### 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 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 ultra-high 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 |
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Title of host publication | Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009 |

Pages | 111-117 |

Number of pages | 7 |

DOIs | |

Publication status | Published - Jul 12 2010 |

Event | ASME 2009 Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009 - Shanghai, China Duration: Dec 18 2009 → Dec 21 2009 |

### Publication series

Name | Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009 |
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Volume | 3 |

### Other

Other | ASME 2009 Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009 |
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Country | China |

City | Shanghai |

Period | 12/18/09 → 12/21/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Fluid Flow and Transfer Processes

### Cite this

*Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009*(pp. 111-117). (Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009; Vol. 3). https://doi.org/10.1115/MNHMT2009-18182

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009.*Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009, vol. 3, pp. 111-117, ASME 2009 Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009, Shanghai, China, 12/18/09. https://doi.org/10.1115/MNHMT2009-18182

}

TY - GEN

T1 - Non-fourier heat conduction in carbon nanotubes

AU - Wang, Hai Dong

AU - Cao, Bing Yang

AU - Guo, Zeng Yuan

PY - 2010/7/12

Y1 - 2010/7/12

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 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 ultra-high 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 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 ultra-high 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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UR - http://www.scopus.com/inward/citedby.url?scp=77954342025&partnerID=8YFLogxK

U2 - 10.1115/MNHMT2009-18182

DO - 10.1115/MNHMT2009-18182

M3 - Conference contribution

AN - SCOPUS:77954342025

SN - 9780791843895

T3 - Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009

SP - 111

EP - 117

BT - Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009

ER -