Jeffery–Hamel flow of a shear-thinning fluid that mimics the response of viscoplastic materials

Abstract

The flow between two divergent plane walls with a source at the vertex (Jeffery–Hamel flow) of a shear-thinning fluid, that mimics the response of a class of seemingly viscoplastic materials, is studied. The semi-inverse approach is used to obtain the governing equations for the velocity profile. The third-order non-linear ordinary differential equation governing the flow is solved numerically, and the effects of the material moduli that characterize the fluid, the angle between plane walls, and the inertial term, on the velocity are reported and discussed. Results show that there is a critical angle beyond which flow reversal occurs, and the number and angular extent of inflow regions varies based on the material moduli and the inertial term.