ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
Thermoelasticity and entropy flow; pp. 142–144
PDF | doi: 10.3176/proc.2008.3.04

Author
József Verhás
Abstract

The well-known theories of thermoelasticity are based on thermal expansion, and recently the theory of heat conduction has been looked into for improvements. The reason is that heat conduction is described with scalar and vector variables but elasticity with second order tensors, and in linear order there is no direct coupling between second order tensors and vectors or scalars if the material is isotropic. The observed deviations from the present theories urge that new tracks for research be sought. Such a new track can be opened by Onsager’s thermodynamics supplemented with dynamic degrees of freedom. This theory is usually referred to as extended thermodynamics. The key moment is in the general form of the entropy current out of local equilibrium, which leads to the formal introduction of the transport of the dynamic degrees of freedom. The skeleton of the possible theories is based on the introduction of one or more vectorial dynamic variables. They can be coupled to the current density of the heat flow, while their ‘diffusion’ intensities are second order tensors coupled directly in linear order to the stress tensor even if the material is isotropic. The possibilities are demonstrated on an example with one dynamic degree of freedom.

References

  1. Onsager, L. Reciprocal relations in irreversible processes. I. Phys. Rev., 1931, 37, 405–426.
doi:10.1103/PhysRev.37.405

  2. Onsager, L. Reciprocal relations in irreversible processes. II. Phys. Rev., 1931, 38, 2265–2279.
doi:10.1103/PhysRev.38.2265

  3. Onsager, L. and Maclup, S. Fluctuations and irreversible processes. Phys. Rev., 1953, 91, 1505–1512.
doi:10.1103/PhysRev.91.1505

  4. Maclup, S. and Onsager, L. Fluctuations and irreversible processes. II. Systems with kinetic energy. Phys. Rev., 1953, 91, 1512–1515.
doi:10.1103/PhysRev.91.1512

  5. De Groot, S. R. Thermodynamics of Irreversible Processes}. North-Holland Publ. Co., Amsterdam, 1951.

  6. De Groot, S. R. and Mazur, P. Non-Equilibrium Thermodynamics. North-Holland Publ. Co., Amsterdam, 1962.

  7. Prigogine, I. Introduction to Thermodynamics of Irreversible Processes. Interscience, New York, 1961.

  8. Gyarmati, I. Non-Equilibrium Thermodynamics. Springer, Berlin, 1970.

  9. Gyarmati, I. On the wave approach of thermodynamics and some problems of non-linear theories. J. Non-Equilib. Thermodyn., 1977, 2, 233–260.

10. Jou, D., Casas-Vázquez, J. and Lebon, G. Extended Irreversible Thermodynamics. Springer, New York, Berlin, Heidelberg, 1993.

11. Jou, D., Casas-Vázquez, J. and Lebon, G. Extended irreversible thermodynamics: An overview of recent bibliography. J. Non-Equilib. Thermodyn., 1992, 17, 383–396.

12. Müller, I. and Ruggeri, T. Extended Thermodynamics. Springer, Berlin, New York, 1993. Second edition: Rational Extended Thermodynamics, 1998.

13. Garcia-Colin, L. S. and Uribe, F. J. Extended irreversible thermodynamics beyond the linear regime. A critical overview. J. Non-Equilib. Thermodyn., 1991, 16, 89–128.

14. Verhás, J. Thermodynamics and Rheology}. Akadémiai Kiadó and Kluwer Academic Publishers, Budapest and Dordrecht, 1997.

15. Ván, P. and Ruszin, É. Derivation of the basic equations of MHD from the governing principle of dissipative processes. Acta Phys. Hung., 1990, 68, 227–239.

16. Ciancio, V., Dolfin, M. and Ván, P. Thermodynamic theory of dia- and paramagnetic materials. J. Appl. Electromagn. Mech., 1996, 7, 237–247.

17. Holló, S. and Nyíri, B. Equation for cathodic glow sheath. Acta Phys. Hung., 1992, 72, 71–88.

18. Nyíri, B. Non-equilibrium thermodynamical discussion of ionization in breakdown and glow. In Fifth International Symposium on the Science and Technology of Light Sources. York, 1989, 61.

19. Kluitenberg, G. A. and Ciancio, V. The stress–strain–temperature relation for anisotropic Kelvin–Voigt media. Atti Acad. Sci. Lett., 1981, XL, ser. 4, f. 2, part 1, 107–122.

20. Turrisi, E., Ciancio, V. and Kluitenberg, G. A. On the propagation of linear transverse acoustic waves. II. Some cases of special interest (Poynting–Thomson, Jeffreys, Maxwell, Kelvin–Voigt, Hooke and Newton media). Physica A}, 1982, 116, 594–603.
doi:10.1016/0378-4371(82)90179-0

21. Dolfin, M., Ciancio, V. and Ván, P. Thermodynamic theory of dia- and paramagnetic materials. Int. J. Appl. Electromagn. Mech., 1996, 7, 237–247.

22. Muschik, W., Ehrentraut, H. and Papenfuβ, C. The connection between Ericksen–Leslie equations and the balances of mesoscopic theory of liquid crystals. Mol. Cryst. Liq. Cryst., 1995, 262, 417–423.
doi:10.1080/10587259508033544

23. Ván, P., Papenfuss, C. and Muschik, W. Mesoscopic dynamics of microcracks. Phys. Rev. E}, 2000, 62(5), 6206–6215.
doi:10.1103/PhysRevE.62.6206

24. Ván, P. Weakly nonlocal irreversible thermodynamics – the Ginzburg–Landau equation. Techn. Mech., 2002, 22(2), 104–110.

25. Papenfuss, C., Ván, P. and Muschik, W. Mesoscopic theory of microcracks. Arch. Mech., 2003, 55(5–6), 459–477.

26. Morse, M. Relation between the critical points of a real function of n independent variables. Trans. Am. Math. Soc., 1925, 27, 345–396.
doi:10.2307/1989110

27. Verhás, J. On the entropy current. Int. J. Non-equilib. Thermodyn., 1983, 8, 201.

28. Smith, G. F. and Rivlin, R. S. The anisotropic tensors. Q. Appl. Math., 1957, 15, 308–314.

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