Revisiting the flat plate laminar boundary layer flow of viscoelastic FENE-P fluids

Abstract

The laminar flat plate boundary-layer flow solution for finitely extensible nonlinear elastic model with Peterlin's closure fluids, originally derived by Olagunju [D. O. Olagunju, Appl. Math. Comput. 173, 593–602 (2006)], is revisited by relaxing some of the assumptions related to the conformation tensor. The ensuing simplification through an order of magnitude analysis and the use of similarity-like variables allows for a semi-analytical approximate similarity solution to be obtained. The proposed solution is more accurate than the original solution, and it tends to self-similar behavior only in the limit of low elasticity. Additionally, we provide a more extensive set of results, including profiles of polymer conformation tensor components, laws of decay for peak stresses and their location, as well as the streamwise variations of boundary layer thickness, displacement and momentum thicknesses. We also provide asymptotic laws for these quantities under low elasticity flow conditions. Comparisons with results from the numerical solution of the full set of governing equations show the approximate similarity solution to be valid up to a high local Weissenberg number ( W i x) between 0.2 and 0.3, corresponding to a local Weissenberg number based on the boundary layer thickness of about 10, for a wide range of values of dumbbell extensibility and solvent viscosity ratio. Above this critical condition, the semi-analytical solution is unable to describe the complex variations of the conformation tensor within the boundary layer, but it still remains accurate in its description of the velocity profiles, friction coefficient, and the variations of displacement, momentum, and boundary layer thicknesses for Weissenberg numbers at least one order of magnitude higher (within 5% up to W i x ≈ 5).