Chaffin, S. and Rees, J.M. orcid.org/0000-0002-6266-5708 (2018) Carreau fluid in a wall driven corner flow. Journal of Non-Newtonian Fluid Mechanics, 253. pp. 16-26. ISSN 0377-0257
Abstract
Taylor’s classical paint scraping problem provides a framework for analyzing wall-driven corner flow induced by the movement of an oblique plane with a fixed velocity U. A study of the dynamics of the inertialess limit of a Carreau fluid in such a system is presented. New perturbation results are obtained both close to, and far from, the corner. When the distance from the corner r is much larger than UΓ , where Γ is the relaxation time, a loss of uniformity arises in the solution near the region, where the shear rate becomes zero due to the presence of the two walls. We derive a new boundary layer equation and find two regions of widths r−nr−n and r−2,r−2, where r is the distance from the corner and n is the power-law index, where a change in behavior occurs. The shear rate is found to be proportional to the perpendicular distance from the line of zero shear. The point of zero shear moves in the layer of size r−2r−2. We also find that Carreau effects in the far-field are important for corner angles less than 2.2 rad.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 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/). |
Keywords: | Carreau fluid; Wall driven corner flow; Matched asymptotic |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/I019790/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Feb 2018 13:11 |
Last Modified: | 11 Apr 2024 11:09 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jnnfm.2018.01.002 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:127067 |