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].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids, vol. I. Wiley, New York (1987)
Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. Wiley, New York (1960)
Böhme, G.: Strömungsmechanik Nichtnewtonscher Fluide (Fluid Mechanics of Non-Newtonian Liquids, in German). Teubner, Stuttgart (2000)
Entov, V.M., Yarin, A.L.: The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91–111 (1984)
Giesekus, H.-W.: Phänomenologische Rheologie - Eine Einführung (Phenomenological Rheology—An Introduction, in German). Springer, Berlin, Heidelberg (1994)
Kudryashov, N.A.: Seven common errors in finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 14, 3507–3529 (2009)
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)
Lord Rayleigh, J.W.S.: On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13 (1878)
Schlichting, H.: Grenzschichttheorie (Boundary Layer Theory, in German), 8th edn. Braun, Karlsruhe (Germany) (1982)
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 seq
Wang, C.Y.: Exact solutions of the unsteady Navier-Stokes equations. Appl. Mech. Rev. 42, S269–S282 (1989)
Wang, C.Y.: Exact solutions of the steady-state Navier-Stokes equations. Annu. Rev. Fluid Mech. 23, 159–177 (1991)
Yarin, A.L.: Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman Scientific & Technical, New York (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Brenn, G. (2017). The Equations of Change in Fluid Mechanics and Their Analytical Solutions. In: Analytical Solutions for Transport Processes. Mathematical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-51423-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-51423-8_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-51421-4
Online ISBN: 978-3-662-51423-8
eBook Packages: EngineeringEngineering (R0)