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Exact solutions to nonlinear diffusion-convection problems on finite domains

Published online by Cambridge University Press:  17 February 2009

G. C. Sander
G. C. Sander
Affiliation:
Division of Science and Technology, Griffith University, Nathan 4111.
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Abstract

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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 QL at the lower boundary z = 1, being a multiple of the flux Qs at the surface z = 0, (that is QL = aQs, 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) Qs = 0 and hence QL = 0, solutions are given for an initial condition which has an arbitrary dependence on z.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 3 , January 1992 , pp. 384 - 401
Copyright
Copyright © Australian Mathematical Society 1992

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