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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Objective time derivatives in nonequilibrium thermodynamics; pp. 127–131

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


Authors

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.

Keywords

nonequilibrium thermodynamics, rheology, objective time derivatives, simple shear, Second Law.

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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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December