We begin with a model for diffusion: the isotropic one-dimensional random walk.1–4 It is so simple that the basic physical processes cannot elude us. It also has a continuum limit, the diffusion equation, whose solutions are our main concern here and some of whose properties we then examine. Conversely, this model forms the basis for numerical methods of solution. We then discuss the diffusion equation’s form in higher dimensions and other physical instances where that equation offers a realistic description. This chapter ends with a brief account of the origin of conservation principles and constitutive relations that pervade transport phenomena.
KeywordsDiffusion Equation Constitutive Relation Explicit Scheme Adjacent Site Jump Distance
Unable to display preview. Download preview PDF.
- 3.P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963).Google Scholar
- 10.G. D. Smith, Numerical Solutions of Partial Differential Equations: Finite Difference Methods, 3rd ed. (Oxford University Press, Oxford, 1985).Google Scholar
- 12.R. D. Richtmeyer and K. W. Morton, Difference Methods for Initial Value Problems, 2nd ed. (Interscience, New York, 1967).Google Scholar
- 14.R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (John Wiley, New York, 1960).Google Scholar
- 15.J. C. Slattery, Momentum, Energy, and Mass Transfer in Continua, 2nd ed. (Robert E. Krieger, New York, 1981).Google Scholar
- 17.L. Woolf, Downhill All the Way: Autobiography of the Years1919–39 (Hogarth Press, London, 1967).Google Scholar