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Advances in Mechanical Engineering

Volume 2010 (2010), Article ID 795478, 9 pages

http://dx.doi.org/10.1155/2010/795478

## Heat Transfer Mechanisms and Clustering in Nanofluids

Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33124, USA

Received 18 May 2009; Accepted 24 November 2009

Academic Editor: Yogesh Jaluria

Copyright © 2010 Kaufui V. Wong and Michael J. Castillo. 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

This paper surveys heat transfer in nanofluids. It summarizes and analyzes the theories regarding heat transfer mechanisms in nanofluids, and it discusses the effects of clustering on thermal conductivity. The heat transfer associated with conduction is presented through various experiments followed by a discussion of the theories developed. Relationships between thermal conductivity and various factors such as temperature, concentration, and particle size are also displayed along with a discussion on clustering. There is a brief discussion on convection where the number of studies is limited. There is research currently being performed on the manipulation of the properties governing the thermal conductivity of nanofluids—the particle size, shape, and surface area. Other factors that affect heat transfer are the material of the nanoparticle, particle volume concentration, and the fluid used. Although the interest in this relatively new class of fluids has generated many experimental studies, there is still disagreement over several aspects of heat transfer in nanofluids, primarily concerning the mechanisms behind the increased thermal conductivity. Although nanoparticles have greatly decreased the risks, there is still evidence of unwanted agglomeration which causes erosion and affect the overall conductivity. Research is currently being conducted to determine how to minimize this unwanted clustering.

#### 1. Introduction

The growth of technology found in high-tech industries, such as microelectronics, transportation, and manufacturing, has created a cornucopia of ideas that would have wide ranging effects on many obstacles facing today’s scientific world including energy efficiency, pollution, and reusability. However, there are many factors hindering further development in these industries, one being the ability to rapidly cool the products being used. Cooling is necessary for maintaining the operational performance and reliability of new products, and as a result of increased heat loads and heat fluxes caused by the increase in power and decrease in feature sizes present in new products, the demand for a more efficient cooling process has increased dramatically in the last decade. Consequently, more companies are beginning to invest more capital into the research of more efficient heat transfer processes.

The conventional method for enhancing heat transfer in a thermal system consists of increasing the heat transfer surface area as well as the flow velocity of the working fluid [1]. The dispersion of solid nanoparticles in heat transfer fluids is a relatively new method. Extended surfaces such as fins and microchannels (width 100 m) have already been used to increase the heat transfer surface area. Their performance in effectively removing as much as 1000 W/cm^{2} has shown a great improvement in the area of cooling. However, further development of this technology is at a standstill because it has already been pushed to its achievable limits. Thus, attention is now turning towards the dispersion of solid particles in fluids.

Since Maxwell’s theories in 1873, scientists have attempted to increase the thermal conductivity of a fluid through the combination of solid particles and a heat transfer fluid. Although liquid cooling is prevalent today (i.e., in automobiles and in some microelectronics), it has been severely limited because of the inherent poor thermal conductivity of traditional heat transfer fluids. Efforts to increase this fundamental limit began with the dispersion of millimeter- or micrometer-sized particles in fluids. Although this action increased the thermal conductivity of the heat transfer fluid, it was not practical because the increase in heat transfer required a large number of particles (10% by volume). This often resulted in a significant pressure drop, thus requiring more pumping power. Furthermore, because of their size, these particles rapidly settled in the liquid, clogged microchannels, and caused wear in pipes, pumps, and bearings.

As technology turned to miniaturization and nanotechnology, the idea of nanofluids was developed at various institutions around the world (initial development was performed at Argonne National Laboratory, and much research is still carried out at this location). Coined by Stephen U. S. Choi in 1995, the term nanofluids (short for nanoparticle fluid suspension) is used to describe stable suspensions of nanoparticles (average size 100 nm) in traditional heat transfer fluids such as water, oil, or ethylene glycol [1]. Experimentation has shown significant improvement in the thermal conductivity of fluids containing oxide and metallic nanoparticles. With volume concentrations between 0.5% and 4%, nanofluids have shown an enhancement of 15%–40% of the thermal conductivity of the base fluid [2]. It has also been observed that nanoparticles stay suspended in the fluid longer than micrometer-sized particles, thus reducing the severity of the obstacles presented by the rapid settling of the particles (such as abrasion and clogging of pipes and microchannels).

