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Rational Extended Thermodynamics beyond the Monatomic Gas

  • Tommaso Ruggeri
  • Masaru Sugiyama

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Tommaso Ruggeri, Masaru Sugiyama
    Pages 1-32
  3. Mathematical Structure and Waves

    1. Front Matter
      Pages 33-33
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 35-53
    3. Tommaso Ruggeri, Masaru Sugiyama
      Pages 55-76
  4. Survey of Rational Extended Thermodynamics of Monatomic Gas

    1. Front Matter
      Pages 77-77
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 79-106
  5. RET of Polyatomic Gas and Dense Gas with 14 Fields

    1. Front Matter
      Pages 107-107
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 109-137
    3. Tommaso Ruggeri, Masaru Sugiyama
      Pages 139-151
  6. Applications of the ET14 Theory

    1. Front Matter
      Pages 153-153
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 155-171
    3. Tommaso Ruggeri, Masaru Sugiyama
      Pages 173-192
    4. Tommaso Ruggeri, Masaru Sugiyama
      Pages 193-210
  7. Maximum Entropy Principle and Nesting Theories of Many Moments

    1. Front Matter
      Pages 211-211
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 213-241
  8. ET6: A Theory of Far-from-Equilibrium Thermodynamics

    1. Front Matter
      Pages 243-243
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 271-278
    3. Tommaso Ruggeri, Masaru Sugiyama
      Pages 279-291
    4. Tommaso Ruggeri, Masaru Sugiyama
      Pages 293-298
    5. Tommaso Ruggeri, Masaru Sugiyama
      Pages 299-305
  9. Mixture of Gases with Multi-Temperature

    1. Front Matter
      Pages 307-307
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 309-337
  10. Maxwellian Iteration and Objectivity

    1. Front Matter
      Pages 351-351
    2. Tommaso Ruggeri, Masaru Sugiyama
      Pages 353-361
    3. Tommaso Ruggeri, Masaru Sugiyama
      Pages 363-364
  11. Back Matter
    Pages 365-376

About this book

Introduction

Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases.
This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas, and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule’s internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and, in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction, and the results are compared with experimental data.
The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors, and nano-scale phenomena.

Keywords

Continuum mechanics and kinetic theory Extended thermodynamic Nonequilibrium thermodynamics Rarefied polyatomic gas and mixture of gases Symmetric hyperbolic systems

Authors and affiliations

  • Tommaso Ruggeri
    • 1
  • Masaru Sugiyama
    • 2
  1. 1.Dept. of Mathematics and Res. Center of Applied Mathematics AM2University of BolognaBolognaItaly
  2. 2.Graduate School of EngineeringNagoya Institute of TechnologyNagoyaJapan

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