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E-raamat: Heat Conduction Using Greens Functions 2nd edition [Taylor & Francis e-raamat]

, , (Michigan State University, East Lansing, MI), (The University of Texas, Arlington, Texas, USA)
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Heat Conduction Using Greens Functions 2nd editionSuurem pilt
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Since its publication more than 15 years ago, Heat Conduction Using Greens Functions has become the consummate heat conduction treatise from the perspective of Greens functionsand 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 Greens functions, making these valuable principles more accessible. As in the first edition, this book applies extensive tables of Greens functions and related integrals, and all chapters have been updated and revised for the second edition, many extensively.

Details how to access the accompanying Greens 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 Greens 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 Greens 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 Greens 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 Greens Functions, Second Edition as a powerful tool for understanding.
Preface to the First Edition xiii
Preface to the Second Edition xv
Authors xvii
Nomenclature xix
Chapter 1 Introduction to Green's Functions
1(46)
1.1 Introduction
1(2)
1.1.1 Advantage of the Green's Function Method
2(1)
1.1.2 Scope of This
Chapter
3(1)
1.2 Heat Flux and Temperature
3(1)
1.3 Differential Energy Equation
4(3)
1.4 Boundary and Initial Conditions
7(1)
1.5 Integral Energy Equation
8(3)
1.6 Dirac Delta Function
11(2)
1.7 Steady Heat Conduction in One Dimension
13(5)
1.7.1 Solution by Integration
13(1)
1.7.2 Solution by Green's Function
14(4)
1.8 GF in the Infinite One-Dimensional Body
18(4)
1.8.1 Auxiliary Problem for G
19(1)
1.8.2 Laplace Transform, Brief Facts
19(1)
1.8.3 Derivation of the GF
20(2)
1.9 Temperature in an Infinite One-Dimensional Body
22(6)
1.9.1 Green's Function Solution Equation
22(1)
1.9.2 Fundamental Heat Conduction Solution
22(6)
1.10 Two Interpretations of Green's Functions
28(1)
1.11 Temperature in Semi-Infinite Bodies
29(6)
1.11.1 Boundary Condition of the First Kind
30(2)
1.11.2 Boundary Condition of the Second Kind
32(3)
1.12 Flat Plates
35(2)
1.12.1 Temperature for Flat Plates
35(1)
1.12.2 Auxiliary Problem for Flat Plates
36(1)
1.13 Properties Common to Transient Green's Functions
37(1)
1.14 Heterogeneous Bodies
37(1)
1.15 Anisotropic Bodies
38(1)
1.16 Transformations
38(3)
1.16.1 Orthotropic Bodies
39(1)
1.16.2 Moving Solids
39(1)
1.16.3 Fin Term
40(1)
1.17 Non-Fourier Heat Conduction
41(6)
Problems
43(3)
References
46(1)
Chapter 2 Numbering System in Heat Conduction
47(16)
2.1 Introduction
47(1)
2.2 Geometry and Boundary Condition Numbering System
48(4)
2.3 Boundary Condition Modifiers
52(1)
2.4 Initial Temperature Distribution
53(1)
2.5 Initial Descriptors
54(1)
2.6 Numbering System for g(x, t)
55(2)
2.7 Examples of Numbering System
57(1)
2.8 Advantages of Numbering System
58(5)
2.8.1 Data Base in Transient Heat Conduction
58(1)
2.8.2 Algebra for Linear Cases
59(2)
Problems
61(1)
References
62(1)
Chapter 3 Derivation of the Green's Function Solution Equation
63(38)
3.1 Introduction
63(1)
3.2 Derivation of the One-Dimensional Green's Function Solution Equation
63(7)
3.3 General Form of the Green's Function Solution Equation
70(9)
3.3.1 Temperature Problem
70(2)
3.3.2 Derivation of the Green's Function Solution Equation
72(7)
3.4 Alternative Green's Function Solution Equation
79(3)
3.5 Fin Term m2T
82(4)
3.5.1 Transient Fin Problems
83(3)
3.5.2 Steady Fin Problems in One Dimension
86(1)
3.6 Steady Heat Conduction
86(3)
3.6.1 Relationship between Steady and Transient Green's Functions
87(1)
3.6.2 Steady Green's Function Solution Equation
87(2)
3.7 Moving Solids
89(12)
3.7.1 Introduction
89(2)
3.7.2 Three-Dimensional Formulation
91(4)
Problems
95(4)
References
99(2)
Chapter 4 Methods for Obtaining Green's Functions
101(48)
