far more than that predicted by the Hamilton-Crosser model. Another feature brought out in this work was the nonlinear dependence of enhancement in thermal conductivity on particle concentration at lower volume fractions. Metallic Nanofluids Even though the potential of nanofluids was evident from ceramic nanofluids, the emergence of metallic particle-based nanofluids was a big step forward. Xuan and Li [19] were the first to try copper particle-based nanofluids of transformer oil. Though they used much larger ( 100 nm) particles, the enhancement reported was 55% with 5% volume fraction. However, the real breakthrough came when the ANL group reported a 40% enhancement of conductivity with only 0.3% concentration of 10 nm-sized copper particles suspended in ethylene glycol [22]. This report clearly showed the particle size effect and the potential of nanofluids with smaller particles. The nanofluids were stabilized with thioglycolic acid. Figure 3 shows the measured values of thermal conductivity for Cu ethylene glycol nanofluids. In another study, Patel et al. [27] used gold and silver for the first time to prepare nanofluids. They also used a transient hot wire method for measuring thermal conductivity. The most important observation in their study was a perceptible enhancement in thermal conductivity for vanishingly small concentrations. It was reported that at room temperature, the conductivity of toluene-gold nanofluid was enhanced by 3 7% for a volume fraction of only 0.005 0.011%, whereas the enhancement for water gold nanofluid was 3.2 5% for a vanishingly small concentration of 0.0013 0.0026% volume fraction. The main reason for such an enhancement was the small size ( 10 20 nm) of the particles. The enhancement was greater with water-based nanofluids because bare particles were used, and was lower for toluene-based nanofluids where the nanoparticles were protected by a layer of thiolate coating, which was used to prevent agglomeration. Another important observation of their study was the relatively lower conductivity of water S. K. DAS ET AL. 7 Figure 3 Thermal conductivity enhancement for various nanofluids [22]. Reprinted with permission from the American Institute of Physics. k/k o denotes the ratio of thermal conductivity of nanofluid to that of the base fluid. silver nanofluids. It clearly showed that even though silver is higher in conductivity, it provided less enhancement because its size was relatively larger ( 60 80 nm). This finding indicates that particle size can override the particle conductivity or concentration effects. Xie et al. [31] studied the dependency of thermal conductivity of nanoparticle fluid mixtures on the base fluid. These investigators studied nano-sized α-al 2 O 3 dispersed in deionized water, glycerol, ethylene glycol, pump oil, ethylene glycol-water mixture, and glycerol-water mixture. It was found that thermal conductivity ratios decrease with the increased thermal conductivity of the base fluid. Hong et al. [32] achieved an enormous increase in the thermal conductivity of nanofluids of 10 nm-sized Fe nanoparticles suspended in ethylene glycol. They obtained an enhancement of 18% with just 0.55% volume fraction. They also showed that the sonication of the nanofluid has an important effect on the thermal conductivity of nanofluid, indirectly proving the effect of particle size on the thermal conductivity of nanofluid. Carbon and Polymer Nanotube Nanofluids The greatest enhancement of thermal conductivity was observed in a subsequent study performed at ANL [33]. Fig. 4, a plot of the enhancement of thermal conductivity of multiwalled carbon nanotubes (MWCNTs) engine oil (among other nanofluids) vs. nanotube volume fraction, shows a phenomenal 150% increase in thermal conductivity with just 1% volume fraction of the nanotubes. This sudden jump in enhancement is interesting. With polymer nanotubes, a similar enhancement was reported by Biercuk et al. [34]. The reason for the abnormal rise

8 S. K.DASET AL. Figure 4 Enhancement of the thermal conductivity of MWNT vs. volume fraction [75]. k e /k f denotes the ratio of thermal conductivity of nanofluid to that of the base fluid. of enhancement and the nonlinear behavior is yet to be explained, but one can look at two facts. First, the thermal conductivity of carbon nanotubes is very high ( 3000 W/mK); second, the nanotubes have a very high aspect ratio ( 2000). The article will indicate the implications of the aspect ratio of the nanotubes when the possible theories of thermal conductivity of nanofluids are considered. Xie et al. [35] have measured thermal conductivity of MWC- NTs with a 15 nm average diameter and 30 µm length, suspended in water, ethylene glycol, and decene. The suspensions in water and ethylene glycol were without any surfactant but coated with oxygen-containing functional groups. Those suspended in decene had the help of oleylamine as a surfactant. It was found that there was more enhancement for same volume fraction in the fluid that has a lower thermal conductivity. Maximum enhancement in thermal conductivity was found in decene, which was 20% for 1% volume of CNTs. Also it was found to be increasing linearly with volume fraction. However, the enhancement is far smaller than that achieved by Choi et al. [33]. Assael et al. [36] measured thermal conductivity of multiwalled as well as double-walled CNTs. Thermal conductivity of MWCNTs of around a 130 nm average diameter and 40 µm average length was found to be 34% for 0.6% volume, whereas that of double walled CNTs was found to be 8% for 1% volume suspension in water. Hwang et al. [37] have also obtained similar results for MWCNT suspensions in water as well as ethylene glycol. Liu et al. [38] measured thermal conductivity of MWC- NTs 20 50 nm in diameter and observed an increase of 12.4% in the thermal conductivity