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Research Papers: Micro/Nanoscale Heat Transfer

# Thermal Conductivity Equations Based on Brownian Motion in Suspensions of Nanoparticles (Nanofluids)

[+] Author and Article Information
Bao Yang

Nanoscale Heat Transfer and Energy Conversion Laboratory, Mechanical Engineering Department, University of Maryland, College Park, MD 20742baoyang@umd.edu

J. Heat Transfer 130(4), 042408 (Mar 18, 2008) (5 pages) doi:10.1115/1.2789721 History: Received January 24, 2007; Revised March 04, 2007; Published March 18, 2008

## Abstract

Thermal conductivity equations for the suspension of nanoparticles (nanofluids) have been derived from the kinetic theory of particles under relaxation time approximations. These equations, which take into account the microconvection caused by the particle Brownian motion, can be used to evaluate the contribution of particle Brownian motion to thermal transport in nanofluids. The relaxation time of the particle Brownian motion is found to be significantly affected by the long-time tail in Brownian motion, which indicates a surprising persistence of particle velocity. The long-time tail in Brownian motion could play a significant role in the enhanced thermal conductivity in nanofluids, as suggested by the comparison between the theoretical results and the experimental data for the $Al2O3$-in-water nanofluids.

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## Figures

Figure 1

A nanoparticle with coordinates (Xi, Yi, Zi) moves at velocity up toward the Z=0 plane. The origin of the local coordinate system (x, y, z) is at the center of the moving particle. The hydrodynamic layer thickness is lB.

Figure 2

Stokes flow around a spherical particle moving at up in the fluid. The origin of the local spherical coordinate system is at the center of the particle.

Figure 3

The velocity autocorrelation function R(t) evaluated using Eq. 13 (heavy particle approximation), Eq. 15 (neutrally buoyant particle approximation), and Eq. 16 (general particle, M=0.999967). ρp=3.9g∕cm3 (alumina), ρf=1.0g∕cm3 (water), and a=23.5nm.

Figure 4

Comparison of the thermal conductivity equations with experimental data for nanofluids consisting of Al2O3 nanoparticles dispersed in water, for varying temperatures and particle diameters. Experimental data are from Ref. 5.

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