4.1 Introduction
101(1)
4.2 Method of Images
101(4)
4.3 Laplace Transform Method
105(10)
4.3.1 Definition
106(1)
4.3.2 Temperature Example
106(2)
4.3.3 Derivation of Green's Functions
108(7)
4.4 Method of Separation of Variables
115(8)
4.4.1 Plate with Temperature Fixed at Both Sides (X11)
115(8)
4.5 Product Solution for Transient GF
123(5)
4.5.1 Rectangular Coordinates
123(5)
4.5.2 Cylindrical Coordinates
128(1)
4.6 Method of Eigenfunction Expansions
128(6)
4.7 Steady Green's Functions
134(15)
4.7.1 Integration of the Auxiliary Equation: The Source Solutions
135(4)
4.7.2 Pseudo-Green's Function for Insulated Boundaries
139(2)
4.7.3 Limit Method
141(3)
Problems
144(3)
References
147(2)
Chapter 5 Improvement of Convergence and Intrinsic Verification
149(32)
5.1 Introduction
149(4)
5.1.1 Problems Considered in This
Chapter
149(1)
5.1.2 Two Basic Functions
150(1)
5.1.3 Convergence of the GF
151(2)
5.2 Identifying Convergence Problems
153(5)
5.2.1 Convergence Criterion
153(2)
5.2.2 Monitor the Number of Terms
155(1)
5.2.3 Slower Convergence of the Derivative
156(2)
5.3 Strategies to Improve Series Convergence
158(11)
5.3.1 Replacement of Steady-State Series
158(6)
5.3.2 Alternate GF Solution Equation
164(3)
5.3.3 Time Partitioning
167(2)
5.4 Intrinsic Verification
169(12)
5.4.1 Intrinsic Verification by Complementary Transients
170(2)
5.4.2 Complementary Transient and 1D Solution
172(1)
5.4.3 Intrinsic Verification by Alternate Series Expansion
172(3)
5.4.4 Time-Partitioning Intrinsic Verification
175(3)
Problems
178(2)
References
180(1)
Chapter 6 Rectangular Coordinates
181(56)
6.1 Introduction
181(1)
6.2 One-Dimensional Green's Functions Solution Equation
181(1)
6.3 Semi-Infinite One-Dimensional Bodies
182(10)
6.3.1 Initial Conditions
183(2)
6.3.2 Boundary Conditions
185(6)
6.3.3 Volume Energy Generation
191(1)
6.4 Flat Plates: Small-Cotime Green's Functions
192(5)
6.4.1 Initial Conditions
193(2)
6.4.2 Volume Energy Generation
195(2)
6.5 Flat Plates: Large-Cotime Green's Functions
197(6)
6.5.1 Initial Conditions
197(2)
6.5.2 Plane Heat Source
199(3)
6.5.3 Volume Energy Generation
202(1)
6.6 Flat Plates: The Nonhomogeneous Boundary
203(8)
6.7 Two-Dimensional Rectangular Bodies
211(7)
6.8 Two-Dimensional Semi-Infinite Bodies
218(7)
6.8.1 Integral Expression for the Temperature
218(1)
6.8.2 Special Cases
219(1)
6.8.3 Series Expression for the Temperature
219(3)
6.8.4 Application to the Strip Heat Source
222(2)
6.8.5 Discussion
224(1)
6.9 Steady State
225(12)
Problems
230(5)
References
235(2)
Chapter 7 Cylindrical Coordinates
237(54)
7.1 Introduction
237(1)
7.2 Relations for Radial Heat Flow
237(1)
7.3 Infinite Body
238(4)
7.3.1 The ROO Green's Function
238(2)
7.3.2 Derivation of the ROO Green's Function
240(1)
7.3.3 Approximations for the ROO Green's Function
240(1)
7.3.4 Temperatures from Initial Conditions
240(2)
7.4 Separation of Variables for Radial Heat Flow
242(4)
7.5 Long Solid Cylinder
246(8)
7.5.1 Initial Conditions
246(2)
7.5.2 Boundary Conditions
248(3)
7.5.3 Volume Energy Generation
251(3)
7.6 Hollow Cylinder
254(4)
7.7 Infinite Body with a Circular Hole
258(2)
7.8 Thin Shells, T = T(φ, t)
260(3)
7.9 Limiting Cases for 2D and 3D Geometries
263(2)
7.9.1 Fourier Number
263(1)
7.9.2 Aspect Ratio
264(1)
7.9.3 Nonuniform Heating
264(1)
7.10 Cylinders with T = T (r, z, t)
265(3)
7.11 Disk Heat Source on a Semi-Infinite Body
268(7)
7.11.1 Integral Expression for the Temperature
269(2)
7.11.2 Closed-Form Expressions for the Temperature
271(1)
7.11.3 Series Expression for the Surface Temperature at Large Times
272(2)
7.11.4 Average Temperature
274(1)
7.12 Bodies with T = T(r, φ, t)
275(5)
7.13 Steady State
280(11)
Problems
285(3)
References
288(3)
Chapter 8 Radial Heat Flow in Spherical Coordinates
291(42)
8.1 Introduction
291(1)
8.2 Green's Function Equation for Radial Spherical Heat Flow
292(1)
8.3 Infinite Body
292(5)
8.3.1 Derivation of the RS00 Green's Function
294(3)
8.4 Separation of Variables for Radial Heat Flow in Spheres
297(6)
8.5 Temperature in Solid Spheres
303(16)
8.6 Temperature in Hollow Spheres
