Handbook of Integrals Related to Heat Conduction and Diffusion

By Donald E. Amos

Sandia National Laboratories, Retired



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This handbook is presented in four parts. Chapter 1 presents a Table of Integrals with references to Chapter 2 where the main formulae are presented in handbook format. Formulae presented in Chapter 2 reference Chapter 3 where the derivations are presented in full detail in sub-sections called Folders. The Table of Contents of Chapter 3 lists the titles of 29 Folders along with a brief summary of the results of each Folder. Chapter 4 is devoted to the description of files containing FORTRAN codes used to test the formulae of Chapter 3 numerically.

The research in this volume was directed toward numerical evaluation of diffusion related integrals in subroutines which would return accurate answers over stated ranges of variables. In keeping with the goal of high accuracies, all subroutines were developed in double precision arithmetic. For the IBM PC and similar machines, this means about 16 digits. In many fundamental integrals, much effort was devoted to achieving relative accuracy (significant digits) rather than absolute accuracy (decimal places). Since it is difficult to compute to full precision and avoid all losses of significance, most subroutines returned overall accuracies of 13 digits or better over common ranges of variables. This specification allows several orders of magnitude latitude in the application to problems where only accuracies of 10 digits are required.


This work was funded in part by Beck Engineering Consultants Company 1935 Danbury West Okemos, MI 48864-1873 For Sandia National Laboratories Purchase Order No. 30629 Kevin Dowding, Project Manager

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Researchers should cite this work as follows:

  • Donald E. Amos (2012), "Handbook of Integrals Related to Heat Conduction and Diffusion," https://nanohub.org/resources/13874.

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