Rational Extended Thermodynamics

  • Ingo Müller
  • Tomasso Ruggeri

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 37)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ingo Müller, Tomasso Ruggeri
    Pages 1-7
  3. Ingo Müller, Tomasso Ruggeri
    Pages 27-49
  4. Ingo Müller, Tomasso Ruggeri
    Pages 79-104
  5. Ingo Müller, Tomasso Ruggeri
    Pages 105-154
  6. Ingo Müller, Tomasso Ruggeri
    Pages 155-169
  7. Ingo Müller, Tomasso Ruggeri
    Pages 171-196
  8. Ingo Müller, Tomasso Ruggeri
    Pages 197-220
  9. Ingo Müller, Tomasso Ruggeri
    Pages 221-264
  10. Ingo Müller, Tomasso Ruggeri
    Pages 265-275
  11. Wolf Weiss
    Pages 277-308
  12. H. Struchtrup
    Pages 309-341
  13. H. Struchtrup
    Pages 343-355
  14. Ingo Müller, Tomasso Ruggeri
    Pages 357-365
  15. Ingo Müller, Tomasso Ruggeri
    Pages 367-377
  16. Back Matter
    Pages 379-397

About this book

Introduction

Ordinary thermodynamics provides reliable results when the thermodynamic fields are smooth, in the sense that there are no steep gradients and no rapid changes. In fluids and gases this is the domain of the equations of Navier-Stokes and Fourier. Extended thermodynamics becomes relevant for rapidly varying and strongly inhomogeneous processes. Thus the propagation of high­ frequency waves, and the shape of shock waves, and the regression of small-scale fluctuation are governed by extended thermodynamics. The field equations of ordinary thermodynamics are parabolic while extended thermodynamics is governed by hyperbolic systems. The main ingredients of extended thermodynamics are • field equations of balance type, • constitutive quantities depending on the present local state and • entropy as a concave function of the state variables. This set of assumptions leads to first order quasi-linear symmetric hyperbolic systems of field equations; it guarantees the well-posedness of initial value problems and finite speeds of propaga­ tion. Several tenets of irreversible thermodynamics had to be changed in subtle ways to make extended thermodynamics work. Thus, the entropy is allowed to depend on nonequilibrium vari­ ables, the entropy flux is a general constitutive quantity, and the equations for stress and heat flux contain inertial terms. New insight is therefore provided into the principle of material frame indifference. With these modifications an elegant formal structure can be set up in which, just as in classical thermostatics, all restrictive conditions--derived from the entropy principle-take the form of integrability conditions.

Keywords

Boltzmann equation acoustics dynamics entropy evolution experiment heat kinetic theory mathematics metals quality radiation scattering thermodynamics wave

Authors and affiliations

  • Ingo Müller
    • 1
  • Tomasso Ruggeri
    • 2
  1. 1.FB 6 — Institut für VerfahrenstechnikTechnische Universität, BerlinGermany
  2. 2.Departimento de Matematica C.I.R.A.M. Centro Interdipartimentelle di Ricerca per le Applicazioni della MatematicaUniversita degli Studi di BolognaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2210-1
  • Copyright Information Springer-Verlag New York 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7460-5
  • Online ISBN 978-1-4612-2210-1
  • Series Print ISSN 0081-3877
  • About this book