Ingo Mueller, Tommaso Ruggeri

Rational extended thermodynamics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 396
• Erscheinungstermin: 7. März 2013
• Englisch
• ISBN-13: 9781461222101
• Artikelnr.: 44179930

Inhaltsangabe

1 Tour d'Horizon.- 2 Early Version of Extended Thermodynamics and Kinetic Theory of Gases.- 1 Paradoxes of Heat Conduction and Shear Diffusion.- 2 Paradox Removed.- 3 Kinetic Theory of Monatomic Gases.- 3 Formal Structure of Extended Thermodynamics.- 1 Field Equations.- 2 Entropy Inequality and Symmetric Hyperbolic Systems.- 3 Main Subsystems.- 4 Galilean Invariance.- 5 Thermodynamics of an Euler Fluid.- 4 Extended Thermodynamics of Monatomic Gases.- 1 The Equations of Extended Thermodynamics of Monatomic Gases.- 2 Constitutive Theory.- 3 Field Equations and the Thermodynamic Limit.- 4 Thermal Equations of State and Ideal Gases.- 5 Thermodynamics of Mixtures of Euler Fluids.- 1 Ordinary Thermodynamics of Mixtures (TIP).- 2 Extended Thermodynamics of Mixtures of Euler Fluids.- 3 Ordinary and Extended Thermodynamics of Mixtures.- 6 Relativistic Thermodynamics.- 1 Balance Equations and Constitutive Restrictions.- 2 Constitutive Theory.- 3 Identification of Viscosities and Heat-Conductivity.- 5 An Application: The Mass Limit of a White Dwarf.- 6 The Relativistic Kinetic Theory for Nondegenerate Gases.- 7 The Nonrelativistic Limit of Relativistic Thermodynamics.- 7 Extended Thermodynamics of Reacting Mixtures.- 1 Motivation, Results, and Discussion.- 2 Fields.- 3 Field Equation.- 4 Entropy Inequality.- 5 Nonrelativistic Limit.- 8 Waves in Extended Thermodynamics.- 1 Hyperbolicity and Symmetric Hyperbolic Systems.- 2 Linear Waves.- 3 Hyperbolicity and Nonlinear Waves..- 4 Acceleration Waves.- 5 Weak Solutions and Shock Waves.- 9 Extended Thermodynamics of Moments.- 1 Field Equations for Moments.- 2 Characteristic Speeds.- 3 Mean Eigenfunctions.- 4 Maximization of Entropy.- 10 Extended Thermodynamics and Light Scattering.- 1 Basic Electrodynamics.- 2 A Modicum of FluctuationTheory.- 3 Measuring the Spectral Density.- 4 Navier-Stokes-Fourier Fluid.- 5 Extended Thermodynamics.- 6 Extrapolation of S(q, ?) for y ? 0.- 11 Testing Extended Thermodynamics by Sound.- 1 Basic Acoustics.- 2 Dispersion Relations.- 3 Maximum Speed.- 12 Structure of Shock Waves.- 1 Experimental Evidence.- 2 Review of Previous Work.- 3 Preliminaries on Singular Points and Characteristic Speeds.- 4 Numerical Calculation of the Shock Structure.- 5 Conclusion.- 6 Addendum on Initial Value Problem for 13 Moments.- 7 Quantitative Results and Conclusions.- 13 Extended Thermodynamics of Radiation.- 1 Structure of Extended Thermodynamics of Photons.- 2 Equilibrium.- 3 Near Equilibrium.- 4 Field Equations.- 5 Local Radiative Equilibrium.- 6 Compression of Radiation.- 7 Penetration of a Beam of Radiation into Matter.- 8 Radiative Entropy in Gray Bodies.- 14 Extended Thermodynamics of Phonons.- 1 Phonon Transfer Equation.- 2 Moments and Moment Equations.- 3 The Heat Pulse Experiment.- 15 Thermodynamics of Metal Electrons.- 1 Equations of Balance.- 2 Extended Thermodynamics and Kinetic Theory.- 16 Viscoelastic Fluids.- 1 Viscoelastic Fluids of Second Grade.- 2 Rate-Type versus Differential-Type Constitutive Equations.- 3 Toward Extended Thermodynamics of Viscoelasticity.