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 (2021): 1.024
Thermodynamic hierarchies of evolution equations; pp. 389–395
PDF | doi: 10.3176/proc.2015.3S.09

Authors
Peter Ván, Robert Kovács, Tamás Fülöp
Abstract

Non-equilibrium thermodynamics with internal variables introduces a natural hierarchical arrangement of evolution equations. Three examples are shown: a hierarchy of linear constitutive equations in thermodynamic rhelogy with a single internal variable, a hierarchy of wave equations in the theory of generalized continua with dual internal variables, and a hierarchical arrangement of the Fourier equation in the theory of heat conduction with current multipliers.

References

 

  1. Grmela, M., Lebon, G., and Dubois, C. Multiscale thermodynamics and mechanics of heat. Phys. Rev. E, 2011, 83, 061134.
http://dx.doi.org/10.1103/PhysRevE.83.061134

  2. Liboff, R. L. Kinetic Theory (Classical, Quantum, and Relativistic Descriptions). Prentice Hall, Englewood Cliffs, New Jersey, 1990.

  3. Kluitenberg, G. A. Thermodynamical theory of elasticity and plasticity. Physica, 1962, 28, 217–232.
http://dx.doi.org/10.1016/0031-8914(62)90041-1

  4. Verhás, J. Thermodynamics and Rheology. Akadémiai Kiadó and Kluwer Academic Publishers, Budapest, 1997.

  5. Kluitenberg, G. A. and Ciancio, V. On linear dynamical equations of state for isotropic media. Physica A, 1978, 93, 273–286.
http://dx.doi.org/10.1016/0378-4371(78)90221-2

  6. Ciancio, V. and Kluitenberg, G. A. On linear dynamical equations of state for isotropic media II: some cases of special interest. Physica A, 1979, 99, 592–600.
http://dx.doi.org/10.1016/0378-4371(79)90074-8

  7. Maugin, G. A. and Muschik, W. Thermodynamics with internal variables. Part I. General concepts. J. Non-Equil. Thermody., 1994, 19, 217–249.

  8. Asszonyi, Cs., Fülöp, T., and Ván, P. Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory. Continuum Mech. Therm., 2014. arXiv:1407.0882.
http://dx.doi.org/10.1007/s00161-014-0392-3

  9. Ván, P., Berezovski, A., and Engelbrecht, J. Internal variables and dynamic degrees of freedom. J. Non-Equil. Thermody., 2008, 33(3), 235–254. cond-mat/0612491.

10. Berezovski, A., Engelbrecht, J., and Berezovski, M. Waves in microstructured solids: a unified viewpoint of modelling. Acta Mech., 2011, 220, 349–363.
http://dx.doi.org/10.1007/s00707-011-0468-0

11. Ván, P., Papenfuss, C., and Berezovski, A. Thermodynamic approach to generalized continua. Continuum Mech. Therm., 2014, 25(3), 403–420. Erratum: 421–422, arXiv:1304.4977.

12. Berezovski, A., Engelbrecht, J., and Peets, T. Multiscale modeling of microstructured solids. Mech. Res. Commun., 2010, 37(6), 531–534.
http://dx.doi.org/10.1016/j.mechrescom.2010.07.020

13. Berezovski, A. and Engelbrecht, J. Thermoelastic waves in microstructured solids: dual internal variables approach. Journal of Coupled Systems and Multiscale Dynamics, 2013, 1(1), 112–119.
http://dx.doi.org/10.1166/jcsmd.2013.1009

14. Ván, P. and Fülöp, T. Universality in heat conduction theory: weakly nonlocal thermodynamics. Ann. Phys., 2012, 524(8), 470–478. arXiv:1108.5589.
http://dx.doi.org/10.1002/andp.201200042

15. Kovács, R. and Ván, P. Generalized heat conduction in laser flash experiments. International Journal of Heat and Mass Transfer, 2015, 83, 613–620.2014. arXiv:1409.0313v2.

16. Nyíri, B. On the entropy current. J. Non-Equil. Thermody., 1991, 16, 179–186.

 

Back to Issue