of CNT suspension in ethylene glycol for 1% volume fraction and 30% enhancement in the CNT suspension in synthetic oil for 2% volume fraction. Temperature Effect One important contribution on nanofluids was the discovery [17] of a very strong temperature dependence of nanofluids with the same Al 2 O 3 and CuO particles as those used by Lee et al. [18]. Using the temperature oscillation technique, they measured the thermal conductivity of oxide nanofluids over the temperature range of 21 50 C. The results revealed an almost threefold increase in conductivity enhancement (i.e., 10% became 30%) for copper oxide and alumina nanofluids, as shown in Figures 5 and 6, respectively. It is important to note that, contrary to what was observed at room temperature [18], the results for both Al 2 O 3 and CuO do not agree with predictions of the Hamilton-Crosser [13] model because the model is not sensitive to temperature over this temperature range. The agreement of the Al 2 O 3 water nanofluid results with the Hamilton-Crosser model at room temperature was purely accidental because of its larger particle size. These results have revolutionized the concept of nanofluids from the application point of view because they indicate a much larger thermal conductivity in the heated state. They also indicate that some kind of particle movement that dramatically changes with temperature must be taking place within the fluid. Figure 5 Enhancement in the thermal conductivity of copper oxide-water nanofluid with temperature [17]. λ/λ water denotes the ratio of thermal conductivity of nanofluid to that of the base fluid.

Figure 6 Enhancement in the thermal conductivity of aluminum oxide-water nanofluid with temperature [17]. λ/λ water denotes the ratio of thermal conductivity of nanofluid to that of the base fluid. Patel et al. [27] reconfirmed the findings of Lee et al. [18] and Chon et al. [39] and confirmed the temperature effect obtained by Das et al. [17]. They also showed the inverse dependence of particle size on the thermal conductivity enhancement with three sizes of alumina nanoparticles suspended in water. THEORIES ON NANOFLUIDS Since Choi [12] proposed his theory on nanofluids, a continuous effort has ensued to look for the causes of the so-called anomalous increase in thermal conductivity of nanofluids. Starting from simple Brownian motion to complicated fractals, many propositions have been tested. During the last three years, this effort of modeling the nanofluid behavior has intensified; however, it appears that the truth is still to be revealed. Traditional theories [e.g., 8 10, 40 42] explained the thermal conductivity enhancement of usual slurries and suspensions quite extensively. The basic model of Maxwell [8] was extended by the investigators who included the effect of shape [9], particle interactions [43 47], and particle distribution [48]. The Bruggeman model [40] has a similar nature plus the advantage of being S. K. DAS ET AL. 9 valid for a wide range of concentrations. In general, Maxwell s method works well for a low thermal conductivity ratio ( 10) between the solid and the fluid. The failure of the classical theories to predict nanofluid behavior gave rise to hypotheses about the mechanism of heat transfer in nanofluids. Wang et al. [21] attributed the enhancement to particle motion, surface action, and electro-kinetic effects. The hydrodynamic force in the form of micro-convection can also be a cause of the enhancement. A serious look at the various possible enhancement mechanisms was the focus of Keblinski et al. [49]. At first sight, even though the Brownian motion appears to be a probable mechanism, results of a time scale study led to its rejection. The studies of Wang et al. [21] also showed that Brownian motion is not a significant contributor. Keblinski et al. [49] showed that liquid layering around the particle could give a path for rapid conduction. The mechanism of ballistic heat transport gains significance because the phonon mean free path is of the order of nano-particle dimensions. Liquid layering theory was shown to be promising, but it uses an adjustable parameter of the thickness of the liquid layer. The transport at nanoscale is obviously to be modeled with the relevant theories. The nanoscale modeling using Boltzmann transport equation (BTE) appears to be appropriate; however, the solution of BTE with nano-particles in a host medium by Chen [50] indicates a lowering of effective conductivity for nonlocal, nonequilibrium conduction rather than enhancement. Hence, such microscopic treatments also fail to predict the observed enhancement in nanofluid conduction. Wang et al. [51] approached the theory from the standpoint of fractal geometry, which is actually an extension of the Maxwell- Garnett [52] model. Following up on the approach of Pitchumani et al. [53] to fibrous composites, they included a surface adsorption and particle conductivity approach, in contrast to the bulk conductivity used by other models. The results indicate that, for CuO water nanofluids, the fractal model shows good promise when adsorption is included in the analysis, but it underpredicts the enhancement in the absence of adsorption. A very novel approach in the modeling of nanofluids was taken by Xue [54]. The model utilizes field factor approach, with a depolarization factor and an effective dielectric constant. The model is essentially based on liquid layering theory. With two adjustable parameters (i.e., the thickness and conductivity value of the liquid layer), the theory matches the measured value. A similar model that does not consider the liquid layering was proposed by the same author [55] for the prediction of thermal conductivities of CNTs. The model is found to be working fairly well in predicting the thermal conductivities of CNT suspensions. In the same vein, a model [56] that considers only temperature distribution function and liquid layering was presented by the same author for the prediction of the thermal conductivities of nanoparticle suspensions. The model predicts the thermal conductivities of CuO particle suspensions in water as well as ethylene glycol; however, both of the above models carry the same drawbacks as the original [54]. Yu and Choi [47] used the liquid layer around particles to find effective

