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 (2020): 1.045

Objective time derivatives in nonequilibrium thermodynamics; pp. 127–131

Full article in PDF format | doi: 10.3176/proc.2008.3.02

Author
Péter Ván

Abstract
In this paper we outline a framework of a thermodynamic theory where objective time derivatives appear in a natural way. The entropy production of a single component fluid with a tensorial internal variable is calculated as an example. Dependence on material quantities leads to objective derivatives in the constitutive relations resulting in a new rheological model. The viscosity and the viscometric functions are calculated for simple shear.
References

  1. Matolcsi, T. Spacetime Without Reference Frames. Akadémiai Kiadó Publishing House of the Hungarian Academy of Sciences, Budapest, 1993.

  2. Matolcsi, T. and Gohér, A. Spacetime without reference frames and its application to the Thomas rotation. Publ. Appl. Anal., 1996, 5, 1–11.

  3. Matolcsi, T. and Gruber, T. Spacetime without reference frames: An application to the kinetic theory. Int. J. Theor. Phys., 1996, 35(7), 1523–1539.
doi:10.1007/BF02084958

  4. Matolcsi, T. and Matolcsi, M. Thomas rotation and Thomas precession. Int. J. Theor. Phys., 2005, 44(1), 63–77.
doi:10.1007/s10773-005-1437-y

  5. Matolcsi, T., Matolcsi, M. and Tasnádi, T. Abstract mathematical treatment of relativistic phenomena. Ulmer Seminare, 2005, 10, 253–270.

  6. Noll, W. A mathematical theory of the mechanical behavior of continuous media. Arch. Rational Mech. Anal., 1958/59, 2, 197–226.
doi:10.1007/BF00277929

  7. Matolcsi, T. and Ván, P. Can material time derivative be objective? Phys. Lett. A, 2006, 353, 109–112.
doi:10.1016/j.physleta.2005.12.072

  8. Öttinger, H. C. Beyond Equilibrium Thermodynamics. Wiley-Interscience, 2005.

  9. Verhás, J. Thermodynamics and Rheology. Akadémiai Kiadó and Kluwer Academic Publisher, Budapest, 1997.

10. Matolcsi, T. and Ván, P. Absolute time derivatives. J. Math. Phys., 2007, 48, 053507–19.
doi:10.1063/1.2719144

11. Truesdell, C. and Noll, W. The Non-Linear Field Theories of Mechanics. Springer Verlag, Berlin, 1965.

12. Ván, P. Weakly nonlocal irreversible thermodynamics. Ann. Phys. (Leipzig), 2003, 12(3), 146–173.
doi:10.1002/andp.200310002

13. Bird, R. B., Armstrong, R. C. and Hassager, O. Dynamics of Polymeric Liquids. John Wiley and Sons, New York, 1977.

14. Larson, R. G. Constitutive Equations for Polymer Melts. Butterworths, Boston, 1988.


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