Experiments, such as those found in references [3–10], are continuously being conducted to achieve a deeper understanding of the mechanisms behind the increase in thermal conductivity caused by these nanoparticle suspensions. In addition, the paper by Sandhu [11] declared the improved thermal conductivity of magnetic nanofluids. Philip et al. [12] showed that arranging the linear aggregation length from nano- to micron-scales, the thermal conductivity of the nanofluid was enhanced up to 216%, using 4.5 volume percentage of nanoparticles. Repeated magnetic cycling shows that the enhancement is reversible.

There has been a dramatic increase of interest in the field of nanofluids as shown by the exponential increase in the number of publications concerning the subject matter in the Science Citation Index (SCI) journals. Several businesses, corporations, and scientific institutions have begun research towards the common goal of achieving the highest possible thermal properties at the smallest possible concentration (preferably 1% by volume). Nanofluids have the potential of becoming compact, cost-effective liquid cooling systems in high-performance situations.

#### 2. Conduction Heat Transfer in Nanofluids

Maxwell first proposed the idea of suspending metallic particles in conventional heat transfer fluids in 1873 [13]. He believed that the metallic particles (which have thermal conductivities that are significantly larger than that of liquids as shown in Figure 1) would increase the electrical and thermal conductivity of the fluids. This idea was carried on throughout the next century as scientists attempted to create a fluid with millimeter- and micrometer-sized particles that could be used for practical applications. However, even though their efforts showed that particles did increase the heat transfer properties of their base fluids, they could not overcome problems caused by the large size of the particles. It was not until the advent of nanotechnology that the thought of nanoparticles came about.

The idea of nanofluids created an influx of experimentation that has led to the knowledge that we have today. Though experiments have been carried out with nanoparticles formed from a wide array of materials including aluminum oxide (Al_{2}O_{3}), copper (Cu), copper oxide (CuO), gold (Au), silver (Ag), silicon carbide (SiC), titanium carbide (TiC), titanium oxide (TiO_{2}), and carbon nanotubes, the most common nanoparticles are Al_{2}O_{3} and CuO [14]. The base fluids used most commonly are water, engine oil, and ethylene glycol. The nanofluids used in these experiments are created by mixing the base fluid and the nanoparticles together and then stabilizing the suspension.

Nanoparticles can be produced by either physical or chemical means. Current physical processes include mechanical grinding and the inert-gas-condensation technique pioneered by Granqvist and Buhrman. Presented in 1976, the latter technique involves evaporation in a temperature-regulated oven containing an inert gas [15]. Current chemical processes include chemical precipitation, chemical vapor deposition, microemulsions, spray pyrolisis, thermal spraying, and a sonochemical method for the production of iron nanoparticles [16]. The most common processes currently used in the production of metal nanoparticles include mechanical milling, inert-gas-condensation technique, chemical precipitation, spray pyrolisis, and thermal spraying [2]. Although nanoparticles are constantly being produced in small volumes for experimental needs, there is still research being conducted towards achieving more cost-efficient production processes in order to begin the move towards large-scale production.

There are currently two methods used to disperse nanoparticles in the base fluid: the two-step technique and the single-step technique. The *two-step method* involves making the nanoparticles first, by either physical or chemical means and then dispersing them into the base fluid. In combination with the inert-gas-condensation technique (which has been proven to be a viable process for producing bulk quantities of nanopowders), the two-step method can be used to initiate the move towards commercialization by facilitating the mass production of nanofluids [17]. The *single-step method* involves simultaneously making and dispersing nanoparticles into the base fluid [1]. This method is favorable when using metallic nanoparticles—since the nanoparticles are placed in the base fluid as they are produced, this process helps prevent oxidation of the particles.