10 S. K. DAS ET AL. particle concentration, and calculated as indicated by Schwartz [57]. Xie et al. [58] have modeled the thermal conductivity of the liquid layer and incorporated it in effective thermal conductivity of nanofluid. But they too have validated it against only a few experimental results, which also considered a fixed nanolayer thickness of 2 nm, although the nanolayer thickness may be expected to be different for different combinations of liquid and solid. The major drawbacks of work that tries to explain effective thermal conductivity of nanofluids only through liquid layering are that the size of layer is assumed to be very high, an assumption that hasn t been experimentally validated, and that the thermal conductivity of the liquid layer is taken to be as high as the thermal conductivity of the solid. The only experimental proof of a liquid layer shows that it is only a few (three) atomic diameters thick [59]. Also in a numerical work, Xue et al. [60] have confirmed this finding from a fundamental point of view. Using molecular dynamics simulation, they have shown that the effect of high surface energies on nanoparticles and the interactions between the solid and liquid molecules cannot affect the properties of the surrounding liquid for more than five atomic distances. More recently, another approach has gained momentum in explaining the thermal conductivity enhancement the incorporation of particle motion. Even though it has been stated earlier that Brownian motion alone cannot account for this enhancement, a new look at Brownian motion [61, 62] has been presented. Using a drift velocity model, Yu et al. [63] have shown that the collision of particles and the drift velocity can account for a very small part of the enhancement. With a specific example of copper particles in ethylene glycol, they showed that at least the order of the enhancement could be guessed if nano-convection in the space between the particles is assumed. This is quite logical, because in gases, only a void is present between the particles (molecules), whereas in nanofluids, a fluid will be participating in a nano-convection that may even be set by electrical dipole. The authors even pointed out the possibility of a Soret effect [63]. Although this work does not present a complete, accurate model, it does shed light on a very possible mechanism and, more importantly, tries to model the phenomenon on fundamental physics without adjustable parameters. Xuan et al. [64] have presented another model that primarily combines the concept of fractals and Brownian motion. The whole process has been assumed to have two additive parts: the usual static theory of suspension and the Brownian motiondominated dynamic. Naturally, the Brownian motion part is temperature-dependent and was proposed to be proportional to square root of temperature. This model proved to be very weak when compared with experimental results [17]. A more realistic idea of enhancement as well as temperature effect was modeled recently by two groups that essentially used the Brownian motion concept. The model of Jang and Choi [65] is based on conduction, Kapitza resistance at particle surfaces, and convection. In deriving their thermal conductivity model, they considered four modes of energy transport: collisions between base fluid molecules (i.e., thermal conductance of fluid); thermal diffusion in nanoparticles; a collision between nanoparticles due to Brownian motion, which by orderof-magnitude analysis, was neglected; and thermal interaction of dynamic nanoparticles with the base fluid. Brownian motion produced convection-like effects at nanoscale. As particle size is decreased, random motion becomes larger, and convection-like effects become dominant. This model was able to predict a particle size- and temperature-dependent conductivity accurately. Kumar et al. [66] presented a model that accounts for the dependence of thermal conductivity on particle size, concentration, and temperature. The proposed model has two aspects. The stationary particle model accounts for the geometrical effect of an increase in surface area per unit volume with decreasing particle size. It assumes two parallel paths of heat flow through the suspension, one through the liquid particles, and the other through the nanoparticles. Here, the direct dependence of thermal conductivity enhancement on volume fraction and the inverse dependence of thermal conductivity enhancement on particle diameter have been suggested. In the moving particle model, the effective thermal conductivity of particles is modeled by drawing a parallel to the kinetic theory of gases. Predictions from the combined model agree with experimentally observed values of conductivity enhancement of nanofluids with a vanishingly small particle concentration. They also showed, by order-of-magnitude analysis, that the value of the constant c, which is used in the modeling of effective thermal conductivity of particles, is consistent with that predicted by kinetic theory. However, in the Jang and Choi [65] and Kumar et al. [66] models, the constant used is empirical and varies over several orders of magnitude for different combinations of the particle-fluid mixture. A similar approach was adopted by Ren et al. [67], who considered kinetic theory-based micro-convection and liquid layering in addition to liquid and particle conduction. The