Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment

Abstract: Two-dimensional unsteady stagnation-point flow of a viscoelastic fluid is studied assumingthat it obeys the upper-convected Maxwell (UCM) model. The solutions of constitutive equationsare found under the assumption that the components of the extra stress tensor are polynomials inthe spatial variable along a rigid wall. The class of solutions for unsteady flows in aneighbourhood of the front or rear stagnation point on a plane boundary is considered, and therange of possible behaviors is revealed depending on the initial stage (initial data) and on whetherthe pressure gradient is an accelerating or decelerating function of time. The velocity and stresstensor component profiles are obtained by numerical integration of the system of nonlinearordinary differential equations. The solutions of the equations exhibit finite-time singularitiesdepending on the initial data and the type of dependence of pressure gradient on time. © 2022, Pleiades Publishing, Ltd.