Viscous Fluid Flow - Papanastasiou,Georgiou.pdf
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VISCOUS
FLUID FLOW
VISCOUS
FLUID FLOW
by
Tasos C. Papanastasiou
Georgios C. Georgiou
Department of Mathematics and Statistics
University of Cyprus
Nicosia, Cyprus
Andreas N. Alexandrou
Department of Mechanical Engineering
Worcester Polytechnic Institute
Worcester, MA
CRC Press
Boca Raton London New York Washington, D.C.
To
Androula, Charis
and
Yiangos Papanastasiou
and to
Dimitra, Nadia
and
Lisa
Contents
PREFACE
1
VECTORANDTENSORCALCULUS
1.1
SystemsofCoordinates
1.2
Vectors
1.2.1
VectorsinFluidMechanics
1.2.2
UnitTangentandNormalVectors
1.3
Tensors
1.3.1
PrincipalDirectionsandInvariants
1.3.2
IndexNotationandSummationConvention
1.3.3
TensorsinFluidMechanics
1.4
DifferentialOperators
1.4.1
TheSubstantialDerivative
1.5
IntegralTheorems
1.6
Problems
1.7
References
2
INTRODUCTIONTOTHECONTINUUMFLUID
2.1
PropertiesoftheContinuumFluid
2.2
MacroscopicandMicroscopicBalances
2.3
LocalFluidKinematics
2.4
ElementaryFluidMotions
2.5
Problems
2.6
References
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