The Finite Element Method with Heat Transfer and Fluid Mechanics Applications

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.

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; 9. One-dimensional transient problems; 10. Fluid mechanics finite-element applications; 11. Use of nodeless degrees of freedom; 12. Finite element analysis in curvilinear coordinates; 13. Finite element modeling in annular passages; 14. Extracting the F.E. domain from a larger flow system; 15. Finite element application to unsteady flow problems; 16. F.E.-based perturbation approach to unsteady flows.

Erian A. Baskharone is Professor Emeritus of Mechanical and Aerospace Engineering at Texas A&M University. He is a member of the ASME Turbomachinery Executive Committee. Dr Baskharone was a Senior Engineer with Allied-Signal Corporation, responsible for the aerothermodynamic design of various turbofan and turboprop engines. His research covered a wide spectrum of turbomachinery topics including the unsteady stator/roto flow interaction and the fluid-induced vibration of the Space Shuttle Main Engine turbopumps. His finite-element based perturbation approach to the problem of turbomachinery fluid-induced vibration is well known. At Texas A&M, he received the General Dynamics Award of Excellence in Engineering teaching (1991) and the Amoco Foundation Award for Distinguished Teaching (1992). He is the author of Principles of Turbomachinery in Air-Breathing Engines (Cambridge University Press, 2006) and Thermal Science: Essentials of Thermodynamics, Fluid Mechanics and Heat Transfer (2012).