10 November 2006

 

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  Laplace Transform

Drop listing of properties of Laplace transform and cite new Appendix L Consider dropping example 4.1 on case X10

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)

  • B. Bessel Functions
  • D. (NEW)  Dirac Delta Function
  • E.  Error Function  (remove listings of Fortran code)
  • F.  Functions and Series (from old appendix SE “series expressions”)
  • I.   Integrals (from old appendix F “functions and integrals”)
  • L.  (NEW)  Laplace Transform
  • P.  (NEW) Properties (brief listing of thermal properties of solids)
  • R.  Green’s Functions for Cylindrical Coordinates, Radial
  • R-Phi. Green’s Functions for Cylindrical Coordinates, (r,f)
  • Phi.  Green’s Functions for Cylindrical  Coordinates  f Thin Shell
  • RS. Green’s Functions Spherical Coordinates, Radial
  • X.  Green’s Functions for Rectangular Coordinates
    • Drop approximations to Eigenvalues
    • Completely fill out Tables X.1 and X.2 steady 1D cases (and move these tables to a better place in Appendix X)
  • N.  Index of Solutions by Numbering System

 

Subject Index (increase number of entries)

 

Author Index