Wärme - und Stoffübertragung

, Volume 17, Issue 1, pp 27–30 | Cite as

Application of Gyarmati's variational principle to laminar stagnation flow problem

  • D. K. Bhattacharya


Gyarmati's principle for the evolution of irreversible processes has been applied to construct the variational solutions of laminar stagnation flow of incompressible Newtonian fluid in two dimensions. Variational solutions obtained in three different representations approximate closely the exact numerical result of longitudinal velocity component and the Gyarmati's principle in force representation yield the same result as obtained by Doty and Blick with the help of local potential method of Glansdorff and Prigogine.


Velocity Component Apply Physic Variational Principle Newtonian Fluid Flow Problem 
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Die Anwendung des Variationsprinzips von Gyarmati auf die laminare Stauströmung


Gyarmatis Prinzip für die Entwicklung irreversibler Prozesse wurde verwendet, um Variationslösungen für die laminare Stauströmung einer inkompressiblen Newtonschen Flüssigkeit in zwei Dimensionen aufzustellen. In drei verschiedenen Darstellungen erhaltene Variationslösungen approximieren gut die exakte numerische Lösung der longitudinalen Geschwindigkeitskomponente; Gyarmatis Prinzip in der Kraft-Darstellung ergibt das gleiche Ergebnis, wie es Doty and Blick mit Hilfe der Methode des lokalen Potentials nach Glansdorff und Prigogine erhalten haben.


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  1. 1.
    Gyarmati, I.: On the governing principle of dissipative processes and its extension to nonlinear problem. Ann. Phys. 23 (1969) 353–378Google Scholar
  2. 2.
    Gyarmati, I.: Non-equilibrium thermodynamics, field theory and variational principles. Berlin, Heidelberg, New York: Springer 1970Google Scholar
  3. 3.
    Gyarmati, I.: Generalization of GPDP to complex scaler fields. Ann. Phys. 31 (1974) 18–32Google Scholar
  4. 4.
    De Groot, S. R.; Mazur, P.: Non-equilibrium thermodynamics. Amsterdam North-Holland 1962Google Scholar
  5. 5.
    Farkas, H.: On the sufficient condition of the extremum of Gyarmati's Governing Principle for Dissipative Processes. J. Non. Equilib. Thermodyn. 1 (1976) 117–123Google Scholar
  6. 6.
    Vincze, Gy.: Deduction of quasi-linear transport equations of hydro-termodynamics from the Gyarmati Principle. Ann. Phys. 7 (1971) 225–236Google Scholar
  7. 7.
    Schlichting, H.: Boundary layer theory. New York: McGraw-Hill 1969Google Scholar
  8. 8.
    Stark, A.: Approximation methods for the solution of heat conduction problems using Gyarmati's principle. Ann. Phys. 31 (1974) 53–75Google Scholar
  9. 9.
    Doty, R.; Blick, E.: Local potential variational method applied to Hiemenz flow. A.I.A.A.J. 11 (1973) 880–881Google Scholar
  10. 10.
    Glansdorff, P.; Prigogine, I.: The thermodynamic theory of Structure. Stability and Fluctuations. New York: Wiley and Sons 1971Google Scholar
  11. 11.
    Lebon, G.; Casas-Vázquez, J.; Jou, D.: Variational solutions for some steady and non-steady laminar viscous flows with stagnation points. App. Sci. Res. 32 (1976) 371–379Google Scholar
  12. 12.
    Gyarmati, I.: On the wave approach to thermodynamics and some problems of non-linear theories. J. Non. Equilib. Thermodyn. 2 (1977) 233–260Google Scholar
  13. 13.
    Lebon, G.; Jou, D.; Casas-Vázquez, J.: An extension of the local equilibrium hypothesis. J. Phys. A: Math. Gen. 13 (1980) 275–290Google Scholar
  14. 14.
    Lebon, G.; Rubi, J. M.: A generalized theory of thermoviscous fluids. J. Non. Equilib. Thermodyn. 5 (1980) 285Google Scholar
  15. 15.
    Bampi, F.; Morro, A.: Non stationary thermodynamics and wave propagation in heat conducting viscous fluids. J. Phys. A: Math. Gen. 14 (1981) 631–638Google Scholar
  16. 16.
    Nonnenmacher, T. F.: On the derivation of second order hydrodynamic equations. J. Non. Equilib. Thermodyn. 5 (1980) 361–379Google Scholar
  17. 17.
    Wilhelm, H. E.; Hong, S. H.: Stress relaxation waves in fluids. Phys. Rev. A 22 (1980) 1266–1271Google Scholar
  18. 18.
    Bhattacharya, D. K.: A variational principle for thermodynamical waves. Ann. Phys. (in press).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • D. K. Bhattacharya
    • 1
  1. 1.Institute of Physics, Department of Chemical EngineeringTechnical University of BudapestBudapestHungary

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