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A follow on from the author's work "Finite Elements in Heat Transfer" which we published 11/94, and which is a powerful CFD programme that will run on a PC. The fluid flow market is larger than the previous, and this package is good value in comparison with other software packages in Computational Fluid Dynamics, which are generally very expensive. The work in general copes with non-Newtonian laminar flow using the finite element method, and some basic theory of the subject is included in the opening chapters of the book.
Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.
Designed for those interested in using finite element methods in the study of fluid mechanics and heat transfer, The Finite Element Method in Heat Transfer and Fluid Dynamics presents this useful methodology tailored for a limited but significant class of problems dealing with heat conduction, incompressible viscous flows, and convection heat transfer. The authors' approach consists of a series of incremental steps of increasing complexity. The text is divided into 8 chapters. Chapter 1 describes in detail the continuum boundary value problems that form the central focus of the book. Chapters 2 and 3 introduce and extend the finite element method by application to a simplified, two- and three-dimensional heat conduction problems. Chapters 4 and 5 describe isothermal viscous fluid mechanics formulations and the solution of nonlinear equations developed from the flow problem. Chapter 6 covers inelastic non-Newtonian flows and free surface problems. Chapter 7 surveys the complex topic of viscoelastic flow simulation, while Chapter 8 discusses several advanced topics, including turbulence modeling. Each chapter includes example problems ranging from simple benchmarks to practical engineering solutions. In The Finite Element Method in Heat Transfer and Fluid Dynamics, readers will find a pragmatic treatment that views numerical computation as a means to and end and does not dwell on theory or proof. Mastering its contents brings a firm understanding of the basic methodology, the competence to use existing simulation software, and the ability to develop some simpler, special purpose computer codes.
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Discussing the fundamentals of how to use the finite element method to solve heat transfer and fluid mechanics problems, this work explains how to solve various heat transfer problems with different types of boundary conditions.