Exact solutions using symmetry methods and conservation laws for the viscous flow through expanding–contracting channels

We present a range of definitions and methods dealing with the reduction of partial differential equations on the basis of the underlying symmetry structure, conservation laws and a combination of these. The method is used to reduce a complex system to an easy-to-handle second-order ordinary differential equation system independent of restrictions on any physical parameters. In particular, we construct exact solutions of a system modelling viscous flow between slowly expanding and contracting walls.