Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids)

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Abstract

Recent measurements on nanofluids have demonstrated that the thermal conductivity increases with decreasing grain size. However, such increases cannot be explained by existing theories. We explore four possible explanations for this anomalous increase: Brownian motion of the particles, molecular-level layering of the liquid at the liquid/particle interface, the nature of heat transport in the nanoparticles, and the effects of nanoparticle clustering. We show that the key factors in understanding thermal properties of nanofluids are the ballistic, rather than diffusive, nature of heat transport in the nanoparticles, combined with direct or fluid-mediated clustering effects that provide paths for rapid heat transport.

Introduction

It has long been recognized that suspensions of solid particles in liquids have great potential as improved heat-management fluids. The key idea is to exploit the very high thermal conductivities of solid particles, which can be hundreds or even thousands of times greater than those of conventional heat-transfer fluids such as water and ethylene glycol. In this context, numerous theoretical and experimental studies of the effective thermal conductivity of solid–particle suspensions have been conducted dating back to the classic work of Maxwell [1]. However, the vast majority of these studies have been confined to suspensions with millimeter- or micron-sized particles. Although such suspensions do indeed display the desired increase in thermal conductivity, they suffer from stability and rheological problems. In particular, the particles tend to quickly settle out of suspension and thereby cause severe clogging, particularly in mini and microchannels. However, a notable exception is provided by magnetic colloids [2] (involving solutions of ferromagnetic nanoparticles), which appear to be stable because of their very small particle size.

A novel approach to engineering fluids with better heat-transfer properties, based on the rapidly emerging field of nanotechnology, has recently been proposed [3]. In particular, it was demonstrated that solid nanoparticle colloids (i.e., colloids in which the grains have dimensions of ≈10–40 nm) are extremely stable and exhibit no significant settling under static conditions, even after weeks or months [4]. Furthermore, the enhancement of thermal-transport properties of such “nanofluids” was even greater than that of suspensions of coarse-grained materials [5]. For example, the use of Al2O3 particles ≈13 nm in diameter at 4.3% volume fraction increased the thermal conductivity of water under stationary conditions by 30% [6]. Use of somewhat larger particles (≈40 nm in diameter) only led to an increase of less than ≈10% at the same particle volume fraction [5]; more in accord with theoretical predictions [7]. An even greater enhancement was recently reported for Cu nanofluids, where just a 0.3% volume fraction of 10 nm Cu nanoparticles led to an increase of up to 40% in thermal conductivity [8], a result that is more than an order of magnitude above the increase predicted by macroscopic theory. Currently, the origin of such remarkable increases in the thermal conductivity of nanofluids eludes theoretical understanding.

The existing understanding of the effective thermal conductivity of composites and mixtures is derived from continuum-level phenomenological formulations that typically incorporate only the particle shape and volume fraction as variables and assume diffusive heat transport in both liquid and solid phases; no effects of solid/liquid interfaces or particle mobility are taken into account. This approach, while providing a good description of systems with micrometer or larger-size particles, fails to describe thermal transport in nanofluids.

In this article we examine the various factors that could potentially be responsible for the inadequacy of macroscopic analysis in the description of heat transfer in nanofluids and expose new mechanisms capable of explaining the experimentally observed enhanced thermal conductivity of nanofluids. We limit our considerations to stationary nanofluids, because they already exhibit unusual thermal properties; we do not consider effects of macroscopic flow or convection on heat transfer in nanofluids [9], [10]. The conclusions of our arguments are supported by the results of atomic-level molecular dynamics (MD) simulations that do not require the assumptions that underlie continuum-level formulations, and are thus well suited for studies of nanofluids. Our analysis and simulation results provide significant insights into the unusual heat transport properties of solid nanoparticle colloids and allow us to formulate the roadmap of an integrated experimental/modeling program toward developing a systematic understanding of the remarkable thermal transport properties of nanofluids.

Section snippets

Macroscopic theory of heat transport in composites

A large body of theoretical work is available on the effective thermal conductivity of two- or multi-component materials, e.g., the approaches of Hamilton and Crosser (HC) [7], and others [11], [12], [13]. The key assumption of such theoretical approaches is that the heat transport in each component is described by a diffusion equation [14], which in terms of the temperature field T assumes the formTt=χ∇2T,where χ is the thermometric conductivity defined as [14]χ=k/ρcp,where k is thermal

Potential mechanisms of enhanced heat conduction in nanofluids

Based on the above comparison with experimental results, one must conclude that the macroscopic theory of heat transport in composite materials fails for the case of nanofluids. In the following, we examine a comprehensive list of the factors that are potentially responsible for the inadequacy of the theory. First, we discuss the possibility that the enhancement of thermal conductivity arises from the Brownian motion of the particles. Second, we analyze how much of an increase in the thermal

Molecular-level simulations

In the previous section, we used simple physical arguments to place upper limits on the possible effects that various mechanisms could have on enhancing thermal transport. To investigate the effects in more detail, a more sophisticated approach, such as molecular simulation, is required. To illustrate how molecular-level simulation is capable of shedding light on heat transport in nanofluids we present here results of our MD simulations that are related to the issues of Brownian motion and heat

Discussion and outlook

In this paper, we have taken the first steps to developing a fundamental understanding of heat transport in solid nanoparticle colloids under stationary conditions. Most important, we have evaluated the extent to which four specific mechanisms could contribute to the thermal conductivity. Although these are the four most obvious mechanisms (to us), we cannot exclude the possibility that others may be important also. While the role Brownian motion appears not to be important, an understanding of

Acknowledgements

This work was supported by US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. W-31-109-Eng-38. The support and encouragement of Dr. Robert Price are very much appreciated. PK was also supported by the Petroleum Research Fund, Grant No. PRF 36305-G9.

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