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Summary
This compendium of analytical solutions is intended to serve as a handbook or research level course for Petroleum, Chemical, Mechanical, Civil or Electrical engineers and applied scientists. The book, comprising over one thousand solutions, has been written specially for post-graduate students and practitioners in the industry who are searching for ready-made solutions to practical problems.The primary focus of this book is to catalogue solutions to boundary-value problems associated with Dirichlet, Neumann, and Robin boundary conditions. It also offers some variations that are of practical use to the industry. These variations include, subdivided systems where the properties of each continuum are uniform but discontinuous at the interface, solutions involving boundary conditions of the mixed type, where the function is prescribed over part of the boundary and its normal derivative over the remaining part, and problems that involve space and time-dependent boundary conditions. All semi-analytic solutions presented in this book are accompanied by prescriptions for numerical computation.The diffusion coefficient and the initial and boundary conditions used in this book apply to fluid flow in a porous medium. Nonetheless, all solutions can be equally applied to problems in heat conduction and mass transfer.
Table of Contents
Chapter 1. Diffusion mode of transference of heat, mass and pressure; Chapter 2. Integral transforms and their inversion formulae; Chapter 3. Infinite and semi-infinite continuums; Chapter 4. Bounded continuum; Chapter 5. Infinite and semi-infinite (Quadrant) continuums; Chatper 6. Infinite and semi-infinite lamella; Chapter 7. Rectangle; Chapter 8. Infinite and semi-infinite (Octant) continuums; Chapter 9. Quadrant Layer: Infinite and semi-infinite continuums; Chapter 10. Octant Layer: Infinite and semi-infinite continuums; Chapter 11. Cuboid; Chapter 12. Infinite and semi-infinite cylindrical continuums; Chapter 13. Bounded cylindrical continuums; Chapter 14. Infinite and semi-infinite cylindrical continuums; Chapter 15. Bounded cylindrical continuum; Chapter 16. Infinite and semi-infinite cylindrical continuums; Chapter 17. Bounded cylindrical continuum; Chapter 18. Infinite and semi-infinite cylindrical continuums. The continuum is also either infinite or semi-infinite in z; Chapter 19. Infinite and semi-infinite cylindrical continuums bounded by the planes z = 0 and z = d; Chapter 20. Bounded cylindrical continuum. The independent variable z is either infinite or semi-infinite; Chapter 21. Bounded cylindrical continuum. The continuum is also bounded by the planes z = 0 and z = d; Chapter 22. Infinite and semi-infinite cylindrical continuums; Chapter 23. Infinite and semi-infinite cylindrical continuums bounded by the planes z = 0 and z = d; Chapter 24. Bounded cylindrical continuum. The independent variable z is either infinite or semi-infinite; Chapter 25. Bounded cylindrical continuum. The continuum is also bounded by the lxviii planes z = 0 and z = d; Appendix A. Supplement to Chapter 8; Appendix B. Supplement to Chapter 9; Appendix C. Supplement to Chapter 10; Appendix D. Supplement to Chapter 11; Appendix E. Table of Integrals; Appendix F. General properties and a table of Laplace transforms