Because of the attractive van der Waals forces between the particles, they tend to agglomerate before they are dispersed in the liquid (especially if nanopowders are used); therefore, a means of separating the particles is necessary. Groups of particles will settle out of the liquid and decrease the conductivity of the nanofluid. Only by fully separating all nanoparticle agglomerates into their individual particles in the host liquid will a well-dispersed, stable suspension exist, and only under this condition will the optimum thermal conductivity exist. Xuan and Li [19] proposed different methods for the stabilization of the suspension including changing the pH value of the nanofluid, using dispersants, and using ultrasonic vibration. The most commonly used method is the ultrasonic vibration which has been relatively successful in eliminating agglomerated nanoparticles. There is certain hesitation when using dispersants because they can affect the chemical composition of the nanofluid and change the results. If dispersants are used, it cannot be clearly determined if the change in thermal conductivity was affected by the stabilizers placed in the fluid. This problem can be taken into account by comparing the nanofluid conductivity with that of the liquid with dispersant.

There are three methods commonly employed to measure the thermal conductivity of nanofluids: the transient hot wire method, temperature oscillation, and the steady-state parallel plate method [14]. The most commonly used method is the transient hot wire method which involves the use of small diameter wires that act as electrical resistance heaters and resistance thermometers [20]. The wire is heated by passing a current through it, and the rise in temperature over the time elapsed is measured. Since the wire is essentially wrapped in the liquid, the heat generated will be diffused into the liquid. The higher the thermal conductivity of the surrounding liquid, the lower the rise in temperature will be. To calculate the thermal conductivity of the surrounding liquid, a derivation of Fourier’s law for radial transient heat conduction is used [1]. This differential equation for the conduction of heat is

Using a solution presented by Carslaw and Jaeger [21], the conductivity of a solution can be expressed as where and represent the temperature of the heat source at times and , respectively.

Many experiments have been performed using nanofluids, and although the results vary, they show an amplification of the thermal conductivity of the base fluid. Observations show four important characteristics of nanofluids:

(i) increased thermal conductivity at low nanoparticle concentrations,(ii) linear relationship between thermal conductivity and concentration,(iii) thermal conductivity being strongly dependent on temperature,(iv) thermal conductivity being strongly dependent on the size of the particles used.As a result of debates as to why these characteristics are present in nanofluids, various theories have been developed.

Lee et al. [22] measured the thermal conductivity of nanofluids using CuO and Al_{2}O_{3} nanoparticles and water and ethylene glycol as the base fluids. Results showed an enhancement in the thermal conductivity of ethylene glycol of more than 20% at 4% volume fraction of CuO nanoparticles. Further experimentation revealed that the thermal conductivity increased as the volume concentration of nanoparticles was increased; thus, it was determined that the thermal conductivity of nanofluids was dependent on the thermal conductivity of both the particles and the base fluid in most ranges of , where is the conductivity of the particleand is the conductivity of the base fluid. For large values of , the later statement may not be true. Although the thermal conductivity of the nanofluid is always greater than that of the base fluid without nanoparticles, this increase will be different for each base fluid.

Xie et al. [23] measured the thermal conductivity of nanofluids containing Al_{2}O_{3} nanoparticles. They also investigated the effects of the pH value of the suspension and the specific surface area (SSA) of the dispersed particles. In accordance with the previous results, the thermal conductivity of the fluid was enhanced with the addition of the nanoparticles. However they also noted that the thermal conductivity increased as the difference between the pH value and the isoelectric point (pH value at which there is no electric charge) of Al_{2}O_{3} increased and that the enhancements were highly dependent on the specific surface area of the nanoparticles. When compared to theoretical models, the measured thermal conductivity was much higher than the calculated values. A relationship between temperature and thermal conductivity was later presented by Das et al. [24]. In this study, not only it was determined that the thermal conductivity increased with an increase in temperature, but also it was shown that nanofluids composed of smaller particles experienced a greater enhancement than with larger particles. One possible explanation for this could be attributed to the Brownian motion of the particles in the fluid. Since temperature represents the overall kinetic energy of the particles, an increase in temperature will cause increased motion in the particles. It is easier for smaller particles to move; therefore, smaller particles will display a higher level of Brownian motion than larger particles. This results in greater heat conduction among smaller particles as the temperature is increased.

