Abstract
A system of equations for relativistic m.h.d, with finite electric conductivity and no heat flux is proposed, starting from the properties of the systems of conservation laws compatible with a supplementary balance law (entropy balance) with convex density (symmetric-hyperbolic systems). The electric current density is treated as a new field variable which contributes to non equilibrium entropy density (extended thermodynamics). The result is a theory in which only one new constitutive function, representing entropy increment respect to equilibrium, is necessary to characterize the properties of the medium related to electric conductivity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Liu, I. S.; Müller, I.; Ruggeri, T.: Relativistic thermodynamics of gases. Ann. of Phys. 169 (1986) 191–219
Jou, D.; Casas-Vasquez, J.; Lebon, G.: Extended irreversible thermodynamics. Rep. Progr. Phys. 51 (1988) 1105
Friedrichs, K. O.: On the laws of relativistic electro-magneto-fluid dynamics. Comm. Pure Appl. Math. 27 (1974) 749
Ruggeri, T.; Strumia, A.: Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics. Ann. Inst. H. Poincaré 34 (1981) 65
Strumia, A.: Wave propagation and symmetric hyperbolic systems of conservation laws with constrained field variables. II. Symmetric hyperbolic systems with constrained fields. Il Nuovo Cimento 101 B (1988) 19
Boillat, G.: Sur l'existence et la recerche d'équations de conservations supplémnataires pour les systèmes hyperboliques. C. R. Acad. Sc. Paris 278 A (1974) 909
Boillat, G.: Sur une fonction croissante come l'entropie et génératrice des chocs dans les systèmes hyperboliques. C. R. Acad. Sc. Paris 283 A (1976) 409.
Boillat, G.; Ruggeri, T.: Limite de la vitesse des chocs dans les champs à densité d'énergie convexe. C. R. Acad. Sc. Paris 289 A (1979) 257
Boillat, G.; Strumia, A.: Limitation des vitesses d'onde et de choc quand la densité relativiste d'entropie (ou d'énergie) est convexe. C. R. Acad. Sci. Paris 307, série I (1988) 111
Fusco, D.: Alcune consdierazioni sulle onde d'urto in fluidodinamica. Rend. Sem. Mat. di Modena 28 (1979) 223
Boillat, G.; Ruggeri, T.: Symmetric form of nonlinear mechanics equations and entropy growth across a shock. Acta Mechanica 35 (1980) 271
Ruggeri, T.; Strumia, A.: Convex covariant entropy density, symmetric conservative form and shock waves in relativistic magnetohydrodynamics. J. Math. Phys. (N.Y.) 22 (1981) 1824
Strumia, A.: A detailed study of entropy jump across shock waves in relativistic fluid dynamics. Il Nuovo Cimento 92 B (1986) 91
Boillat, G.: Simétrisation des systèmes d'equations aux dérivées partialles avec densité d'énergie convexe et contraintes. C. R. Acad. Sc. Paris 295, série I (1982) 551
Boillat, G.: Chocs avec contraintes et densité d'énergie convexe. C. R. Acad. Sc. Paris 295, série I (1982) 747
Strumia, A.: Some remarks on conservative symmetric-hyperbolic systems governing relativistic theories. Ann. de l'Institut H. Poincaré 38 A (1983) 113
Ruggeri, T.: Convexity and symmetrization in relativistic theories. Privileged time-like congruence and entropy, Continuum Mech. Thermodyn. 2 (1990) 163
Krall, A. N.; Trivelpiece, A. W.: Principles of plasma physics. New York, McGraw-Hill (1973)
Wannier, G. H.: Statistical Physics. New York, Wiley (1966).
Author information
Authors and Affiliations
Additional information
G.N.F.M. of the C.N.R.
Rights and permissions
About this article
Cite this article
Strumia, A. Extended thermodynamics of a relativistic plasma with finite electric conductivity. Continuum Mech. Thermodyn 3, 39–51 (1991). https://doi.org/10.1007/BF01128964
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01128964