Rational extended thermodynamics

1. Front Matter

   Pages i-xv

   PDF

2. Tour d’Horizon

   • Ingo Müller, Tomasso Ruggeri

   Pages 1-7

3. Early Version of Extended Thermodynamics and Kinetic Theory of Gases

   • Ingo Müller, Tomasso Ruggeri

   Pages 9-26

4. Formal Structure of Extended Thermodynamics

   • Ingo Müller, Tomasso Ruggeri

   Pages 27-49

5. Extended Thermodynamics of Viscous, Heat-Conducting Monatomic Gases

   • Ingo Müller, Tomasso Ruggeri

   Pages 51-77

6. Thermodynamics of Mixtures of Euler Fluids

   • Ingo Müller, Tomasso Ruggeri

   Pages 79-104

7. Relativistic Extended Thermodynamics of Gases

   • Ingo Müller, Tomasso Ruggeri

   Pages 105-154

8. Extended Thermodynamics of Reacting Mixtures

   • Ingo Müller, Tomasso Ruggeri

   Pages 155-169

9. Waves in Extended Thermodynamics

   • Ingo Müller, Tomasso Ruggeri

   Pages 171-196

10. Extended Thermodynamics of Moments

    • Ingo Müller, Tomasso Ruggeri

    Pages 197-220

11. Extended Thermodynamics and Light Scattering

    • Ingo Müller, Tomasso Ruggeri

    Pages 221-264

12. Testing Extended Thermodynamics by Sound

    • Ingo Müller, Tomasso Ruggeri

    Pages 265-275

13. Structure of Shock Waves

    • Wolf Weiss

    Pages 277-308

14. Extended Thermodynamics of Radiation

    • H. Struchtrup

    Pages 309-341

15. Extended Thermodynamics of Phonons

    • H. Struchtrup

    Pages 343-355

16. Kinetic Theory and Extended Thermodynamics of Metal Electrons

    • Ingo Müller, Tomasso Ruggeri

    Pages 357-365

17. Toward Extended Thermodynamics of Viscoelastic Fluids

    • Ingo Müller, Tomasso Ruggeri

    Pages 367-377

18. Back Matter

    Pages 379-397

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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.

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

• FB 6 — Institut für Verfahrenstechnik, Technische Universität, Berlin, Germany

  Ingo Müller

• Departimento de Matematica C.I.R.A.M. Centro Interdipartimentelle di Ricerca per le Applicazioni della Matematica, Universita degli Studi di Bologna, Italy

  Tomasso Ruggeri

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