Planned changes for the second edition of
“Heat Conduction using Green’s Functions”
Cole, Beck, Haji-Shiekh, and Litkouhi.
OVERALL CHANGES
Correct known errors
Update references
Cite web site “Green’s Function Library”
Review homework problems
Improve index
DETAILED CHANGES
Chapter 0. Heat Conduction Basics ( Chapter re-numbered from chapter I)
Add discussion of physics behind non-Fourier conduction.
Include W-transformation, taken from problem 3.28 and cite this section later reference this work where the W-transformation is used (fins, etc)
Chapter 1. Introduction to Green’s Functions
1.1 Advantages of the GF method
selling point—GF method produces number from series solution efficiently and accurately
1.2 (new section) Dirac delta function
1.3 (new section) Steady Heat Conduction in
one dimension
1.4 (new section)
Transient GF in the infinite body
1.5 – 1.7 same as previous sections 1.2-1.5, re-numbered.
Figures 1.7 and 1.8, improve labels in figure: replace “alpha” by a
Chapter 2. Numbering System in Heat Conduction (no changes)
Chapter 3. Derivation of the Green’s Function Solution Equation
3.6. Add a discussion of pseudo GF for certain steady problems with all- Neumann boundary conditions (drawn from Cole and Yen, 2001).
3.7 Add citations of recent work of Beck, Yen, McMasters, on special eigenvalues.
Chapter 4. Methods for Obtaining Green’s Functions
Throughout chapter, include language on cotime (long and short)
4.1, 4.2 (no changes)
4.3
Drop listing of properties of
Example 4.2 on case X30, show how it reduces to case X20 when h = 0.
Carefully check all example numbers
4.4 Separation of Variables
Shorten discussion of case X11 and drop example 4.3 on case X22.
Change caption of Table 4.2 to include description “long-cotime form”
Change Table 4.3 to either (a) case by case listing, or (b) drop table altogether
4.5 Product solution (no changes)
4.6 Steady Solution
4.6.1 Shorten discussion of “plane source” solution
4.6.2 Method of embedding (no changes)
4.6.3 Method of Images (drop entire section)
4.6.3 (new section) Eigenfunction Expansion
4.6.4 Limit method (no changes)
New problem: show how X30 reduces to X10 when h goes to infinity, include a hint with the series form of erfc
Chapter 5. (new title) Improvement of Convergence and Intrinsic Verification
Drop: Section on acceleration of series; listings of Fortran codes
5.1, 5.2 (no changes)
5.3 (new section) Strategies for improving convergence (includes replacing steady series; alternate GF method; and, time partitioning
5.4 Integrals occurring in temperature solutions (drop entire section)
5.5 (new section) Intrinsic Verification.
5.6 Numerical Integration (see if program by Don Amos can be cited)
Chapter 6. Rectangular Coordinates
6.1 – 6.4 – include new descriptors “small cotime”, “large cotime”
6.3 Semi-infinite One Dimensional Bodies
Drop Tables 6.1, 6.2, 6.3.
Either drop Table 6.4 or move to Appendix E
6.4 Flat Plates: Small-cotime Green’s Functions
Remove language on “FIN” (from old Table 5.3 which will be dropped)
6.5 Flat Plates: Large-cotime Green’s Functions
Change example 6.5 to discuss replacement of steady-state part
Drop Table 6.5
6.6 Flat Plates: Time Partitioning
Shorten to one example on volume generation that demonstrates time partitioning for 1D, then emphasize that it is best used for 2D and 3D
Chapter 6, continued.
6.7 Two-dimensional Rectangular Bodies.
Add example on swapping out steady solution; and, time-partitioning
6.8 Two-dimensional Semi-infinite Bodies.
6.9 Steady State
Include discussion of GF found from eigenfunction expansion for 2D body
Include alternate GF for steady rectangle example.
Chapter 7 – 11 (no changes)
Chapter 12. Unsteady Surface Element Method
(shorten example 12.3 to remove discussion of T-based solution)
Chapter 13. (new chapter) Steady-Periodic Heat Conduction
Chapter 14. (new chapter) Non-Fourier Heat Conduction
Appendices (add a list of all appendices at the beginning of this section of the book)
Subject Index (increase number of entries)
Author Index