Cole / Beck / Haji-Sheikh Heat Conduction Using Green’s Functions, 2nd Edition

2. Auflage 2010
ISBN: 978-1-4398-9521-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 663 Seiten

Reihe: Series in Computational Methods and Physical Processes in Mechanics and Thermal Sciences

Since its publication more than 15 years ago, Heat Conduction Using Green’s Functions has become the consummate heat conduction treatise from the perspective of Green’s functions—and the newly revised Second Edition is poised to take its place. Based on the authors’ own research and classroom experience with the material, this book organizes the solution of heat conduction and diffusion problems through the use of Green’s functions, making these valuable principles more accessible. As in the first edition, this book applies extensive tables of Green’s functions and related integrals, and all chapters have been updated and revised for the second edition, many extensively.

Details how to access the accompanying Green’s Function Library site, a useful web-searchable collection of GFs based on the appendices in this book

The book reflects the authors’ conviction that although Green’s functions were discovered in the nineteenth century, they remain directly relevant to 21st-century engineers and scientists. It chronicles the authors’ continued search for new GFs and novel ways to apply them to heat conduction.

New features of this latest edition—

- Expands the introduction to Green’s functions, both steady and unsteady

- Adds a section on the Dirac Delta Function

- Includes a discussion of the eigenfunction expansion method, as well as sections on the convergence speed of series solutions, and the importance of alternate GF

- Adds a section on intrinsic verification, an important new tool for obtaining correct numerical values from analytical solutions

A main goal of the first edition was to make GFs more accessible. To facilitate this objective, one of the authors has created a companion Internet site called the Green’s Function Library, a web-searchable collection of GFs. Based on the appendices in this book, this library is organized by differential equation, geometry, and boundary condition. Each GF is also identified and cataloged according to a GF numbering system. The library also contains explanatory material, references, and links to related sites, all of which supplement the value of Heat Conduction Using Green’s Functions, Second Edition as a powerful tool for understanding.

Autoren/Hrsg.

Cole, Kevin D.

Cole, Kevin

Beck, James V.

Beck, James

Haji-Sheikh, A.

Litkouhi, Bahman

Fachgebiete

• Naturwissenschaften Physik Thermodynamik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Inhaltsverzeichnis

Introduction to Green’s Functions
Heat Flux and Temperature
Differential Energy Equation
Boundary and Initial Conditions
Integral Energy Equation
Dirac Delta Function
Steady Heat Conduction in One Dimension
GF in the Infinite One-Dimensional Body
Temperature in an Infinite One-Dimensional Body
Two Interpretations of Green’s Functions
Temperature in Semi-Infinite Bodies
Flat Plates
Properties Common to Transient Green’s Functions
Heterogeneous Bodies
Anisotropic Bodies
Transformations
Non-Fourier Heat Conduction

Numbering System in Heat Conduction
Geometry and Boundary Condition Numbering System
Boundary Condition Modifiers
Initial Temperature Distribution
Interface Descriptors
Numbering System for g(x, t)
Examples of Numbering System
Advantages of Numbering System

Derivation of the Green’s Function Solution Equation
Derivation of the One-Dimensional Green’s Function Solution Equation
General Form of the Green’s Function Solution Equation
Alternative Green’s Function Solution Equation
Fin Term m2T
Steady Heat Conduction
Moving Solids

Methods for Obtaining Green’s Functions
Method of Images
Laplace Transform Method
Method Of Separation of Variables
Product Solution for Transient GF
Method of Eigenfunction Expansions
Steady Green’s Functions

Improvement of Convergence and Intrinsic Verification
Identifying Convergence Problems
Strategies to Improve Series Convergence
Intrinsic Verification

Rectangular Coordinates
One-Dimensional Green’s Functions Solution Equation
Semi-Infinite One-Dimensional Bodies
Flat Plates: Small-Cotime Green’s Functions
Flat Pl