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Student's Guide to the Navier-Stokes Equations [Pehme köide]

4.33/5 (11 hinnangut Goodreads-ist)
(University of Iowa)
  • Formaat: Paperback / softback, 236 pages, kõrgus x laius x paksus: 228x152x12 mm, kaal: 400 g, Worked examples or Exercises
  • Sari: Student's Guides
  • Ilmumisaeg: 09-Feb-2023
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009236164
  • ISBN-13: 9781009236164
Teised raamatud teemal:
Student's Guide to the Navier-Stokes EquationsSuurem pilt
  • Formaat: Paperback / softback, 236 pages, kõrgus x laius x paksus: 228x152x12 mm, kaal: 400 g, Worked examples or Exercises
  • Sari: Student's Guides
  • Ilmumisaeg: 09-Feb-2023
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009236164
  • ISBN-13: 9781009236164
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781009236164.html
Märksõnad:
The Navier-Stokes equations describe the motion of fluids and are an invaluable addition to the toolbox of every physicist, applied mathematician, and engineer. The equations arise from applying Newton's laws of motion to a moving fluid and are considered, when used in combination with mass and energy conservation rules, to be the fundamental governing equations of fluid motion. They are relevant across many disciplines, from astrophysics and oceanic sciences to aerospace engineering and materials science. This Student's Guide provides a clear and focused presentation of the derivation, significance and applications of the Navier-Stokes equations, along with the associated continuity and energy equations. Designed as a useful supplementary resource for undergraduate and graduate students, each chapter concludes with a selection of exercises intended to reinforce and extend important concepts. Video podcasts demonstrating the solutions in full are provided online, along with written solutions and other additional resources.

Arvustused

'The book reads easily and its production quality is good. Graduate students and senior undergraduate students with a good background in differential equations can benefit from using this book. Recommended.' M. Alam, Choice

Muu info

A clear and focused guide to the Navier-Stokes equations that govern fluid motion, including exercises and fully worked solutions.
Preface ix
Acknowledgments xi
1 Mass Conservation and the Continuity Equation
1(31)
1.1 Conservation in Fluid Mechanics
1(3)
1.2 Conservation of Mass in One Dimension
4(4)
1.3 The Continuity Equation
8(8)
1.4 Discussion of the Continuity Equation
16(16)
Problems
30(2)
2 The Material Derivative: The First Step to the Navier--Stokes Equations
32(28)
2.1 Lagrangrian and Eulerian Descriptions
33(7)
2.2 The Advection and Inviscid Burgers' Equation
40(11)
2.3 The Material Derivative and the Continuity Equation
51(4)
2.4 The Material Derivative in the Navier--Stokes Equations
55(2)
2.5 Take Home Points
57(3)
Problems
58(2)
3 Force Balance, the Stress Tensor, and the Navier--Stokes Equations
60(42)
3.1 Forces on a Fluid and the Stress Tensor
60(9)
3.2 General Force Balance: Cauchy's First Law of Motion
69(2)
3.3 The Form of the Stress Tensor
71(9)
3.4 The Navier--Stokes Equations Finally
80(14)
3.5 Incompressible Flow
94(8)
Problems
100(2)
4 The Navier--Stokes Equations: Another Approach
102(22)
4.1 Eulerian Approach to the Navier--Stokes Equations
102(6)
4.2 Take a Breath: Let's Review So Far
108(4)
4.3 Incompressible Equations in 2D Cartesian Coordinates
112(2)
4.4 Boundary Conditions
114(2)
4.5 Examples
116(8)
Problems
122(2)
5 The Energy Equation and a Discussion on Diffusion and Advection
124(58)
5.1 Conservation of Energy
124(16)
5.2 A Very Common Form of the Energy Equation
140(7)
5.3 Initial Discussion of the Energy Equation
147(6)
5.4 Full Governing Equations of Fluid Motion
153(2)
5.5 Diffusion
155(7)
5.6 Convection-Diffusion Equation: Combined Advection and Diffusion
162(3)
5.7 The Boundary Layer
165(8)
5.8 Boundary Conditions for the Energy Equation
173(1)
5.9 Examples
174(8)
Problems
180(2)
6 Nondimensionalization and Scaling
182(39)
6.1 The Idea Behind Nondimensionalization
182(1)
6.2 The Basics of Scaling Analysis
183(6)
6.3 Couette Flow Revisited with Nondimensionalization
189(5)
6.4 Pressure-driven Flow with Nondimensionalization
194(5)
6.5 Scaling the Incompressible Governing Equations
199(6)
6.6 Incompressible Flow with a Compressible Fluid
205(3)
6.7 Scaling to Obtain the Boundary Layer Equations
208(8)
6.8 A Final Note
216(5)
Problems
218(2)
Further Reading
220(1)
Index 221
Justin W. Garvin is Associate Professor of Instruction in the Department of Mechanical Engineering at the University of Iowa. He has previously worked as a Research Engineer at Iowa's IIHR-Hydroscience and Engineering research lab and at the US Air Force Research Laboratory. His primary areas of interest are heat, fluid mechanics, and thermal physics.