Analytical solution of the viscoelastic Maxwell equations with a critical point in cylindrical geometry

This paper examines two-dimensional flows near a free critical point of an incompressible viscoelastic Maxwell medium using the Johnson–Segalman convected derivative. The flow is assumed to be axisymmetric, and its velocity profile is linear along the axial coordinate. A general exact analytical solution is found for the problem of the distribution of the stress tensor components near the stagnation point.