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Research Papers

Non-Fourier Heat Conduction in Carbon Nanotubes

[+] Author and Article Information
Hai-Dong Wang, Bing-Yang Cao

demgzy@tsinghua.edu.cn Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics,Tsinghua University, Beijing 100084, China

Zeng-Yuan Guo1

demgzy@tsinghua.edu.cn Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics,Tsinghua University, Beijing 100084, China

1

Corresponding author.

J. Heat Transfer 134(5), 051004 (Apr 13, 2012) (6 pages) doi:10.1115/1.4005634 History: Received April 12, 2010; Revised November 04, 2010; Published April 11, 2012; Online April 13, 2012

Fourier’s law is a phenomenological law to describe the heat transfer process. Although it has been widely used in a variety of engineering application areas, it is still questionable to reveal the physical essence of heat transfer. In order to describe the heat transfer phenomena universally, Guo has developed a general heat conduction law based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics according to Einstein’s mass–energy relation. The general law degenerates into Fourier’s law when the thermal inertia is neglected as the heat flux is not very high. The heat flux in carbon nanotubes (CNTs) may be as high as 1012 W/m2 . In this case, Fourier’s law no longer holds. However, what is estimated through the ratio of the heat flux to the temperature gradient by molecular dynamics (MD) simulations or experiments is only the apparent thermal conductivity (ATC); which is smaller than the intrinsic thermal conductivity (ITC). The existing experimental data of single-walled CNTs under the high-bias current flows are applied to study the non-Fourier heat conduction under the ultrahigh heat flux conditions. The results show that ITC and ATC are almost equal under the low heat flux conditions when the thermal inertia is negligible, while the difference between ITC and ATC becomes more notable as the heat flux increases or the temperature drops.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Variation of Grüneisen coefficient of phonon gas versus the degree of compression

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Figure 2

An electrically heated CNT suspended between two electrodes with a typical parabolic temperature profile

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Figure 3

The drift velocity and thermal sound speed in the CNT

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Figure 4

Temperature profiles calculated based on the general law and Fourier’s law

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Figure 5

Variation of the average temperature of the nanotube versus the heating power

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Figure 6

Average temperatures based on the general law and Fourier’s law using the existing experimental data from Ref. [9]

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Figure 7

ITC calculated from Ref. [9] under T0  = 250 K

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Figure 8

ITC calculated from Ref. [9] under T0  = 300 K

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Figure 9

ITC calculated from Ref. [9] under T0  = 350 K

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Figure 10

ITC calculated from Ref. [9] under T0  = 400 K

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Figure 11

ATC with varied temperature and heating power

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Figure 12

ITC with varied temperature and heating power

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