model is working well for ceramic particle suspensions. They also considered a fixed nanolayer thickness of 2 nm and determined the thermal conductivity of the nanolayer as the volume-averaged thermal conductivity of the base liquid and particles. Prasher et al. [68] have presented another model in the same vein. They modeled the thermal conductivity of solid particles from the kinetic theory of gases and incorporated the contribution of Brownian motion-based convection to total heat transport in the effective medium approach-based thermal conductivity equation. The Brownian motion velocity considered is based on the equi-partition theorem, whereas the velocities of particles considered for modeling the thermal conductivity of nanoparticles is phonon velocity. For the first time, they considered the effect of multiparticle convection. The model is working well for ceramic particle-based nanofluids for particular values of constants used in modeling. Recently, Patel et al. [69] have modeled the thermal conductivity of nanofluid empirically with a new, semiempirical approach. High enhancements are attributed to the increase in the specific surface area and Brownian motion-based

micro-convection. The micro-convection is modeled with empiricism in the Nusselt number definition. With that, the model is working extremely well over a wide range of nanofluid combinations and parameters. Similarly, a completely empirical model [39] provides a correlation for alumina nanofluids by fitting a curve through regression analysis to the existing experimental data. In this model, when micro-convection around particles is modeled, the mean free path of liquid molecules is considered as a characteristic length to derive the diffusive velocities of the particles. Bhattacharya et al. [70] also performed Brownian dynamics simulation to determine the effective conductivity of nanofluids. The simulation results were within 3% of experimental data for Al 2 O 3 ethylene glycol and in nearly full agreement with Cu ethylene glycol. Recently, Xuan and Yao [71] developed a Lattice Boltzmann model to investigate nanoparticle distribution and flow pattern and found that the main flow and rising temperature of the fluid can improve nanoparticle distribution, which is beneficial to energy transport enhancement of the nanofluids. Nan et al. [72] have presented a simple formula for thermal conductivity enhancement in CNT composites that is derived from the Maxwell-Garnett model [52] by the effective medium approach. The model overpredicts the enhancement in the thermal conductivity of CNT suspensions when calculated with typical values of CNT thermal conductivities. The same authors have also developed a new model [73] by incorporating interface thermal resistance with an effective medium approach. However, the model needs the thermal resistance value at the surface of CNTs, which is difficult to get for different types of CNTs and their combinations with different solvents. Thus, various models and mechanisms that depend on an extension of classical theory, liquid layering, particle aggregation, and particle movement have been developed in an effort to explain the nanofluid behavior. However, the success of these models has been very limited, and no clear picture has emerged until recently. CONVECTION IN NANOFLUIDS It must be understood that thermal conductivity enhancement in nanofluids only creates a necessary condition for its usage; the sufficient condition comes from the hard evidence of the performance of these fluids in convective environments. The first question that arises in the convection of nanofluids is, what is the fluid mechanics of nanofluids? This is important because many colloidal and biological suspensions show strong non-newtonian behavior. Wang et al. [21] measured the viscosity of nanofluids by three methods and did not observe any non-newtonian effects. They found a 30% increase in viscosity for the Al 2 O 3 -water nanofluid when compared with pure water at 3% volume concentration of the particles. However, Pak and Cho [74] measured the viscosity to be much higher. Choi et al. [75] indicated that the discrepancy may be due to the electrostatic repulsion technique used, which may not be suitable for S. K. DAS ET AL. 11 Figure 7 Viscosity of Al 2 O 3 nanofluid at various temperatures and concentrations [76]. Reprinted with permission from Elsevier. fluids that contained acids or bases. However, even here, it was evident that the viscosity was independent of shear rate. Das et al. [76] presented the viscosity at different particle concentrations that was measured by a rotating-disc method. Figure 7 shows the results, which clearly indicate that nanofluid behavior is perfectly Newtonian. Heat transfer studies under convective conditions are rather scarce. Choi [12] presented a theoretical background for the estimation of convection enhancement, which essentially means a dramatic decrease of pumping power for a given heat transfer. Xuan and Roetzel [77] were the first to indicate a mechanism for heat transfer in nanofluids. They proposed thermal dispersion as a major mechanism of heat transfer in flowing fluid, along with the enhancement of nanofluid thermal conductivity. However, no evidence was presented in its support. Pak and Cho [74] presented the somewhat gloomy picture that in nanofluids, even though the Nusselt number increases, the heat transfer coefficient actually decreases by 3 12%. However, this may be due to the large increase in viscosity they observed. On the other hand, Eastman et al. [24] showed that with less than 1% volume fraction of CuO, the convection heat transfer rate increased by more than 15% in water. The work of Putra et al. [78] showed that natural convection in nanofluids deteriorated with particle concentration and was less than that in the pure fluid.

