### Abstract

A two-dimensional analytical solution is derived for the three-omega method for measurement of thermal conductivity of materials with a fine wire. The analytical solution includes the wire heat capacity and the effect of heat losses from the ends of the wire. To derive the solution, finite Fourier transforms are applied in the direction parallel to the wire axis. The solution is compared with a one-dimensional solution and experimental data. It is found that heat losses from the wire ends have a significant effect on the 3ω components at low frequency and tend to be less important at high frequency. Moreover, it is shown that two-dimensional effects will be severe for nano-scale wires, even if the wire length-to-diameter ratio is very large.

Original language | English |
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Pages (from-to) | 833-850 |

Number of pages | 18 |

Journal | International Journal of Thermophysics |

Volume | 30 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

*International Journal of Thermophysics*,

*30*(3), 833-850. https://doi.org/10.1007/s10765-009-0572-8

**End effects in the three-omega method to measure gas thermal conductivity.** / Yusibani, E.; Woodfield, P. L.; Kohno, Masamichi; Shinzato, K.; Takata, Yasuyuki; Fujii, M.

Research output: Contribution to journal › Article

*International Journal of Thermophysics*, vol. 30, no. 3, pp. 833-850. https://doi.org/10.1007/s10765-009-0572-8

}

TY - JOUR

T1 - End effects in the three-omega method to measure gas thermal conductivity

AU - Yusibani, E.

AU - Woodfield, P. L.

AU - Kohno, Masamichi

AU - Shinzato, K.

AU - Takata, Yasuyuki

AU - Fujii, M.

PY - 2009/6/1

Y1 - 2009/6/1

N2 - A two-dimensional analytical solution is derived for the three-omega method for measurement of thermal conductivity of materials with a fine wire. The analytical solution includes the wire heat capacity and the effect of heat losses from the ends of the wire. To derive the solution, finite Fourier transforms are applied in the direction parallel to the wire axis. The solution is compared with a one-dimensional solution and experimental data. It is found that heat losses from the wire ends have a significant effect on the 3ω components at low frequency and tend to be less important at high frequency. Moreover, it is shown that two-dimensional effects will be severe for nano-scale wires, even if the wire length-to-diameter ratio is very large.

AB - A two-dimensional analytical solution is derived for the three-omega method for measurement of thermal conductivity of materials with a fine wire. The analytical solution includes the wire heat capacity and the effect of heat losses from the ends of the wire. To derive the solution, finite Fourier transforms are applied in the direction parallel to the wire axis. The solution is compared with a one-dimensional solution and experimental data. It is found that heat losses from the wire ends have a significant effect on the 3ω components at low frequency and tend to be less important at high frequency. Moreover, it is shown that two-dimensional effects will be severe for nano-scale wires, even if the wire length-to-diameter ratio is very large.

UR - http://www.scopus.com/inward/record.url?scp=67849116874&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67849116874&partnerID=8YFLogxK

U2 - 10.1007/s10765-009-0572-8

DO - 10.1007/s10765-009-0572-8

M3 - Article

AN - SCOPUS:67849116874

VL - 30

SP - 833

EP - 850

JO - International Journal of Thermophysics

JF - International Journal of Thermophysics

SN - 0195-928X

IS - 3

ER -