Research Papers: Micro/Nanoscale Heat Transfer

Instability of Nanofluids in Natural Convection

[+] Author and Article Information
D. Y. Tzou

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211tzour@missouri.edu

J. Heat Transfer 130(7), 072401 (May 16, 2008) (9 pages) doi:10.1115/1.2908427 History: Received March 06, 2007; Revised October 23, 2007; Published May 16, 2008

Instability of natural convection in nanofluids is investigated in this work. As a result of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be much lower, by one to two orders of magnitude, as compared to that for regular fluids. The highly promoted turbulence, in the presence of nanoparticles for as little as 1% in volume fraction, significantly enhances heat transfer in nanofluids, which may be much more pronounced than the enhancement of the effective thermal conductivity alone. Seven dominating groups are extracted from the nondimensional analysis. By extending the method of eigenfunction expansions in conjunction with the method of weighted residuals, closed-form solutions are derived for the Rayleigh number to justify such remarkable change by the nanoparticles at the onset of instability.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The various surfaces bounding the nanofluids

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Figure 4

Effects of (a) ΔT=T0−T1, (b) Δϕ=ϕ0−ϕ1, (c) Rρ, and (d) RN on the Rayleigh number (Ra): a=π∕√2≅2.22144 in all cases; (e) effects of NBT on the Rayleigh number (Ra): a=π∕√2≅2.22144.

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Figure 3

Water-based nanofluids with alumina and copper nanoparticles with ΔT=10K and Δϕ=1vol%. Al2O3: β=6×10−31∕K, Le=8×105, NBT=0.2, Rρ=4, RN=30.18; Cu: β=6×10−41∕K, Le=7×105, NBT=2, Rρ=9, RN=3.018. Critical Rayleigh number occurs at ac=π∕√2≅2.22144.

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Figure 2

Comparisons of the fundamental mode (m=1) for F(z): full expression shown by Eq. 45 and approximate expression shown by Eq. 47



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