Note on unsteady viscous flow on the outside of an expanding or contracting cylinder

In this paper, the viscous flow on the outside of an expanding or contracting cylinder is studied. The governing Navier–Stokes equations are transformed into a similarity equation, which is solved by a shooting method. The solution is an exact solution to the unsteady Navier–Stokes equations. Results show both trivial and non-trivial solutions. For trivial solutions, there is no axial flow induced during the cylinder expansion or contraction. However, for the non-trivial solutions which only exist for cylinder expansion, an axial flow is generated and its strength increases with the increase in expansion speed.

► Exact solutions of Navier–Stokes equations are found.
► Similarity solution for viscous flow over an expanding/contracting cylinder.
► Cylinder expansion generates an axial flow.
► Axial flow strength increases with the increase in expansion speed.