Results from these various experiments may have varied, but they all showed that the thermal conductivity of a fluid containing nanoparticles was greater than that of a base fluid with no particle suspension. Moreover, it was shown that the thermal conductivity was affected by factors such as temperature, particle size, and pH level. Several theoretical models have been proposed to explain the behavior of nanoparticles. Many of these models can be categorized as either static or dynamic models [22]. Static models assume that the nanoparticles are stationary in the base fluid, forming a composite material. In these models, the thermal properties of nanofluids are predicted through conduction-based models such as that of Maxwell. One such model is the modified Maxwell theory of Hamilton and Crosser [25] which gives the enhancement of thermal conductivity as
where is the effective conductivity, is the conductivity of the particle, is the conductivity of the base fluid, is the particle volume fraction, is the particle shape factor, and is the sphericity of the particles [1]. This model was in good agreement with experimental data obtained with the use of Al_{2}O_{3} nanoparticles in a nanofluid, but it was not able to accurately predict the thermal conductivity of nanofluids containing CuO nanoparticles. It should be noted that in (3) the effective thermal conductivity is independent of the thermal conductivity of the particle as the ratio of becomes large.

Dynamic models assume that nanoparticles are in constant, random motion in the base fluid (i.e., Brownian motion), as shown in Figure 2.

In the dynamic models, it is believed that this random motion may be the main cause of the increased thermal properties associated with nanofluids. Taking Brownian motion to be a key mechanism in the thermal properties of nanofluids, Jang and Choi [26] developed a model that portrayed the relationship between conductivity, temperature, concentration, and particle size. However, there is disagreement with the assumption that random motion plays a key role in the transfer of heat in a nanofluid. Keblinski et al. [27] proposed an explanation of four possible factors for the heat transfer mechanism in nanofluids one of which was Brownian motion. However, the study concluded that the movement of nanoparticles due to Brownian motion was too slow in transporting heat through a fluid. To travel from one point to another, a particle moves a large distance over many different paths in order to reach a destination that may be a short distance from the starting point. Therefore, the random motion of particles, no matter how agitated or energetic they may be, cannot be a key factor in the improvement of heat transfer. Jang and Choi [26] also came to a similar conclusion. Here, it was determined that the collision between nanoparticles due to random motion was a very slow process and could, therefore, be neglected in the calculation of thermal conductivity.

Although they contributed to the idea that collisions resulting from Brownian motion did not contribute to the overall conduction of heat, Jang and Choi [26] were able to develop a dynamic model that takes into account convection heat transfer induced by Brownian nanoparticles. The general expression derived in this study introduced four modes of energy transport in nanofluids:

(i) collision between base fluid molecules (i.e., thermal conductivity of base fluid),(ii) thermal diffusion in nanoparticles in fluids,(iii) collision between nanoparticles due to Brownian motion (neglected because it is a very slow process),(iv) thermal interactions of dynamic nanoparticles with base fluid molecules (once overlooked, this mode is now considered to be a key factor in the relationship between conductivity, temperature, and particle size).The major aspect of this model was the introduction of the idea that nanoparticles can produce a convection-like effect in a fluid. The thermal conductivity for their model is given by where is the effective thermal conductivity of the nanofluid, is the base fluid conductivity, is the volume fraction of the nanoparticles, is the thermal conductivity of the nanoparticles, is an empirical constant, is the diameter of the base fluid molecule, and is the diameter of a nanoparticle [1]. is the Reynolds number defined by

where is the dynamic viscosity of the base fluid, and is the random motion velocity of nanoparticles defined by
where is the mean-free path of a base fluid molecule. is the nanoparticle diffusion coefficient given by
where is the viscosity of the base fluid, is the temperature of the base fluid, and is the Boltzmann constant. The predictions presented by this model are in excellent agreement with temperature-dependent conductivity data from experiments involving nanofluids containing Al_{2}O_{3} nanoparticles. Models derived from Maxwell’s equations fail to correlate with this type of experimental data.