319(3)
8.7 Temperature in an Infinite Region outside a Spherical Cavity
322(4)
8.8 Steady State
326(7)
Problems
329(4)
Chapter 9 Steady-Periodic Heat Conduction
333(36)
9.1 Introduction
333(1)
9.2 Steady-Periodic Relations
333(2)
9.3 One-Dimensional GF
335(5)
9.3.1 One-Dimensional GF in Cartesian Coordinates
335(1)
9.3.2 One-Dimensional GF in Cylindrical Coordinates
336(2)
9.3.3 One-Dimensional GF in Spherical Coordinates
338(2)
9.4 One-Dimensional Temperature
340(5)
9.5 Layered Bodies
345(4)
9.6 Two- and Three-Dimensional Cartesian Bodies
349(5)
9.6.1 Rectangles and Slabs
349(3)
9.6.2 Infinite and Semi-Infinite Bodies
352(1)
9.6.3 Rectangular Parallelepiped
353(1)
9.7 Two-Dimensional Bodies in Cylindrical Coordinates
354(7)
9.7.1 GF with Eigenfunctions along r
354(2)
9.7.2 GF with Eigenfunctions along z
356(3)
9.7.3 Axisymmetric Half-Space
359(2)
9.8 Cylinder with T= T (r,φ, z,ω)
361(8)
9.8.1 GF with Eigenfunctions along z
362(1)
9.8.2 GF with Eigenfunctions along r
363(3)
Problems
366(1)
References
367(2)
Chapter 10 Galerkin-Based Green's Functions and Solutions
369(44)
10.1 Introduction
369(1)
10.2 Green's Functions and Green's Function Solution Method
370(17)
10.2.1 Galerkin-Based Integral Method
371(8)
10.2.2 Numerical Calculation of Eigenvalues
379(1)
10.2.3 Nonhomogeneous Solution
380(3)
10.2.4 Green's Functions Expression
383(1)
10.2.5 Properties of Green's Functions
384(1)
10.2.6 Green's Function Solution Equation
385(2)
10.3 Alternative Form of the Green's Function Solution
387(5)
10.4 Basis Functions and Simple Matrix Operations
392(13)
10.4.1 One-Dimensional Bodies
392(1)
10.4.2 Matrices A and B for One-Dimensional Problems
393(3)
10.4.3 Matrix Operations When N = 1 and N = 2
396(9)
10.5 Fins and Fin Effect
405(3)
10.6 Conclusions
408(5)
Problems
409(1)
Note 1 Mathematical Identities
410(1)
Note 2 A Mathematica Program for Determination of Temperature in Example 10.2
410(1)
References
411(2)
Chapter 11 Applications of the Galerkin-Based Green's Functions
413(28)
11.1 Introduction
413(1)
11.2 Basis Functions in Some Complex Geometries
413(10)
11.2.1 Boundary Conditions of the First Kind
414(4)
11.2.2 Boundary Conditions of the Second Kind
418(3)
11.2.3 Boundary Conditions of the Third Kind
421(2)
11.3 Heterogeneous Solids
423(6)
11.4 Steady-State Conduction
429(3)
11.5 Fluid Flow in Ducts
432(5)
11.6 Conclusion
437(4)
Problems
438(2)
References
440(1)
Chapter 12 Unsteady Surface Element Method
441(42)
12.1 Introduction
441(2)
12.2 Duhamel's Theorem and Green's Function Method
443(8)
12.2.1 Derivation of Duhamel's Theorem for Time- and Space- Variable Boundary Conditions
444(4)
12.2.2 Relation to the Green's Function Method
448(3)
12.3 Unsteady Surface Element Formulations
451(14)
12.3.1 Surface Element Discretization
452(2)
12.3.2 Green's Function Form of the USE Equations
454(2)
12.3.3 Time Integration of the USE Equations
456(1)
12.3.4 Flux-Based USE Equations for Bodies in Contact
457(2)
12.3.5 Numerical Solution of the USE Equations for Bodies in Contact
459(4)
12.3.6 Influence Functions
463(2)
12.4 Approximate Analytical Solution (Single Element)
465(5)
12.5 Examples
470(13)
Problems
478(1)
Note 1 Derivation of Equations 12.65a and 12.65b
479(1)
References
480(3)
Appendix B Bessel Functions 483(8)
Appendix D Dirac Delta Function 491(6)
Appendix E Error Function and Related Functions 497(6)
Appendix F Functions and Series 503(2)
Appendix I Integrals 505(14)
Appendix L Laplace Transform Method 519(12)
Appendix P Properties of Selected Materials 531(2)
Appendix R Green's Functions for Radial-Cylindrical Coordinates (r) 533(20)
Appendix R & Φ Green's Functions for Cylindrical Coordinaters (r,φ) 553(10)
Appendix Φ Cylindrical Polar Coordinate, φ Thin Shell Case 563(2)
Appendix RS Green's Functions for Radial Spherical Geometries 565(12)
Appendix X Green's Functions: Rectangular Coordinates 577(36)
Index of Solutions by Number System 613(4)
Author Index 617(2)
Subject Index 619
Kevin Cole, James Beck, A. Haji-Sheikh, Bahman Litkouhi
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