Abstract
We study the non-linear convection-dispersion equation arising in contaminant or solute transport. Here the model contains the non-constant water velocity which depends on spatial variable. The Lie method of algebra is employed to reduce the convection-dispersion equation (CDE) into ordinary differential equations which can be solved by various standard methods of solutions. The double reduction aided the transformation of partial differential equation (PDE) into ordinary differential equation (ODE). The transient and steady state of oil dispersion is considered. Exact solutions are constructed and some given in terms of special functions.
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