The Equations of Change in Fluid Mechanics and Their Analytical Solutions
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].
KeywordsBoundary Layer Flow Field Momentum Equation Momentum Balance Deborah Number
- 1.Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids, vol. I. Wiley, New York (1987)Google Scholar
- 2.Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. Wiley, New York (1960)Google Scholar
- 8.Lord Rayleigh, J.W.S.: On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13 (1878)Google Scholar
- 9.Schlichting, H.: Grenzschichttheorie (Boundary Layer Theory, in German), 8th edn. Braun, Karlsruhe (Germany) (1982)Google Scholar
- 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