Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip

Abstract

This work presents analytical solutions for both Newtonian and inelastic non-Newtonian fluids with slip boundary conditions in Couette and Poiseuille flows using the Navier linear and non-linear slip laws and the empirical asymptotic and Hatzikiriakos slip laws. The non-Newtonian constitutive equation used is the generalized Newtonian fluid model with the viscosity described by the power law, Bingham, Herschel-Bulkley, Sisko and Robertson-Stiff models. While for the linear slip model it was always possible to obtain closed form analytical solutions, for the remaining non-linear models it is always necessary to obtain the numerical solution of a transcendent equation. Solutions are included with different slip laws or different slip coefficients at different walls.