On corner flows of Oldroyd-B fluids (Q1321579)

This paper examines in detail exact series solutions obtained for planar creeping flows of Oldroyd -- \(B\) fluids in the neighbourhood of sharp corners for both reentrant and non-reentrant sectors. The authors have shown that in the case of reentrant sectors Newtonian-like mathematical solutions exist away from the walls but they give rise to inadmissible singularities at the walls. Alternative solutions have been proposed which have the same kind of asymptotics as upper-convected Maxwell fluid at corners. For a \(270^ \circ\) sector, an inadmissible solution has been identified, and comparison with Hinch's solution [\textit{E. J. Hinch}, J. Non-Newtonian Fluid Mech. 50, No. 2-3, 161-171 (1993; Zbl 0794.76008)] shows some disagreement. In the case of non-reentrant corners, Oldroyd -- \(B\) fluids behave like classical fluids away from the walls. The results of this paper certainly do shed further light on the flow of non-Newtonian fluids around corners.