12 S. K. DAS ET AL. Recently TiO 2 water nanofluids were prepared at ph = 3 by Wen and Ding [79] through the dispersive method, and both transient and steady heat transfer coefficients were obtained for various concentrations of nanofluids under natural convective conditions. Distilled water was used as the host liquid, and TiO 2 constituted the nanoparticles. Agglomerates that formed were broken by a high-shear homogenizer to produce stable nanofluids. The nanofluids were found to decrease the natural convective heat transfer coefficient; this deterioration increased with nanoparticle concentration. The results differ from the numerical simulation by Khanafer et al. [80] for natural convective heat transfer behavior of nanofluids in a two-dimensional horizontal enclosure. However the experimental results do agree with the observations by Putra et al. [78], who also observed a decreased natural convective heat transfer coefficient for aqueous CuO and Al 2 O 3 nanofluids inside a horizontal cylinder. They asserted that the decrease was due to the effects of particle/fluid slip and sedimentation of nanoparticles. Here, the authors suggest convection induced by concentration difference, particle surface and particle particle interactions, and modifications of the dispersion properties as possible reasons for the deterioration in heat transfer. They added that the nanoparticles, if not specially treated, will form a layer on the surface that might significantly change surface properties. The agglomerates may stick/sinter on the heating surface and generate a fouling effect. Xuan and Li [81] found that heat transfer by forced convection is enhanced in nanofluids. However, it appears that much of this enhancement has to do with the type of nanoparticles used. The few available convective studies were performed with oxide nanoparticles that enhance conductivity only moderately while increasing the viscosity at the same time. The real advantage is expected in metallic nanofluids, which, because of a high enhancement rate, require only a small volume fraction (< 1%) that will keep viscosity almost unaffected but increase the heat transfer. Laminar heat transfer in the entrance region of a tube flow that was using alumina water nanofluid was the focus of the work by Wen and Ding [82]. Viscosity of the nanofluid was not measured and was assumed to follow the Einstein equation. For nanofluid that contained 1.6% nanoparticles by volume, the local heat transfer coefficient at the entrance region was 41% higher than that at the base fluid with the same flow rate. It was observed that the enhancement is particularly significant in the entrance region and decreases with axial distance. The thermal developing length of nanofluids was greater than that of the pure base liquid and increased with an increase in particle concentration. It was also shown that the classical Shah equation [83] failed to predict the heat transfer behavior of nanofluids. Particle migration [84] was proposed as a reason for the enhancement, which led to a nonuniform distribution of thermal conductivity and viscosity field and reduced the thermal boundary layer thickness. Convective heat transfer of suspensions of CNT nanofluids in a laminar regime with a constant heat flux wall boundary was investigated by the same authors [85]. When they measured the thermal conductivity of CNT, they observed that the effective thermal conductivity increased with an increasing temperature and CNT concentration, and with a significantly greater dependence of the conductivity on temperature. At a given shear rate, the viscosity of nanofluids increased with an increasing CNT concentration and decreasing temperature. A clear shear thinning was also observed at all concentrations. The presence of carbon nanotubes increased the convective heat transfer coefficient significantly, and the increase was more pronounced at high CNT concentrations. It was observed that the convective heat transfer coefficient at ph = 6was slightly higher than that at ph = 10.5. An observed maximum enhancement of 350% at Re = 800 for 0.5 wt.% CNTs clearly reveals that the enhancement of the convective heat transfer coefficient was much more dramatic than that purely due to the enhancement of effective thermal conductivity. Particle rearrangement, shear-induced thermal conduction enhancement, a reduction of the thermal boundary layer thickness due to the presence of nanoparticles, and the very high aspect ratio of CNTs are proposed as possible mechanisms of enhanced convective heat transfer. The enhancement of the experimental convective heat transfer coefficient of graphite nanoparticles dispersed in liquid for laminar flow in a horizontal tube heat exchanger was reported by Yang et al. [86]. Nanoparticles from various sources were used in this study and focused on an aspect ratio (l/d) of 0.02 (like a disc) because the addition of large-aspect-ratio particles into a fluid may dramatically increase viscosity when compared with the viscosity of single-phase fluids. In this study, two series of nanofluids with different base fluids (commercial automatic transmission fluid and a mixture of base oil) were used. The experimental results illustrated that the heat transfer coefficient increased with the Reynolds number and the particle volume fraction and decreased with fluid temperature. The two graphite nanoparticle sources at the same particle loading gave different heat transfer coefficients, which suggested that particle shape, morphology, or surface treatment were the cause of the difference. All of