On the generalization of velocity slip in fluid flows using a steady-state series expansion of the wall shear stress: Case of simple Newtonian fluids

Abstract

This paper is one of two articles, where we present a new wall slip formulation based on a series expansion involving both differential in space and exponential forms of wall shear stress. In the first of these articles, we presented and described this new formulation using Phan-Thien–Tanner fluid as case study. Meanwhile, this second paper analyzes the new slip formulation for Newtonian Fluid. Unlike in the first paper, here, we have considered both the exponential and differential forms, though truncated at three terms each. Thus, we use our new truncated triple-slip-coefficients wall slip law to analyze Newtonian fluid in different systems. In particular, we study the planar Couette and planar Poiseuille problem, where two infinitely long and parallel plates have been used.For this part also, slip velocities and shear stresses at the walls are scrutinized for both problems. Further, as the Couette problem is pressure independent; the differential form of the slip law is considered for Poiseuille problem only. In addition, the pressure and flow-rate are studied for various slip coefficients for Poiseuille flow case using condensed forms of the triple-slip-coefficients. Our results obtained prove reasonable as represented by physically realistic plots herein. This feasibility is especially dictated by the velocity profile across channel width for both application problems. More importantly, results obtained for Poiseuille problem is corroborated with experimental data. Therefore, we can infer from all these, that this new model has the potential of providing results which can match experimental data, that is, if the three slip-coefficients are properly chosen.