Numerical Investigation of Stick–Slip Flow in Shear-Thinning and Shear-Thickening Power-Law Inelastic Fluids

This research focuses on studying an incompressible, non-Newtonian fluid within an axisymmetric straight channel in cylindrical coordinates, divided under the influence of two zones, subject to two boundary conditions: one without slip and the other with slip. This is known as a complex problem called the “stick–slip problem.†Navier–Stokes partial differential equations are used to model the fluid flow, while the inelastic power-law model is employed simultaneously to treat the variation of viscosity, involving shear-thinning and shear-thickening situations. To simulate this problem, an efficient algorithm named the Taylor–Galerkin/pressure-correction (TG/PC) method, which is based on the finite element method, is used. The fundamental contribution of this study is in establishing an efficient numerical simulation to simulate thinning and shear-thickening inelastic fluid flow. In addition, a comprehensive analysis of the influence of applying two different boundary conditions on both sticking and slipping zones and the effect of a singular point located in the transitional region between the two zones. Moreover, this study focused on exploring the effect of the power law index (n), the consistency coefficient (k), and the dimensionless Reynolds number (Re) on the principal variables' components, with a comparison of the effect of stick–slip boundary conditions on it. Also, understanding the impact of these factors on the convergence performance of components was investigated. The results indicate that these rates, as well as the corresponding velocity and pressure’s temporal convergence rates, are greatly affected by characteristics of the power-law inelastic model. In summary, the present work observes that shear-thickening flow displays a higher convergence rate as compared to shear-thinning flow.