In an attempt to generalize wall slip in fluid flows using a series expansion of the wall shear stress: Case of non-Newtonian [Phan–Thien–Tanner fluid]

In this paper, we address a new wall slip formulation based on a series expansion of both differential and exponential forms of wall shear stress. As this is initially considered as an infinite series, we use a truncated version of it to get a slip law having three slip coefficients, where we have considered the exponential form only. We use our new truncated triple-slip-coefficients wall slip law to analyze a particular class of viscoelastic non-Newtonian fluid. This special case follows the Phan–Thien–Tanner fluid model. Moreover, for this fluid, we identify Weissenberg number as one salient parameter affecting slip. In particular, our new model is tested on a familiar planar Couette and planar Poiseuille flow problem, where two parallel and infinitely long plates have been used. Furthermore, slip-dependent analytical expressions for field quantities such as velocity and shear stress at the walls and beyond, are derived and numerically analyzed for both problems. In addition, the pressure and flow-rate are derived for various slip coefficients for Poiseuille flow case.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. Thus, 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.