Description
Book SynopsisThis book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the NavierâStokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the b
Table of Contents1. Introduction; 2. Eulerian and Lagrangian viewpoints, paths and streamlines; 3. Stream function; 4. Helmholtz decomposition; 5. Sources, sinks and vortices; 6. Doublets and their applications; 7. Complex potential; 8. Accelerating reference frames; 9. Fluids at rest; 10. Incompressibility and mass conservation; 11. Stress tensor - existence and symmetry; 12. Stress tensor in Newtonian fluids; 13. Navier–Stokes equation; 14. Thermodynamic considerations; 15. Energy equation; 16. Complete equations of motion; 17. Applications of Bernoulli's equation and control volumes; 18. Vorticity; 19. Applications to viscous flow; 20. Laminar boundary layers; 21. Some applications to convective heat and mass transfer.
