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

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.

► Analytical and semi-analytical solutions for generalized Newtonian fluids with wall slip.
► The stress models are the power law, Bingham, Herschel–Bulkley, Sisko and Robertson-Stiff.
► Four slip models are studied: linear and non-linear Navier, Hatzikriakos and asymptotic.
► The existence and uniqueness of solutions for the non-linear slip models are proved.