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ADVANCED FLUID MECHANICS
Advanced Fluid Mechanics
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By
William Graebel, Professor Emeritus,Department of Mechanical Engineering,University of Michigan

Description
Fluid mechanics is the study of how fluids behave and interact under various forces and in various applied situations, whether in liquid or gas state or both. The author compiles pertinent information that are introduced in the more advanced classes at the senior level and at the graduate level. ?Advanced Fluid Mechanics? courses typically cover a variety of topics involving fluids in various multiple states (phases), with both elastic and non-elastic qualities, and flowing in complex ways. This new text will integrate both the simple stages of fluid mechanics (?Fundamentals?) with those involving more complex parameters, including Inviscid Flow in multi-dimensions, Viscous Flow and Turbulence, and a succinct introduction to Computational Fluid Dynamics. It will offer exceptional pedagogy, for both classroom use and self-instruction, including many worked-out examples, end-of-chapter problems, and actual computer programs that can be used to reinforce theory with real-world applications. Professional engineers as well as Physicists and Chemists working in the analysis of fluid behavior in complex systems will find the contents of this book useful.All manufacturing companies involved in any sort of systems that encompass fluids and fluid flow analysis (e.g., heat exchangers, air conditioning and refrigeration, chemical processes, etc.) or energy generation (steam boilers, turbines and internal combustion engines, jet propulsion systems, etc.), or fluid systems and fluid power (e.g., hydraulics, piping systems, and so on)will reap the benefits of this text.

Audience
Graduate-level students in Mechanical, Aerospace & Aeronautical, Chemical, Environmental and Biomechanical Engineering; Graduate-level students in Chemistry and Physics ; Professional engineers in mechanical, chemical, materials, environmental, and biomedical engineering; Physicists and Chemists working in the analysis of fluid behavior in complex systems

