The Finite Element Method with Heat Transfer and Fluid Mechanics Applications

Erian A. Baskharone

• Publisher: Cambridge University Press
• Year: 2013
• Print ISBN:
  9781107039810
• eBook ISBN:
  9781107454569
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Intended for advanced undergraduate and graduate students, the first four chapters of this book are devoted to the introduction of the finite element concept. The focus then covers two essential areas - heat transfer and fluid mechanics: topics with different finite element formulations. Heat transfer applications begin with the classical one-dimensional thin-rod problem, followed by the two-dimensional heat transfer problem including a variety of boundary conditions. Finally, a complicated-geometry three-dimensional problem, involving a cooled radial turbine rotor, is presented, with the cooling passages treated as 'heat sinks' in the finite element analysis. For fluid mechanics, the concept of 'nodeless' degrees of freedom is introduced, with real-life fluid-flow applications. The time-dependent finite-element analysis topic is addressed through the problem of unsteady stator/rotor flow interaction within a turbomachinery stage. Finally, the concept of 'virtually-deformable finite elements', as it relates to the problem of fluid-induced vibration, is explained in detail with many practical applications.

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Brief Contents
• Detailed Contents
• Preface
• 1 The Finite Element Method: Introductory Remarks
• 2 Some Methods for Solving Continuum Problems
• 3 Variational Approach
• 4 Requirements for the Interpolation Functions
• 5 Heat Transfer Applications
• 6 One-Dimensional Steady-State Problems
• 7 The Two-Dimensional Heat-Conduction Problem
• 8 Three-Dimensional Heat-Conduction Applications with Convection and Internal Heat Absorption
• 9 One-Dimensional Transient Problems
• 10 Fluid Mechanics Finite Element Applications
• 11 Use of Nodeless Degrees of Freedom
• 12 Finite Element Analysis in Curvilinear Coordinate
• 13 Finite element Modeling of Flow in Annular Axisymmetric Passages
• 14 Extracting the Finite Element Domain from a Larger Flow System
• 15 Finite Element Application to Unsteady Flow Problems
• 16 Finite Element-Based Perturbation Approach to Unsteady Flow Problems
• Appendix A Natural Coordinates for Three-Dimensional Surface Elements
• Appendix B Classification and Finite Element Formulation of Viscous Flow Problems
• Appendix C Numerical Integration
• Appendix D Finite Element-Based Perturbation Analysis: Formulation of the Zeroth-Order Flow Field
• Appendix E Displaced-Rotor Operation: Perturbation Analysis
• Appendix F Rigorous Adaptation to Compressible-Flow Problems
• Index