### Abstract

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 10^{12} W/m ^{2}. 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.

Original language | English |
---|---|

Article number | 051004 |

Journal | Journal of Heat Transfer |

Volume | 134 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jan 1 2012 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of Heat Transfer*,

*134*(5), [051004]. https://doi.org/10.1115/1.4005634

**Non-fourier heat conduction in carbon nanotubes.** / Wang, Hai Dong; Cao, Bing Yang; Guo, Zeng Yuan.

Research output: Contribution to journal › Article

*Journal of Heat Transfer*, vol. 134, no. 5, 051004. https://doi.org/10.1115/1.4005634

}

TY - JOUR

T1 - Non-fourier heat conduction in carbon nanotubes

AU - Wang, Hai Dong

AU - Cao, Bing Yang

AU - Guo, Zeng Yuan

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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/m 2. 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.

AB - 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/m 2. 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.

UR - http://www.scopus.com/inward/record.url?scp=84859913091&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859913091&partnerID=8YFLogxK

U2 - 10.1115/1.4005634

DO - 10.1115/1.4005634

M3 - Article

AN - SCOPUS:84859913091

VL - 134

JO - Journal of Heat Transfer

JF - Journal of Heat Transfer

SN - 0022-1481

IS - 5

M1 - 051004

ER -