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Application of the Pi-Theorem to Establish Self-Similarity and Reduce Partial Differential Equations to the Ordinary Ones

  • L. P. Yarin
Chapter
Part of the Experimental Fluid Mechanics book series (FLUID, volume 1)

Abstract

Chapter 3 deals with the application of the Pi-theorem to reduce partial differential equations (PDEs) of certain hydrodynamic and heat transfer problems to the ordinary differential equations (ODEs). In the cases which allow for such transformation (including the initial and boundary conditions), solution of the problem reduces to a much simpler problem posed for an ODE, i.e. depends on a single compound variable. The latter represent itself a combination of variables and dimensional constants involved in the problem formulation.

Keywords

Boundary Layer Vortex Line Gravity Current Capillary Wave Governing Parameter 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • L. P. Yarin
    • 1
  1. 1.Dept. of Mechanical Engineering Technion CityTechnion-Israel Institute of TechnologyHaifaIsrael

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