the experimental data were used to develop a new heat transfer correlation for the prediction of the heat transfer coefficient of laminar-flow nanofluids in a more convenient form by modifying the Seider-Tate equation to incorporate two constants, a and b, to give the form, where = Nu Pr 1/3 ( L D = are b (3) ) 1/3 ( µb µ w ) 0.14 and Re = Reynolds number, Nu = Nusselt number, Pr = Prandtl number, D = channel hydraulic diameter, L = channel length, µ b = dynamic viscosity at bulk temperature, and µ w = dynamic viscosity at wall temperature. On the theoretical side, Goldstein et al. [87] proposed the use of the Boussinesq equation for convection in nanofluids, seeking to use nanofluids for Rayleigh-Bernard convection and microwave irradiation in nanofluids. Khanafer et al. [80] performed a numerical study of buoyancy-driven heat transfer

enhancement in a two-dimensional enclosure. The effective stagnant thermal conductivity [10] with an enhancement term due to thermal dispersion in porous media was used for the modeling. A wide range of numerical experiments with varying Grashof number and volume fraction were performed. The results show that nanofluids behave more like a fluid than a conventional solid/fluid mixture. Kim et al. [88] analytically investigated convective instability driven by buoyancy and heat transfer characteristics of nanofluids. They proposed a factor that describes the effect of nanoparticle addition on the convective instability and heat transfer characteristics of a base fluid. The results show that as the density and heat capacity of nanoparticles increase and the thermal conductivity and shape factor of nanoparticles decrease, the convective motion in a nanofluid sets in easily. Recently, Daungthongsuk and Wongwises [89] summarized and reviewed the published articles that are pertinent to the forced convective heat transfer of the nanofluids of both experimental and numerical investigations. Maiga et al. [90] numerically investigated the forced convective heat transfer of nanofluids. They considered local thermal equilibrium and assumed that the nanofluid behaved as a conventional single-phase fluid with properties evaluated as functions of those of the constituents, knowing their respective concentrations. In their analysis, they used the Hamilton-Crosser model [9] to model the effective thermal conductivity of the nanofluid. The use of this model is highly questionable because the model does not bring in the anomalous thermal conductivity enhancement observed in experiments. In another recent study, using a two-component, four-equation, nonhomogeneous equilibrium model for convective transport, Boungiorno et al. [91] conducted a numerical study of the turbulent heat transfer of nanofluids. In the model, the wall layer consisted of two regions, both of which were considered: the viscous sublayer and the turbulent sublayer. Viscosity and particle volume fraction were less in the viscous sublayer, whereas conductivity in that region was greater. The heat transfer enhancement was explained mainly by a reduction in viscosity within and the consequent thinning of the viscous sublayer, and a new correlation was developed that agreed with existing experimental results. BOILING IN NANOFLUIDS Often, the results of heat transfer studies are in the direction opposite to what intuition might suggest. Encouraged by the enhancement of thermal conductivity, Das et al. [76] used nanofluids for boiling applications, but the results were negative. The effect of nanofluids on boiling was deteriorating with oxide nanoparticles suspension, as shown in Figure 8. In Figures 9a and 9b, the nondimensional plot of boiling Reynolds number versus boiling Nusselt number shows that the deterioration is greater on a rough surface (R a = 1.15 µm) than on a smooth surface (R a = 0.4 µm). While investigating the reason for this, the investigators found that the nanoparticles plugged the microsized surface cavities, thus reducing the nucleation site density, S. K. DAS ET AL. 13 Figure 8 Pool boiling characteristic of nanofluids [76]. Reprinted with permission from Elsevier. Ra denotes the roughness parameter, (T w Ts)isthe wall superheat, and q is the input heat flux. the prime cause of deterioration of boiling. The deterioration increased with reducing diameter of narrow tubes [92], as shown in Figure 10. However, the investigators indicated that, even the deterioration can have a practical application in that it involves engineered fluids that will inhibit boiling or boil at a preassigned surface temperature, a characteristic that may be important for heat treatment or material processing. This predicted practical application proved to be correct when Tsai et al. [93] used nanofluids in heat pipes to delay a boiling limit. However, the need to investigate whether suspended nanoparticles can act as nucleation sites to provide homogeneous nucleation in the situation when heating is done volumetrically with the help of sources such as microwaves or LASERs still remains. In another study, You et al. [94] measured the critical heat flux (CHF) in the pool boiling of Al 2 O 3 water nanofluids. They discovered an unprecedented phenomenon: a three-fold increase in CHF over that of pure water at the mass fraction O (10 5 ). The average size of departing bubbles increased and the bubble frequency decreased significantly in nanofluids when compared with those in pure water. Vassallo et al. [95] confirmed these results in similar studies on SiO2 nanoparticles. They observed a two- to three-fold increase in CHF, as shown in Figure 11.

