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The Equations of Change in Fluid Mechanics and Their Analytical Solutions

  • Günter BrennEmail author
Chapter
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

In our discussion of problems in fluid mechanics, we restrict the theoretical basis to incompressible fluid continua with negligible effects of dissipative heating. The rheological constitutive equation may be the Stokesian law for Newtonian fluids or may involve linear viscoelasticity. We put together the equations of change in fluid mechanics first and then discuss the concepts for solving them analytically. We put together solutions for a selection of problems of interest in transport processes of engineering applications. Extensive discussions of exact solutions of the Navier-Stokes equations and of common errors in finding exact solutions of nonlinear differential equations are found in [6, 7, 12].

Keywords

Boundary Layer Flow Field Momentum Equation Momentum Balance Deborah Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids, vol. I. Wiley, New York (1987)Google Scholar
  2. 2.
    Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. Wiley, New York (1960)Google Scholar
  3. 3.
    Böhme, G.: Strömungsmechanik Nichtnewtonscher Fluide (Fluid Mechanics of Non-Newtonian Liquids, in German). Teubner, Stuttgart (2000)CrossRefGoogle Scholar
  4. 4.
    Entov, V.M., Yarin, A.L.: The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91–111 (1984)CrossRefzbMATHGoogle Scholar
  5. 5.
    Giesekus, H.-W.: Phänomenologische Rheologie - Eine Einführung (Phenomenological Rheology—An Introduction, in German). Springer, Berlin, Heidelberg (1994)CrossRefGoogle Scholar
  6. 6.
    Kudryashov, N.A.: Seven common errors in finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 14, 3507–3529 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Popovych, R.O., Vaneeva, O.O.: More common errors in finding exact solutions of nonlinear differential equations: part I. Commun. Nonlinear Sci. Numer. Simul. 15, 3887–3899 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lord Rayleigh, J.W.S.: On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13 (1878)Google Scholar
  9. 9.
    Schlichting, H.: Grenzschichttheorie (Boundary Layer Theory, in German), 8th edn. Braun, Karlsruhe (Germany) (1982)Google Scholar
  10. 10.
    Spurk, J.H.: Strömungslehre - Eine Einführung in die Theorie der Strömungen (Fluid Mechanics—An Introduction to the Theory of Fluid Flow, in German), 5th edn. Springer, Berlin, Heidelberg (2004), p. 234 et seqGoogle Scholar
  11. 11.
    Wang, C.Y.: Exact solutions of the unsteady Navier-Stokes equations. Appl. Mech. Rev. 42, S269–S282 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Wang, C.Y.: Exact solutions of the steady-state Navier-Stokes equations. Annu. Rev. Fluid Mech. 23, 159–177 (1991)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Yarin, A.L.: Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman Scientific & Technical, New York (1993)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of Fluid Mechanics and Heat TransferGraz University of TechnologyGrazAustria

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