An asymptotic solution for the planar Poiseuille flow of a power-law fluid with pressure-dependent wall slip

In this paper we study the plane Poiseuille flow of power-law fluids with pressure-dependent wall slip. In particular, we assume wall slip conditions which depend exponentially on pressure with a pressure-dependence slip decay parameter ε. The governing equations of the 2D, steady, symmetric flow are transformed into a system of nonlinear integro-differential equations with auxiliary (boundary, symmetry and integral) conditions. We use a regular perturbation scheme to obtain asymptotic solutions written as power series of ε, which is assumed to be a small parameter. We find approximate analytical solutions for all the components of both velocity field and pressure up to the first order. We investigate the behaviour of the longitudinal velocity, the slip velocity, the shear stress and the average pressure-drop for different values of the involved parameters. Our results show that the effects of pressure-dependent wall slip are more pronounced when wall slip is weak, while, for larger values of the slip coefficient, they are gradually eliminated. With regard to inertia, we show that the average pressure-drop remains constant untill the Reynolds number is sufficiently large.