14 S. K. DAS ET AL. Figure 9 Nusselt number (Nu) Reynolds number (Re) plots for nanofluids on (a) smoother heater and (b) roughened heater [76]. Reprinted with permission from Elsevier. Ra denotes the roughness parameter. Later, Bang and Chang [96] observed similar phenomena during their pool boiling studies with water alumina nanofluid. The measured pool boiling curves of nanofluids saturated at 60 C demonstrated that the CHF increased dramatically (a 200% increase) when compared with pure water; however, the nucleate boiling heat transfer coefficients appeared to be approximately the same. In yet another experimental study on a smooth horizontal surface with alumina water nanofluid, Bang and Chang [97] found Figure 10 q T curves for nanofluids in tubes of various diameters [92]. Reprinted with permission from Elsevier. (T w T s) denotes the wall superheat and q is the input heat flux. Figure 11 Critical heat-flux increase in nanofluids [95]. Reprinted with permission from Elsevier.

that the heat transfer performance of these nanofluids is poor when compared with pure water in natural convection and nucleate boiling. This finding is consistent with the observations of Das et al. [76], who reported that in the case of nanofluids, the natural convection stage continues relatively longer and nucleate boiling is delayed, or a higher superheat of the boiling surface is needed for boiling. On the other hand, CHF has been enhanced in not only horizontal but also vertical pool boiling. The change of CHF was proposed to be due to a possible surface coating effect that would change the nucleation site density. The enhancement of the observed CHF is much lower than that observed by Vassallo et al. [94]. Suggested possible reasons for this finding were that the nanofluids and heated surface geometries used were different. Bang and Chang [97] conducted experiments that confirmed the existence of a liquid film that separated a vapor bubble from the heated solid surface. Alumina nanofluid was used as a colored fluid to distinguish between the liquid phase and the vapor phase in a complex boiling environment. They showed that a liquid film under a massive vapor bubble adheres to a heated solid surface and observed that the liquid film gets trapped in a dynamic coalescence environment of nucleate bubbles, which grow and depart continuously from the heated surface. However, so far, no study on boiling of metallic nanofluids or flow boiling of nanofluids is available. APPLICATIONS OF NANOFLUIDS S. K. DAS ET AL. 15 While applying nanofluids for commercial cooling, Tzeng et al. [98] studied the effect of nanofluids when used as engine coolants. CuO (4.4% wt) and Al 2 O 3 (4.4% wt) nanoparticles and antifoam were individually mixed with automatic transmission oil. The experimental platform was a real-time four-wheel-drive (4WD) transmission system. The experimental results showed that, under the similar conditions, antifoam oil provided the highest temperature distribution in rotary blade coupling and, accordingly, the worst heat transfer effect, and CuO oil provided the lowest temperature distribution both at high and low rotating speed and, accordingly, the best heat transfer effect. Gosselin and Silva [99] explored the optimization of particle fraction for maximizing the thermal performance of nanofluid flows under appropriate constraints. They argued that when few particles are present, the heat transfer rate that is achieved is small, whereas too many particles lead to large shear stresses and large required pumping power. This competition reveals a trade-off opportunity to maximize the heat transfer rate at constant pumping power by selecting the appropriate amount of particles. Using nanofluids as coolants, Chein and Huang [100] numerically considered silicon microchannel heat sink performance. The nanofluid was a mixture of pure water and nanoscale Cu particles at various volume fractions. Due to the increased thermal conductivity and thermal dispersion effects, they found that performance was greatly improved when nanofluids were used as the coolant. In addition, they observed that the presence of nanoparticles in the fluid did not produce any extra pressure drop because of small particle size and low particle volume fraction. Koo and Kleinstreuer [101] numerically investigated the conjugate heat transfer problem for microheat sinks considering two types of nanofluids (i.e., CuO nanospheres at low volume concentrations in water and in ethylene glycol). The effect of Brownian motion on the effective fluid viscosity was considered and found to be less significant than that on the effective thermal conductivity. Based on the studies, they suggested that high Prandtl number fluids and thermal conductivity nanoparticles be used to attain better microchannel heat transfer. They suggested that to minimize particle particle and particle wall interactions, particles with a dielectric constant close to that of the base fluid and a wall material such that particle wall attraction is minimized should be selected. REMARKS AND FUTURE DIRECTION The present review gives a comprehensive overview of the fascinating research progress made in the area of nanofluids. The previous review by Eastman et al. [102] gives a good idea about nanotubes and role of the contact resistance in the thermal transport of nanofluids, besides addressing the issues about thermal conductivity and other properties of nanofluids. However, in recent times, the number of papers published in the area of nanofluids has increased exponentially, and a clearer picture about the future direction of research in this area can be depicted at this point of time. The first major conclusion that can be drawn from the reviewed studies