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An Introduction to Nonlinear Finite Element Analysis$
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J. N. Reddy

Print publication date: 2004

Print ISBN-13: 9780198525295

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198525295.001.0001

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Flows of Viscous Incompressible Fluids

Flows of Viscous Incompressible Fluids

Chapter:
(p.229) 7 Flows of Viscous Incompressible Fluids
Source:
An Introduction to Nonlinear Finite Element Analysis
Author(s):

J. N. REDDY

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525295.003.0007

Fluid mechanics is concerned with the motion of gases and liquids and their interaction with the surroundings. A fluid can either be inviscid (the viscosity is assumed to be zero) or incompressible (with constant density). Both an inviscid and an incompressible fluid are termed an ideal or a perfect fluid. A real fluid is one with finite viscosity, and it may or may not be incompressible. When the viscosity of a fluid depends only on thermodynamic properties, and the stress is linearly related to the strain rate, the fluid is said to be Newtonian. This chapter reviews the governing equations of flows of incompressible fluids, develops finite element models based on alternative formulations, and discusses computer implementation of the finite element models. Simple examples of applications of the finite element models are given. The boundary conditions are also discussed, along with the conservation of mass, conservation of energy, conservation of momenta, and stresses.

Keywords:   finite element models, incompressible fluids, viscosity, computer implementation, boundary conditions, conservation of mass, conservation of energy, conservation of momenta, stresses, governing equations

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