Research Papers: Micro/Nanoscale Heat Transfer

The Classical Nature of Thermal Conduction in Nanofluids

[+] Author and Article Information
Jacob Eapen

Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695jacob.eapen@ncsu.edu

Roberto Rusconi

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

Roberto Piazza

Dipartimento di Ingegneria Nucleare, Politecnico di Milano, Milano 20133, Italy

Sidney Yip

Department of Nuclear Science and Engineering and Department of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Heat Transfer 132(10), 102402 (Jul 23, 2010) (14 pages) doi:10.1115/1.4001304 History: Received December 30, 2008; Revised December 18, 2009; Published July 23, 2010; Online July 23, 2010

We show that a large set of nanofluid thermal conductivity data falls within the upper and lower Maxwell bounds for homogeneous systems. This indicates that the thermal conductivity of nanofluids is largely dependent on whether the nanoparticles stay dispersed in the base fluid, form large aggregates, or assume a percolating fractal configuration. The experimental data, which are strikingly analogous to those in most solid composites and liquid mixtures, provide strong evidence for the classical nature of thermal conduction in nanofluids.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

A two-dimensional representation of (a) a series mode and (b) a parallel mode of thermal conduction in a binary nanofluid. Note that a typical nanofluid system is not inhomogeneous, as shown.

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Figure 2

A two-dimensional representation of the nanofluid configuration for the (a) lower and (b) upper Maxwell bounds

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Figure 3

Mathematical abstraction and physical realization for the Maxwell upper bound for dilute nanofluids

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Figure 4

THW data for Ludox (ρ∼2200 kg/m3, d=32 nm), MFA (ρ∼2140 kg/m3, d=44 nm), Al2O3(ρ∼4000 kg/m3, d=38 nm), and CuO (ρ∼6300 kg/m3, d=29 nm) suspensions, plotted as a function of βϕ. The deviation of microconvection model from the Maxwell lower bound for Al2O3 and CuO are comparable to the experimental uncertainty.

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Figure 5

Typical instantaneous and thermophoretic drift velocities in the z-direction of a 100 atom solid nanoparticle in a generic LJ fluid with NEMD simulations (97). The rms velocity of the nanoparticle (0.1) is very close to V=kBT/m.

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Figure 6

Classical bounds for thermal conductivity in solid composites. The thin solid and thin dashed-dotted lines denote enhancements in thermal conductivity (or diffusivity) with the series and parallel modes, respectively. The upper Maxwell bound is delineated by the thick solid line while the lower Maxwell bound is given by the thick dashed line. The experimental data are represented by symbols. A fifth bound given by (1−3ϕ/2) for polyethylene–Cu, polyethylene–Zn, and ZnS–diamond (dotted line) denotes the limiting condition α→∞. Table 1 in the Appendix gives the numerical values used in the calculation of classical bounds. Experimental data are taken from 55, 56, and 116-120.

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Figure 7

Classical bounds for thermal conductivity in liquid mixtures. The line and symbol codes are the same as in Fig. 6 with the addition of a thin solid line between the Maxwell bounds, denoting the unbiased or Bruggeman model. Table 2 in the Appendix gives the numerical values used in the calculation of classical bounds. Experimental data are taken from 123, 124, and the current study.

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Figure 8

Thermal conductivity of Kerosene–Fe3O4 magnetic nanofluid, as a function of the external magnetic field (B) in the direction of the heat flux (data from Ref. 45). The configuration of the nanoparticles range from dispersed arrangement (at low B) to the chainlike formation in the direction of the heat flux (at high B). The line and symbol codes are the same as in Fig. 6. The classical bounds are calculated based on the data listed in Table 3 of the Appendix.

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Figure 9

Thermal conductivity of water–Fe magnetic nanofluid as a function of the external magnetic field (B) perpendicular to the direction of the heat flow (data from Ref. 125). The nanoparticles are dispersed or form clusters perpendicular to the heat flux. The dashed and solid lines correspond to the lower Maxwell and series bounds, respectively. The classical bounds are calculated based on the data listed in Table 3 of the Appendix.

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Figure 10

The classical bounds for thermal conductivity/diffusivity in nanofluids. The line and symbol codes are the same as in Fig. 6. Since thermal conductivities of the dispersed media (nanoparticles) are generally not measured or reported, representative values listed in Table 3 of the Appendix are used to compute for the classical bounds. It is observed that κp⪢κf for most nanofluids. The bounds shown are for a given temperature, while the experimental data shown may not correspond to the same temperature. This is largely of no consequence, given the rather small deviation in base fluid thermal conductivity in the range of experimentation. The assessment that most nanofluids respect the classical bounds, therefore, remains unchanged even after factoring in different experimental temperatures, and uncertainties in the experimental methods (46) and thermal conductivities. Experimental data are taken from 8-11, 13-15, 17, 18, 26-29, 33, 34, 36, 41, 43, 44, 91, and 131-137.

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Figure 11

Temperature dependence of magnetite nanofluid thermal conductivity (6). While no strong correlation is generally observed to the thermal motion of the nanoparticles, there appears to be a dependence on the thermal conductivity variation of the base fluid. The base fluid (transformer oil) thermal conductivity decreases slightly with temperature for the range of temperatures shown (6).



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