Another model developed by Kumar et al. [29] involves the combination of the stationary particle model and the moving particle model. The stationary particle model looks at the increased surface area as the particle size decreases. By assuming two parallel paths of heat flow (one through base fluid molecules and the other through the nanoparticles), this model shows the linear dependence of thermal conductivity on particle concentration and the inverse dependence of thermal conductivity on the size of the particle. The moving particle model accounts for the temperature effect and is derived from the Stokes-Einstein formula. The effective thermal conductivity of the nanofluids, , for this model is given by where is the base fluid conductivity, is the nanoparticle volume fraction, is the radius of the base fluid molecules, and is the radius of the nanoparticles. The nanoparticle’s thermal conductivity, , is defined as. The mean velocity of the nanoparticle is derived from the Stokes-Einstein formula where is the fluid temperature, is the dynamic viscosity of the fluid, and is the diameter of the nanoparticle. The combination of the stationary particle model and the moving particle model shows the dependence of thermal conductivity on particle size, concentration, and temperature. Although this model correlates with the experimental data for nanofluids containing gold at small concentrations, there is a discrepancy in the stationary particle model. It has been pointed out that if the radius of the nanoparticles is larger than that of the liquid molecules, then the calculated thermal conductivity for the nanofluid will equal that of the base fluid, an unrealistic situation. Therefore, when using this model, an unphysical assumption that the mean-free path of a nanoparticle is on the order of 1 cm is made in the moving particle model [29]. There are still some issues over the benefits of this model, and as a result, it is the source of some debates today concerning the dynamic model.

The influence of particle anisotropy on the effective thermal conductivity of a suspension was experimentally studied by Cherkasova and Shan [30]. Suspensions of micron-sized, silicon-carbide particles with varying aspect-ratio distributions were prepared and measured. It was shown that the conductivity of the silicon-carbide suspensions can be quantitatively predicted by the effective medium theory presented by Nan et al. [31], as long as the volume-weighted aspect ratio of the particles is used.

The effect of Kapitza resistance between the particle and fluid can significantly impact the effective thermal conductivity of nanofluids. This effect was included into the model by Nan et al. [31], which predicted the experimental data of carbon nanotube suspensions reasonably well. Ju and Li [32] and Xue [33] also presented models for the effective thermal conductivities of carbon nanotube-based mixtures with an interfacial thermal resistance effect.

References [34, 35] discuss experiments where the interfacial layers of nanoparticles were examined. Document [36] discusses the relationship between temperature, particle size, and the thermal conductivity of the nanofluids examined. The survey done here does not include any work involving synthetic nanofluids, which form a class by themselves [37–39].

#### 3. Convective Heat Transfer in Nanofluids

If nanofluids can improve the heat transfer coefficient of heat exchangers and energy systems, then they can aid in reducing the size of such systems while leading to increased energy and fuel efficiencies. Nanofluid convective heat transfer research may be classified by fluid conditions of laminar flow, turbulent flow, and pool boiling. The number of studies in these areas is limited, with the smallest number of studies having been reported in the last class of pool boiling.

Works in laminar flow include references [40–44]. Some of the works show heat transfer enhancements for laminar flow with different particle types (alumina and copper oxide) and sizes. Nanofluid heat transfer results for multiwalled carbon nanotubes (MWCNTs) show excellent heat transfer and thermal conductivity enhancement [42]. The results published by Yang et al. [44] displayed a heat transfer enhancement trend that is opposite to that for thermal conductivity—there is a drop in enhancement with increased temperature. But the temperature range studied is small, and the temperature dependency is not strong. More test data needs to be obtained before any definite conclusions can be drawn.

Heat transfer enhancements in turbulent flow of nanofluids include references [45–48]. The studies were performed on water-based nanofluids containing alumina, titanium oxide, copper particles, and amorphous carbonic nanoparticles. There seems to be a consensus that the Reynolds number has little or no effect on the enhancement of heat transfer. Furthermore, the heat transfer improvement increased as the particle volume concentration was increased.

