Thermal Conductivity of Nanofluids

In the last decades, scientists have proposed several methods to improve the heat transfer, and one of the most popular methods is to enhance the thermal conductivity of heat transfer fluids. As shown in Table 1.1 [2], the thermal conductivity of solid is much higher than that of liquids. In order to increase the thermal conductivity of heat transfer fluids, originally, the solid particles had been added in the heat transfer fluids. Since Maxwell prediction model [11] was proposed over one hundred years ago, considerable experimental and theoretical studies of suspensions containing solid particles have been proposed. However, due to the large size and higher density of solid particles, the solid particles cannot suspend in the liquid for a long time, and the precipitation may result in the wear of container and additional flow resistance. For the reasons mentioned above,

the fluids containing the large-sized particles are not practical.

Today, the nano-sized particles with average diameter below 50 nm can be produce by the novel nanotechnology. The fluids in which nanoparticles suspended are named

“nanofluids” by Choi [1] in 1995. Comparing to the conventional heat transfer fluids and the fluids containing microparticles, nanofluids have better performance. The smaller size and larger relative surface area of nanoparticles results in great enhancement of heat transfer and help nanoparticles suspend stably in fluids and also improve the wearing problem of container. For the reason mentioned above, nanofluids can be regarded as the next-generation heat transfer fluids and bring the smaller heat transfer systems. Although the use of nanofluids appears promising, however, there are some factors hinder the development of nanofluids [12], such as the lack of agreement between results obtained in different laboratories, the often poor characterization of suspensions and the lack of theoretical understanding of the mechanisms responsible for the observed changes in properties.

The metal and oxide of Al and Cu are the most commonly used materials of nanoparticles. Almost all the experimental results have indicated the enhancement of thermal conductivity of nanofluids. Eastman et al. [2] suspended Al2O3, CuO and Cu nanoparticles in water and HE-200 oil and got 60% enhancement of thermal conductivity with 5% volume fraction of nanoparticles. Lee et al. [3] suspended CuO

and Al2O3 nanoparticles of different diameters in water and EG and obtain higher thermal conductivity. It also suggested that the size of nanoparticles should be a dominant factor of enhancement on thermal conductivity. Wang et al. [4] suspended Al2O3 and CuO nanoparticles in water, EG, vacuum pump oil and engine oil.

Experimental results indicated that the high thermal conductivity of nanofluids is dependent on the structure and microscopic motion of nanoparticles. Xuan and Li [5]

suspended Cu nanoparticles in water and transformer oil and found that Cu nanoparticles in transformer oil had higher enhancement on thermal conductivity than those in water. Xie et al. [6] suspended different kinds of Al2O3 nanoparticles in water and EG and found that the increase in difference between the pH value of nanofluids and isoelectric point of Al2O3 nanoparticles. And the enhancement on thermal conductivity highly depended on the specific surface area (SSA) of nanoparticles.

Eastman et al. [7] suspended Cu nanoparticles of less than 10 nm size in EG and obtained 40% enhancement on thermal conductivity with 0.3% volume fraction of Cu nanoparticles. It indicated that the high SSA should be an important factor and the additive acid may help nanoparticles suspend well.

There are also other materials of nanoparticles applied. Hong et al. [13] suspended Fe nanoparticles in EG and obtained the higher enhancement on thermal conductivity than those of Cu nanofluids. The experimental results showed the non-linearly increase

of thermal conductivity with increase of nanoparticles volume fraction. They also investigated the effect of clustering of Fe nanoparticles on the thermal conductivity of nanofluids and found that the agglomeration of Fe nanoparticles influences the thermal conductivity of nanofluids [14]. Murshed et al. [15] suspended TiO2 nanoparticles of rod shape and spherical shape in water and found that the size and shape of nanoparticles influence the thermal conductivity of nanofluids. Xie et al. [16, 17]

suspended SiC nanoparticles of 26 nm and 0.6 μm diameters in water and EG and found that the nanofluids with the same particles in different base fluid had the same enhancement on thermal conductivity, which differ from Lee et al. [3]. And the results showed that Hamilton-Crosser model [18] predicted the thermal conductivity of 0.6 μm SiC nanofluids precisely but underestimated that of 26 nm SiC nanofluids.

