Exact solutions to nonlinear diffusion-convection problems on finite domains

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.