Putra et al. [49] investigated the convection of Al_{2}O_{3} and CuO in water-based nanofluids. It was discovered that the natural convection of nanofluids was less intense than that of the base fluid. Moreover, it deteriorated as the particle density and concentration were increased. Smaller particles experienced even worse convective heat transfer because the particle density increases as the particle size decreases. However, Khanafer et al. [50] developed a model for the convective heat transfer of nanofluids that produced different results. With the assumption that the base fluid and the nanoparticles were in thermal equilibrium and flowed at the same velocity (i.e., nanofluid is in single phase), it was shown that the heat transfer rate increased as the particle volume fraction increased. Another model proposed by Kim et al. [51] introduced a factor to include the effect of the thermal conductivity ratio between the nanoparticles and the base fluid, the shape factor and volume fraction of particles, and the ratio of density and heat capacity of nanoparticles to the base fluid. Results from this model showed that the amount of heat transfer in the nanofluid increased as the particle volume fraction was increased.

It is evident that the results of Kim and Khanafer contradict the results of Putra. Possible explanations for these differences could be dependent on the assumptions made in each model. Before nanofluids can be introduced to industrialized applications, there must be a better understanding of convection heat transfer and its effects on the overall thermal conductivity of the nanoparticle suspension.

#### 4. Clustering in Nanofluids

One of the main obstacles encountered in microfluid experiments was the agglomeration of particles. Even though research, such as that documented in [22, 23], shows a substantial increase in the thermal conductivity of the base fluid with the addition of nanoparticles, the movement towards practical applications has been hampered by the rapid settling of the nanoparticles. The settling of particles not only decreased the overall heat transfer of the fluid (by decreasing the effective surface area used for heat transfer), but also led to the abrasion of surfaces, clogging of microchannels, and a decrease in pressure—which resulted in an increase in pumping power [14].

Although nanosized particles have greatly reduced the problem of agglomerated particles, it still occurs and can hinder the thermal conductivity of the nanofluid, especially at concentrations over 5%—agglomeration is more apparent when using oxide nanoparticles because they require a higher volume concentration compared to metallic nanoparticles in order to achieve the same thermal conductivity enhancement [2]. The tendency of particles to group together before they are dispersed in the fluid is due to the van der Waals forces. This is particularly seen in metallic particles since dipoles can occur easily in the molecules of these particles. The creation of dipoles prompts the attraction of other dipoles in the vicinity. The van der Waals forces stem from the attraction of these dipoles, which can be induced even in neutral particles. This attractive force is considered to be the main culprit behind the agglomeration of particles, especially in nanopowders.

To alleviate this problem, there have been various proposals for the manufacture and dispersion of nanoparticles in fluids. One proposal involves adding surface treatments to the nanoparticles. It was seen that when copper nanoparticles were coated with a 2–10 nm thick organic layer a stable suspension would be achieved in ethylene glycol [16]. There is research currently being conducted towards improving the two-step process to produce well-dispersed nanofluids. Moreover, there exist a few one-step processes that result in nanoparticles being uniformly dispersed and stably suspended in the base fluid. One such method involves condensing copper nanopowders directly from the vapor phase into flowing ethylene glycol in a vacuum chamber [52]. Documents [53–55] also show stable, well-dispersed suspensions in nanofluids containing TiO2, CuO, and Cu. In these experiments, a one-step process called submerged arc nanoparticle synthesis was used to create the nanoparticles.

Various techniques have been implemented to reduce the clustering of particles once they are in the fluid [56, 57]. Usually, they involve some sort of agitation within the nanofluid to separate the clusters into individual particles and keep them from settling. These methods include the use of dispersants, changing the pH value of the base fluid, and using ultrasonic vibration to excite the particles [6]. Among these methods, the most commonly used ones are ultrasonic vibration and the use of dispersants. Both techniques are relatively effective, but when using dispersants, the amount added to the fluid must be a very low percentage (usually 1% or less). This is done so as to minimize its effects on the thermal conductivity of the nanofluid.

However, it should be noted that loose particle chains may be responsible for some of the high thermal conductivities of nanofluids; see Prasher et al. [58].