One of important factors, temperature, had also been investigated. Das et al. [19]

suspended Al2O3 and CuO nanoparticles in water and observed that thermal conductivity of nanofluids increased 2 to 4 times with the temperature range of 21℃ to 52℃. They also mention that the motion of nanoparticles could be a probable factor for the enhancement on thermal conductivity. Li and Peterson [20] suspended CuO and Al2O3 in water. The results indicated that the material, diameter, volume fraction and temperature are significant factors. They also derived simple linear regression of two factors. Patel et al. [21] suspended Au and Ag coating citrate and thiolate of low volume

fraction in water and toluene based fluids and indicated that there are important factors related to the motion of nanoparticles, since the great enhancement occurs with the temperature range 30-60℃.

Experimental results mentioned above shows the unusual enhancement on thermal conductivity which the conventional prediction model fails to explain. To explain the reason for the anomalous enhancement on thermal conductivity of nanofluids, Keblinski et al. [22] and Eastman et al. [23] proposed four possible mechanisms: Brownian motion of nanoparticles, molecular-level layering of the liquid at the liquid/particle interface, the nature of heat transport in nanoparticles, and the effect of cluster of nanoparticles. Many scientists adopted the concept of liquid/solid interface layer to explain the anomalous enhancement on thermal conductivity of nanofluids. Yu and Choi [24, 25] proposed the models based on Maxwell model and Hamilton model which consider the liquid molecular layer around the nanoparticles. But Xue et al. [26] applied molecular dynamic simulation to show that the liquid layer had no effect on thermal transport properties. Koo and Kleinstreuer [27] found that the impact of Brownian motion is much more significant than that of thermophoretic and osmophoretic motion.

Evans et al. [28] proposed that the hydrodynamics effects associated with Brownian motion have only a minor effect on the thermal conductivity of nanofluids. Besides the Brownian motion, liquid layer and agglomeration, Lee et al. [29] investigated the effect

of surface charge state of nanoparticles and showed that the pH value of nanofluids strongly affected the thermal conductivity of nanofluids. Based on these postulated mechanisms, numerous theoretical studies had also proposed to predict the thermal conductivity of nanofluids. Most of these studies are sourced from the classic model of Maxwell [11] of which the effective thermal conductivity, keff, is given by:

φ

where kp is the thermal conductivity of particles, kb is the thermal conductivity of base fluids and φ is the volume fraction of particles. Yu and Choi [24] proposed a modified Maxwell model to present the effect of the liquid layer around nanoparticles. The thermal conductivity of particles kp in (1.1) is replaced with the modified thermal conductivity of particles. They also proposed a modified Hamilton-Crosser model including the liquid layer for non-spherical particles [25]. There are also other modified models including the effect of liquid layer around particles [30-32]. However, these prediction models fail to predict some cases showed the great enhancement on thermal conductivity at low concentrations [21]. According to previous studies [19-21], the thermal conductivity of nanofluids depends strongly on temperature. The Brownian motion of nanoparticles may be a key factor ruling the thermal properties of nanofluids.

Xuan et al. [33] proposed a modified model based on the Maxwell model with

weak and not in agreement with the study of Das et al. [19]. Kumar et al. [34] proposed a model based on the Stokes-Einstein formula and depended strongly on temperature.

Bhattacharya et al. [35] developed a technique based on parallel model and using the Brownian motion simulation. Jang and Choi [36, 37] proposed a model based on the parallel model and involving four modes of energy transport in nanofluids: the collision between base fluid molecules, the thermal diffusion in nanoparticles involving the Kapitza resistance [38], the collision between nanoparticles due to Brownian motion, and the thermal interactions of dynamic or dancing nanoparticles with base fluid molecules. Prasher [39] proposed a model based on the Maxwell model and including the convection of liquid near nanoparticles due to Brownian motion. Koo and Kleinstreuer [40, 41] proposed a model based on the Maxwell and taking the effects of particle size, particle volume fraction and temperature dependence as well as properties of base liquid and particle phase into consideration by considering surrounding liquid traveling with randomly moving nanoparticles. Although many possible mechanisms and theoretical researches are proposed, no models can predict the thermal conductivity precisely and satisfactorily for all nanofluids. It still needs further understanding to develop a comprehensive and convincing model.