Unsteady flow of Maxwell viscoelastic fluid near a critical point with countercurrent at the initial moment

Two-dimensional unsteady stagnation-point flow of viscoelastic fluids is studied assuming that the fluid obeys the upper-convected Maxwell (UCM) model. The solutions of governing equations are found in assumptions that components of extra stress tensor are polynomials of spatial variable along solid wall. A class of solutions for unsteady flow in the neighbourhood of a front or rear stagnation point on a plane boundary is considered, and a range of possible behaviour is revealed, depending on an initial stage (initial data) and on whether the pressure gradient is accelerating or decelerating function of time. The velocity and stress tensor's components profiles are obtained by numerical integration the system of nonlinear ordinary differential equation. The solutions of equations exhibit finite-time singularities depending on the initial data and the type of pressure gradient dependence on time.