The Argonne National Laboratory also developed the single-step and two-step processes for the dispersion of nanoparticles in a fluid [1]. The single-step process consists of simultaneously making and dispersing the particles in the fluid. The two-step method separates the manufacture and dispersion of particles into two steps (particles are manufactured first and then dispersed into the base fluid). The two-step process is the more commonly used method and is usually used in conjunction with ultrasonic vibration to reduce the amount of clustered particles in the fluid.

Analysis of the reviewed literature shows that there is still no conclusive theory concerning the prevention of clustering in the nanoparticle suspensions. Before using nanofluids in practical applications, the problem of clustering must be consistently kept to a minimum. When looking at long-term effects, clustering of the particles will eventually cause a decrease in the thermal conductivity of the nanofluid and may also cause wear in the pipes or pumps through which it is flowing. Therefore, nanofluids cannot be used in systems designed for long-term use until this problem is solved. Otherwise, the use of nanofluids may decrease the life expectancy of a system, even if it improves the overall efficiency. In the mean time, an optimization and design problem persists when nanofluids are used in the field.

#### 5. Conclusion

Even though nanofluids are still relatively new, they have caused a dramatic increase in the interest of ultra-high performance cooling. Experiments are continuously being conducted to achieve a deeper understanding of the mechanisms behind the increase in thermal conductivity caused by these nanoparticle suspensions. As a result, various conclusions have been drawn regarding the characteristics of nanofluids including the relationship between thermal conductivity, particle size, nanoparticle concentration, and temperature.

Heat can be transferred through conduction, convection, and radiation. There is a more thorough understanding of conduction in nanofluids than the other two, and various models have been formulated to predict the thermal behavior of nanofluids. Static models investigate the thermal conductivity of a nanofluid assuming a stationary suspension of particles in the base fluid. This allows for the use of derived forms of Maxwell’s equation. Dynamic models assume that the particles are in constant, random motion while dispersed in the fluid. These models are the source of much debate today over the involvement of Brownian motion in the thermal conductivity of nanofluids. While some scientists believe that this random motion is the source of conduction in nanofluids, studies show that it is insignificant compared to other factors because the transfer of heat is a very slow process in Brownian motion. However, some researchers were able to develop a dynamic model that portrayed four modes of energy transport. The major aspect of this model was the convection heat-transfer induced by Brownian motion in particles. Results from this model correlated excellently with experimental data of nanofluids containing aluminum oxide particles.

Convection heat transfer is recognized within nanofluids, but there is not enough research results published to develop a model that fully explains this behavior in nanofluids. Furthermore, several of the research papers available seem to contradict each other as some data shows an increase in convection as the particle volume fraction is increased, while other data shows deterioration in convective heat transfer as the particle density and concentration were increased.

Clustering still poses a problem in nanofluids even though the occurrence of agglomeration has decreased from the previous micrometer-sized particles suspensions. Various methods are currently used to keep particles from clustering together, but in the long run, it is inevitable. Clustering is a problem that must be solved before nanofluids can be considered for long-term practical uses. Although the increase in thermal conductivity would increase the efficiency of the systems where nanofluids are used, the life of the system may be decreased over time if particles begin to form clusters.

Nanofluids have the potential to open the doors to major advancements in many high-tech industries where limits on cooling have posed limits on innovation. Since all other cooling options have been exhausted, nanofluids are the only option left with the possibility of increasing heat transfer capabilities of current systems. However, a full understanding of the mechanisms behind the enhancement of thermal conductivity in nanofluids has not been reached and there is still disagreement between some of the experimental results. This lack of agreement has led to the generation of various models. Once a general model that fully explains the behavior of nanoparticle suspensions has been developed, steps can be taken towards practical uses. Moreover, better techniques for the dispersion of particles in fluids must be created so as to minimize clustering. When these objectives have been reached, nanofluids will enter the practical arenas of science in a more meaningful way.

At the present time, there is quite an amount of work going on to create synthetic nanofluids for various applications. This is evidenced by the number of patented nanofluids. However, the literatures on these are not generally available.

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