Revisiting boundary layer flows of viscoelastic fluids

Abstract

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form. Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter.

Publication DOI: https://doi.org/10.1016/j.jnnfm.2022.104976
Divisions: College of Engineering & Physical Sciences
College of Engineering & Physical Sciences > School of Computer Science and Digital Technologies > Applied Mathematics & Data Science
College of Engineering & Physical Sciences > School of Computer Science and Digital Technologies
Funding Information: The authors wish to acknowledge support from the UKRI EPSRC, UK (Grant No. EP/V006614/2 ). We also wish to acknowledge the insightful comments of the anonymous reviewers.
Additional Information: © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Funding Information: The authors wish to acknowledge support from the UKRI EPSRC, UK (Grant No. EP/V006614/2). We also wish to acknowledge the insightful comments of the anonymous reviewers.
Uncontrolled Keywords: Boundary-layer,Viscoelastic,Self-similar
Publication ISSN: 0377-0257
Last Modified: 28 Feb 2024 08:25
Date Deposited: 10 Jan 2023 15:46
Full Text Link:
Related URLs: https://www.sci ... 1951?via%3Dihub (Publisher URL)
http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2023-02
Published Online Date: 2022-12-22
Accepted Date: 2022-12-16
Authors: Griffiths, Paul (ORCID Profile 0000-0002-2078-0118)
Escott, Liam (ORCID Profile 0000-0002-6491-4931)

Download

[img]

Version: Published Version

License: Creative Commons Attribution

| Preview

Export / Share Citation


Statistics

Additional statistics for this record