Contents
Chapter 1 - Fundamentals 1.1 Introduction 1.2 Velocity, acceleration and the material derivative 1.3 The local continuity equation 1.4 Path lines, stream lines and the stream function a. Lagrange?s stream function for two-dimensional flows b. Stream functions for three-dimensional flows,including Stokes stream function 1.5 Newton?s momentum equation 1.6 Stress 1.7 Rates of deformation 1.8 Constitutive relations for Newtonian fluids 1.9 Equations for Newtonian fluids 1.10 Boundary conditions 1.11 Vorticity and circulation 1.12 The vorticity equation 1.13 The work-energy equation 1.14 The first law of thermodynamics 1.15 Dimensionless parameters 1.16.Non-Newtonian fluids 1.17 Moving coordinate systems Problems Chapter 2 - Inviscid irrotational flows 2.1 Inviscid flows 2.2 Irrotational flows and the velocity potential a. Intersection of velocity potential lines and streamlines in two dimensions b. Basic two-dimensional irrotational flows c. Hele-Shaw flows d. Basic three-dimensional irrotational flows e. Superposition and the method of images f. Vortices near walls g. Rankine half body h. Rankine oval i. Circular cylinder or sphere in a uniform stream 2.3 Singularity distribution methods a. Two and three-dimensional slender body theory b. Panel methods 2.4 Forces acting on a translating sphere 2.5 Added mass and the Lagally theorem 2.6 Theorems for irrotational flow a. Mean value and maximum modulus theorem b. Maximum-minimum potential theorem c. Maximum-minimum speed theorem d. Kelvin?s minimum kinetic energy theorem e. Maximum kinetic energy theorem f. Uniqueness theorem g. Kelvin?s persistence of circulation theorem h. Weiss and Butler sphere theorems Problems Chapter 3 - Irrotational Two-Dimensional Flows 3.1 Complex variable theory applied to two-dimensional irrotational flows 3.2 Flow past a circular cylinder with circulation 3.3 Flow past an elliptical cylinder with circulation 3.4 The Joukowski airfoil 3.5 Karman-Trefftz and Jones-McWilliams airfoils 3.6 NACA airfoils 3.7 Lifting line theory 3.8 Karman vortex street 3.9 Conformal mapping and the Schwarz-Christoffel transformation 3.10 Cavity flows 3.11 Added mass and forces and moments for two-dimensional bodies Problems Chapter 4 - Surface and interfacial waves 4.1 Linearized free surface wave theory a. Infinitely long channel b. Waves in a container of finite size 4.2 Group velocity 4.3 Waves at the interface of two dissimilar fluids 4.4 Waves in an accelerating container 4.5 Stability of a round jet 4.6 Local surface disturbance on a large body of fluid - Kelvin?s ship wave 4.7 Shallow depth free surface waves - cnoidal and solitary waves 4.8 Ray theory of gravity waves for non-uniform depths Problems Chapter 5 - Exact solutions of the Navier-Stokes equations 5.1 Solutions to the steady-state Navier-Stokes equations when convective acceleration is absent a. Two-dimensional flow between parallel planes b. Poiseuille flow in a rectangular conduit c. Poiseuille flow in a round tube d. Poiseuille flow in tubes of arbitrarily shaped cross-section e. Couette flow between circular cylinders 5.2 Unsteady flows when convective acceleration is absent a. Stokes? first problem-impulsive motion of a plate b. Stokes? second problem-oscillation of a plate 5.3 Other unsteady flows when convective acceleration is absent a. Impulsive plane Poiseuille and Couette flows b. Impulsive circular Couette flow 5.4 Steady flows when convective acceleration is present. a. Plane stagnation point flow b. Three-dimensional stagnation point flow c. Flow into convergent or divergent channels d. Flow in a spiral channel e. Flow due to a round laminar jet f. Flow due to a rotating disk Problems Chapter 6 - The Boundary Layer Approximation 6.1 Introduction to boundary layers 6.2 The boundary layer equations 6.3 Boundary layer thickness 6.4 Falkner-Skan solutions for flow past a wedge a. Boundary layer on a flat plate b. Stagnation point boundary layer flow c. General case 6.5 The integral form of the boundary layer equation 6.6 Axisymmetric laminar jet 6.7 Flow separation 6.8 Transformations for non-similar boundary layer solutions a. Falkner transformation b. von Mises transformation c. Combined Mises-Falkner transformation d. Crocco?s transformation e. Mangler?s transformation for bodies of revolution 6.8 Boundary layers in rotating flows Problems Chapter 7 - Thermal Effects 7.1 Thermal boundary layers 7.2 Forced convection on a horizontal flat plate a. Falkner-Skan wedge thermal boundary layer b. Isothermal flat plate c. Flat plate with constant heat flux 7.3 The integral method for thermal convection a. Flat plate with a constant temperature region b. Flat plate with constant heat flux 7.4 Heat transfer near the stagnation point of an isothermal cylinder 7.5 Natural convection on an isothermal vertical plate 7.6 Natural convection on a vertical plate with uniform heat flux 7.7 Thermal boundary layer on inclined flat plates 7.8 Integral method for natural convection on an isothermal vertical plate 7.9 Temperature distribution in an axisymmetric jet Problems Chapter 8 - Low Reynolds number Flows 8.1 Stokes approximation 1. Doublet 2a. Stokeslet for steady flows 2b. Stokeslet for unsteady flows 3a. Rotlet for steady flows 3b. Rotlet for unsteady flows 8.2 Slow steady flow past a solid sphere 8.3 Slow steady flow past a liquid sphere 8.4 Flow due to a sphere undergoing simple harmonic motion 8.5 General translation of a sphere 8.6 Oseen?s approximation for slow viscous flow 8.7 Resolution of the Stokes/Whitehead paradoxes Problems Chapter 9 - Flow stability 9.1 Linear stability theory of fluid flows 9.2 Thermal instability in a viscous fluid - Rayleigh-Benard convection 9.3 Stability if flow between rotating circular cylinders - Couette-Taylor instability 9.4 Stability of plane flows Problems Chapter 10 - Turbulence and transition to turbulence 10.1 The why and the how of turbulence 10.2 Statistical approach - one point averaging 10.3 Zero-equation turbulent models 10.4 One-equation turbulent models 10.5 Two-equation turbulent models 10.6 Stress-equation models 10.7 Equations of motion in Fourier space 10.8 Quantum theory models 10.9 Large eddy models 10.10 Phenomenologic observations 10.11 Conclusions Chapter 11 - An Introduction To Computational Fluid Dynamics 11.1 Introduction 11.2 Numerical calculus 11.3 Numerical integration of ordinary differential equations 11.4 The finite element method 11.5 Linear stability problems - invariant imbedding and Riccati methods 11.6 Errors, accuracy, and stiff equations Problems Chapter 12 - Numerical solution of partial differential equations 12.1 Introduction 12.2 Relaxation methods 12.3 Surface singularities 12.4 One step methods a. Forward time, centered space - explicit b. Dufort-Frankel method - explicit c. Crank-Nicholson method - implicit d. Boundary layer equations - Crank-Nicholson e. Boundary layer equations - hybrid method f. Richardson extrapolation g. Further choices for dealing with nonlinearities h. Upwind differencing for convective acceleration terms 12.5 Multi-step, or alternating direction, methods a. Alternating direction explicit (ADE) method b.Alternating direction implicit (ADI) method 12.6 Method of characteristics 12.7 Leapfrog method - explicit 12.8 Lax-Wendroff method - explicit 12,9 MacCormack?s methods a. MacCormack?s explicit method b. MacCormack?s implicit method 12.10 Discrete vortex methods (DVM) 12.11 Cloud in cell method (CIC) Problems Appendix - Mathematical aids A1. Vector differential calculus A2. Vector integral calculus A3. Fourier series and integrals A4. Solution of ordinary differential equations a. Method of Frobenius b. Mathieu equation c. Finding eigenvalues - the Riccatti method A5. Index notation A6. Tensors in Cartesian coordinates A7. Tensors in orthogonal curvilinear coordinates a. Cylindrical polar coordinates b. Spherical polar coordinates A8. Tensors in general coordinates References Index

Bibliographic details
Hardbound, 368 pages, publication date: JUN-2007
ISBN-13: 978-0-12-370885-4
ISBN-10: 0-12-370885-0
Imprint: ACADEMIC PRESS

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Last update: 5 Sep 2009
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