Skip to main content
SpringerLink
Log in

On a supplementary conservation law for the governing equations in a rigid, magnetizable body with thermal and electrical conduction

  • Published:
Meccanica Aims and scope Submit manuscript

Sommario

Si considera un corpo rigido in quiete, conduttore di calore, immerso in un campo elettromagnetico esterno. Nell'ambito della teoria termodinamica proposta da I. Müller [1] si mettono in evidenza alcune proprietà del modello proposto che può essere scritto sotto forma simmetrica e conservativa assicurando, così, la buona posizione del problema di Cauchy.

Summary

We consider a rigid heat conductor at rest immersed in an electromagnetic field. The interactions between thermodynamic and electromagnetic fields are decribed, in the frame work of the theory proposed by I. Müller [1]. Some properties related to the model equations proposed are pointed out. Specifically we are able to show as the governing equations may be written in symmetric and conservative form so that the Cauchy problem results well posed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Müller, I.,The coldness, an universal function in thermoelastic bodies, Arch. Rat. Mech. Analysis, 41, 1971, pp. 319–332.

    MATH  Google Scholar 

  2. Hutter K.,The fundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics Acta. Mech., 27, 1977, pp. 1–54.

    Article  ADS  MathSciNet  Google Scholar 

  3. Donato A. eSusco D.,Su alcune proprietà di un modello iperbolico per la propagazione del calore, Atti Sem. Mat. Fis. Modena, 30, 1981, pp. 191–206.

    Google Scholar 

  4. Donato A.,On a supplementary conservation law for the energy equation in a rigid heat conductor, Int. Journal of Non-linear Mech., 18, n. 1, 1983, pp. 11–19.

    MATH  MathSciNet  Google Scholar 

  5. Donato A.,On a supplementary conservation law for the balance laws in thermoelastic bodies, Meccanica, 18, 1983, pp. 229–232.

    Article  MATH  MathSciNet  Google Scholar 

  6. Truesdell C. andToupin R.,The classical field theories, Handbuch der Physik, vol. III/1, Berlin-Göttingen-Heidelberg: Springer 1960.

    Google Scholar 

  7. Ruggeri T.,Sistema iperbolico in forma simmetrica conservativa per le equazioni di un fluido viscoso conduttore di calore, Atti del Convegno «Onde e Stabilità nei mezzi continui». Catania 3–6/11/1981, Tip. Univ. Catania, 1982, pp. 107–128.

  8. Ruggeri, T.,Generators of hyperbolic heat equation in nonlinear Thermoelasticity. Rend. Sem. Mat. Univ. Padova, 68, 1982, pp. 79–91.

    MATH  MathSciNet  Google Scholar 

  9. Ruggeri, T.,Symmetric-hyperbolic system of conservative equations for a viscous heat conducting fluid, Acta, Mech., 47, 1983, pp. 167–183.

    Article  MATH  MathSciNet  Google Scholar 

  10. Boillat G.,Symmétrisation des systèmes d'équations aux dérivées partielles avec densité d'énergie convexe et contraintes, C.R. Acad. Sc. Paris, 295 I, 1982, pp. 551–554.

    MATH  MathSciNet  Google Scholar 

  11. I-Shih Liu,Method of Lagrange multipliers for exploitation of the entropy principle, Arch. Rat. Mech. Analysis, 46, 1972, pp. 131–148.

    MATH  Google Scholar 

  12. Hutter K.,On thermodynamics and thermostatics of viscous thermoelastic solids in the electromagnetic fields. A Lagrangian formulation, Arch. Rat. Mech. Analysis, 58, 1975, pp. 339–368.

    ADS  MATH  MathSciNet  Google Scholar 

  13. Hutter K.,A thermodynamic theory of fluids and solids in electromagnetic fields, Arch. Rat. Mech. Analysis, 64, 1977, pp. 269–298.

    MATH  MathSciNet  Google Scholar 

  14. Friedrichs K.O. andLax P.D.,System of conservation equations with a convex extension, Proc. Nat. Acad. Sc. USA, 68, 1971, pp. 1686–1688.

    ADS  MathSciNet  Google Scholar 

  15. I-Shih Liu andMuller I.,On the thermodynamics and thermostatics of fluids in electromagnetic fields, Arch. Rat. Mech. Analysis, 46, 1972, pp. 149–176.

    MathSciNet  Google Scholar 

  16. Graffi D.,Su alcune questioni di elettromagnetismo, Lezioni tenute all'Ist. Mecc. Raz. Ing. Napoli e all'Ist. Matematico Bologna, nel 1977 e 1978, Ist. Mecc. Raz. Ing. Napoli, pp. 55–61, e p. 211.

  17. Coleman B.D. andDill E.H.,On the thermodynamics of electromagnetic fields in materials with memory, Arch. Rat. Mech. Analysis, 41, 1971, pp. 132–162.

    MathSciNet  Google Scholar 

  18. Boillat G.,Sur l'existence et la recherche d'equations de conservation supplementaires pour les systemes hyperboliques, C.R. Acad. Sc. Paris, 270A, 1974, pp. 909–912.

    MathSciNet  Google Scholar 

  19. Boillat G.,Sur une function croissante comme l'entropie et génératrice des chocs dans les systemes hyperboliques. C.R. Acad. Sc. Paris, 283A, 1976, pp. 409–412.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Catania, Viale A. Doria 6, 95125, Catania, Italy

    Antonino Valenti

Authors
  1. Antonino Valenti
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by C.N.R. through the G.N.F.M.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Valenti, A. On a supplementary conservation law for the governing equations in a rigid, magnetizable body with thermal and electrical conduction. Meccanica 20, 195–198 (1985). https://doi.org/10.1007/BF02336931

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02336931

Keywords

Search

Navigation