J Austral Math Soc Ser B 33 pp384--401, 1992.

Exact solutions to nonlinear diffusion-convection problems on finite domains

G. C. Sander

Abstract

New exact solutions are presented for nonlinear diffusion and convection on a finite domain 0 £ z £ 1. These solutions are developed for the conditions of constant fluxes at both boundaries z = 0 and z = 1. In particular, solutions for the flux Q_L, at the lower boundary z = 1, being a multiple of the flux Q_S , at the surface z = 0, (that is Q_L = aQ_S , where a = constant), are presented. Solutions for any constant, a, are given for an initial condition which is independent of space z. For the special cases (i) a = 1, and (ii) Q_S = 0 and hence Q_L = 0, solutions are given for an initial condition which has an arbitrary dependence on z.

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Author

G. C. Sander

Division of Science and Technology, Griffith University, Nathan 4111.