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Acta Applicandae Mathematicae

, Volume 132, Issue 1, pp 15–25 | Cite as

A Study of Linear Waves Based on Extended Thermodynamics for Rarefied Polyatomic Gases

  • Takashi ArimaEmail author
  • Shigeru Taniguchi
  • Tommaso Ruggeri
  • Masaru Sugiyama
Article

Abstract

We study the dispersion relation for sound in rarefied polyatomic gases basing on the recently developed theory of extended thermodynamics (ET) for both dense and rarefied polyatomic gases. For hydrogen and deuterium gases in a wide temperature range where the rotational and vibrational modes in a molecule play a role, we compare the dispersion relations with those obtained in experiments and by the classical Navier–Stokes Fourier theory. From the comparison with experiments, we estimate the bulk viscosity and evaluate its temperature dependence. We study the characteristics of attenuation in a gas which has a larger relaxation time related to the dynamic pressure than the other relaxation times related to the shear stress and the heat flux by adopting the ET theory with 6 fields.

Keywords

Extended thermodynamics Rarefied polyatomic gas Dispersion relation for sound Phase velocity and absorption Bulk viscosity Relaxation time 

Mathematics Subject Classification (2000)

76J20 82C35 76N15 76P05 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Takashi Arima
    • 1
    Email author
  • Shigeru Taniguchi
    • 2
  • Tommaso Ruggeri
    • 3
  • Masaru Sugiyama
    • 2
  1. 1.Department of Mechanical Engineering, Faculty of EngineeringKanagawa UniversityYokohamaJapan
  2. 2.Department of Control and Information Systems EngineeringKitakyushu National College of TechnologyKitakyushuJapan
  3. 3.Department of Mathematics & Research Center of Applied Mathematics (CIRAM)University of BolognaBolognaItaly

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