Selected Problems for Newtonian and Maxwellian Fluids

  • Wolfgang H. Müller
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 210)


This chapter is dedicated to the art of modeling, in particular modeling problems involving viscous gases and fluids. We start with the previously introduced Navier-Stokes constitutive law in context with transient flow through a channel. We shall see that this constitutive relations results in a parabolic partial differential equation for the velocity of the fluid, which immediately leads to the artefact of infinite speeds of propagation. This can be avoided by application of the Maxwell fluid model, which accounts for memory effects. Further examples of gas dynamics in spherical coordinates include expanding and contracting stars as well as the whole universe, which are modeled by means of classical continuum theory.


Mass Density Constitutive Relation Outer Radius Lower Plate Length Scale Parameter 
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.


  1. 1.
    Butkov E (1968) Mathematical physics. Addison-Wesley Publishing Company, Reading, MAGoogle Scholar
  2. 2.
    Coleman BD, Markovitz H, Noll W (1966) Viscometric flows of non-newtonian fluids—theory and experiment. Springer, Berlin, Heidelberg (Springer Tracts in Natural Philosophy)Google Scholar
  3. 3.
    Kippenhahn R, Weigert A, Weiss A (2013) Stellar structure and evolution, 2nd edn. Springer, Berlin, HeidelbergGoogle Scholar
  4. 4.
    Müller I, Ruggieri T (1998) Rational extended thermodynamics. Springer, New York (Springer Tracts in Natural Philosophy)Google Scholar
  5. 5.
    Oertel H (2002) Prandtl—Führer durch die Strömungslehre. 11. Auflage. Vieweg, BraunschweigGoogle Scholar
  6. 6.
    Truesdell C, Noll W (1965) The non-linear theories of mechanics. In: Flügge S (ed) Encyclopedia of physics, vol III/3. Springer, Berlin, GöttingenGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute of MechanicsTechnical University of BerlinBerlinGermany

Personalised recommendations