Analytical solution of steady 2D wall-free extensional flows of UCM fluids

•Full analytical solution of upper convected Maxwell fluid in steady extensional flow.•Wall free stagnation flow.•Normal stresses and pressure dependence on both flow coordinates.•Stresses equal to stress particular solutions required to ensure bounded stresses. The general analytical solution for the two-dimensional steady planar extensional flow with wall-free stagnation point is obtained for viscoelastic fluids described by the upper convected Maxwell model providing the stress and pressure fields. The two normal stress fields contain terms that are unbounded for |a|De½ and even for any |a|De, where De denotes the Deborah number and |a|De denotes the Weissenberg number, but the pressure field is only unbounded for |a|De