### Abstract

The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic
boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain
are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as
hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that
describes viscothermal wave propagation is needed to model such devices.
For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can
range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with
negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately
described by the low reduced frequency model. This model’s major drawback is that it is only defined for
simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries.
To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the
LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to
the LRF model, the viscothermal finite element can be used to analyze complicated geometries.
This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in
which the results of the finite element models are compared to measurements.

Original language | English |
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Title of host publication | Proceedings of ISMA2008 |

Subtitle of host publication | International Conference on Noise and Vibration Engineering |

Editors | P. Sas, B. Bergen |

Place of Publication | Leuven |

Publisher | Katholieke Universiteit Leuven |

Pages | 4271-4278 |

Number of pages | 8 |

ISBN (Print) | 978 9073802865 |

Publication status | Published - 15 Sep 2008 |

Event | 2008 International Conference on Noise and Vibration Engineering, ISMA 2008 - Leuven, Belgium Duration: 15 Sep 2008 → 17 Sep 2008 http://past.isma-isaac.be/isma2008 |

### Conference

Conference | 2008 International Conference on Noise and Vibration Engineering, ISMA 2008 |
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Abbreviated title | ISMA |

Country | Belgium |

City | Leuven |

Period | 15/09/08 → 17/09/08 |

Internet address |

### Keywords

- IR-70026
- METIS-255513

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## Cite this

Kampinga, W. R., Wijnant, Y. H., & de Boer, A. (2008). A finite element for viscothermal wave propagation. In P. Sas, & B. Bergen (Eds.),

*Proceedings of ISMA2008: International Conference on Noise and Vibration Engineering*(pp. 4271-4278). Leuven: Katholieke Universiteit Leuven.