is that nanofluids show great promise for use in cooling and related technologies. Oxide nanoparticle-based nanofluids are relatively less promising in the enhancement of thermal conductivity of fluids. Also the enhancement diminishes rapidly with the increase in particle size. Metallic nanoparticles seem to enhance thermal conductivity anomalously, with very large enhancement at very low volume fraction. This finding opens the prospect of increasing thermal conductivity enhancement without making large changes in viscosity, which can erode the gain in convective conditions. On the other hand, maximum enhancement ( 160%) with 1% volume fraction was observed with multi-walled carbon nanotubes dispersed in engine oil. This type of nanofluid shows unexplained nonlinear enhancement. Thus, the future direction should be to first standardize a technology to measure the conductivity of nanofluids. Next, major attention should be given to the acquisition of extensive data with controlled parameter variation. Until now, only few ceramics (Al 2 O 3, CuO, TiO 2, SiC, and SiO 2 ) and afew metallic particles (Cu, Fe, Au, and Ag) have been studied in differing concentration ranges. Most importantly, particle size must be studied. From the theoretical perspective, the mechanism of thermal conductivity enhancement is still unclear. Many attempts to identify and model this mechanism have been carried out with only very limited success. Quite a few studies analyze the same type of particle clustering by fractal dimensions. Liquid layering

16 S. K. DAS ET AL. studies that assume a liquid shell around the particles that behave like solids have also been performed. The predictions, however, were matched with adjustable parameters of shell thickness and shell conductivity that are questionable. Some of the studies modeled both oxide nanofluids and carbon nanotube nanofluids. These studies are commendable. The efforts to include particle motion in the form of Brownian motion appear to be controversial, and these efforts need to be revisited, particularly with respect to temperature effect. A very encouraging concept is the nano-convection of fluid around the particles due to their motion. In this concept, the particles transport some amount of heat with them and contribute to the total heat transfer through agitation in the liquid. From a physical point of view, this phenomenon seems to be a potential explanation for the behavior of nanofluids. 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[99] Gosselin, L., and Da Silva, A. K., Combined Heat Transfer and Power Dissipation Optimization of Nanofluid Flows, Applied Physics Letters, vol. 85, no. 18, pp. 4160 4162, 2004. [100] Chein, R., and Huang, G., Analysis of Microchannel Heat Sink Performance Using Nanofluids, Applied Thermal Engineering, vol. 25, pp. 3104 3114, 2005. [101] Koo, J., and Kleinstreuer, C., Laminar Nanofluid Flow in Micro Heat-Sinks, International Journal of Heat and Mass Transfer, vol. 48, pp. 2652 2661, 2005. [102] Eastman, J. A., Phillpot, S. R., Choi, S. U. S., and Keblinski, P., Thermal Transport in Nanofluids, Annual Reviews in Material Research, vol. 34, pp. 219 246, 2004. Sarit Kumar Das is a professor of the mechanical engineering department at the Indian Institute of Technology Madras, India. He received his M.E. and Ph.D. degrees from Jadavpur University and Sambalpur University, India, in 1986 and 1994, respectively. He carried out post-doctoral research at the University of Federal Armed Forces, Hamburg. He has published about 100 research papers in international journals and conferences and two textbooks. He had been a visiting professor at the Helmut Schmidt University, Hamburg and University of Lund, Sweden. He is a member of the editorial board of International Journal of the Heat Exchangers and Journal of Heat Transfer Engineering. His research interests include heat exchangers, two-phase heat transfer, heat transfer in nano-fluids, transport in fuel cells, jet instabilities, porous media, and computational fluid dynamics. He is the recipient of DAAD and Alexander von Humboldt Fellowship of Germany. He is also the recipient of the K. N. Seetharamu 2006 award for research from the Indian Society for Heat and Mass Transfer. Stephen U.S. Choi joined Argonne National Laboratory (ANL) in 1983 and has conducted research in advanced fluids. He proposed the concept of nanofluids in 1993 and has led the nanofluids team to develop stable nanofluids that showed high thermal conductivities. He currently serves as the principal investigator of the nanofluids team. His pioneering work created anew, active area of interdisciplinary research in the field of nanoscale thermal sciences. The nanofluid work was recognized as one of the top research accomplishments in the Department of Energy Basic Energy Sciences Office in 2002. Prior to ANL, he was a staff scientist at Lawrence Berkeley Laboratory. He received his B.S. from the Seoul National University in Korea, his M.S. from the University of Texas at Austin, and his Ph.D. from the University of California, Berkeley, all in mechanical engineering. Recently, he received the University of Chicago Distinguished Performance Award for pioneering scientific achievements and outstanding leadership in nanofluid research. He is author or co-author of more than 100 technical publications and holds three U.S. patents. Hrishikesh E. Patel is a Ph.D. student in the Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, India. He received his Master s degree from the same institute in 2003 and Bachelor s degree from Government Engineering College, Aurangabad, India in 2000. Currently, he is working on the experimental and theoretical analysis of the thermal behavior of nanofluids.