Handle URI:
http://hdl.handle.net/10754/600007
Title:
Thermoviscous Coating and Rimming Flow
Authors:
Leslie, G. A.; Wilson, S. K.; DUFFY, B. R.
Abstract:
A comprehensive description is obtained of steady thermoviscous (that is, with temperature-dependent viscosity) coating and rimming flow of a thin film of fluid on a uniformly rotating horizontal cylinder that is uniformly hotter or colder than the surrounding atmosphere. It is found that, as in the corresponding isothermal problem, there is a critical solution with a corresponding critical load (which depends, in general, on both the Biot number B and the thermoviscosity number V) above which no 'full-film' solutions corresponding to a continuous film of fluid covering the entire outside or inside of the cylinder exist. The effect of thermoviscosity on both the critical solution and the full-film solution with a prescribed load is described. In particular, there are no full-film solutions with a prescribed load M for any value of B when for positive V and when M ≥ f-1/2 Mc0 for negative V, where is a monotonically decreasing function of V and M c0 ≃ 4.44272 is the critical load in the constant-viscosity case. It is also found that, for the exponential viscosity model, when the prescribed load satisfies M < 1.50315 there is a narrow region of the B-V parameter plane in which backflow occurs. © 2012 The Author. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oup.com.
Citation:
Leslie GA, Wilson SK, DUFFY BR (2012) Thermoviscous Coating and Rimming Flow. The Quarterly Journal of Mechanics and Applied Mathematics 65: 483–511. Available: http://dx.doi.org/10.1093/qjmam/hbs013.
Publisher:
Oxford University Press (OUP)
Journal:
The Quarterly Journal of Mechanics and Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
22-Oct-2012
DOI:
10.1093/qjmam/hbs013
Type:
Article
ISSN:
0033-5614; 1464-3855
Sponsors:
The first author (G. A. L.) gratefully acknowledges the financial support of the United Kingdom Engineering and Physical Sciences Research Council (EPSRC) via a Doctoral Training Account (DTA) research studentship. Part of this work was undertaken while the corresponding author (S. K. W.) was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, Princeton University, USA, and it was completed while he was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM), Mathematical Institute, University of Oxford, UK. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLeslie, G. A.en
dc.contributor.authorWilson, S. K.en
dc.contributor.authorDUFFY, B. R.en
dc.date.accessioned2016-02-28T06:34:15Zen
dc.date.available2016-02-28T06:34:15Zen
dc.date.issued2012-10-22en
dc.identifier.citationLeslie GA, Wilson SK, DUFFY BR (2012) Thermoviscous Coating and Rimming Flow. The Quarterly Journal of Mechanics and Applied Mathematics 65: 483–511. Available: http://dx.doi.org/10.1093/qjmam/hbs013.en
dc.identifier.issn0033-5614en
dc.identifier.issn1464-3855en
dc.identifier.doi10.1093/qjmam/hbs013en
dc.identifier.urihttp://hdl.handle.net/10754/600007en
dc.description.abstractA comprehensive description is obtained of steady thermoviscous (that is, with temperature-dependent viscosity) coating and rimming flow of a thin film of fluid on a uniformly rotating horizontal cylinder that is uniformly hotter or colder than the surrounding atmosphere. It is found that, as in the corresponding isothermal problem, there is a critical solution with a corresponding critical load (which depends, in general, on both the Biot number B and the thermoviscosity number V) above which no 'full-film' solutions corresponding to a continuous film of fluid covering the entire outside or inside of the cylinder exist. The effect of thermoviscosity on both the critical solution and the full-film solution with a prescribed load is described. In particular, there are no full-film solutions with a prescribed load M for any value of B when for positive V and when M ≥ f-1/2 Mc0 for negative V, where is a monotonically decreasing function of V and M c0 ≃ 4.44272 is the critical load in the constant-viscosity case. It is also found that, for the exponential viscosity model, when the prescribed load satisfies M < 1.50315 there is a narrow region of the B-V parameter plane in which backflow occurs. © 2012 The Author. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oup.com.en
dc.description.sponsorshipThe first author (G. A. L.) gratefully acknowledges the financial support of the United Kingdom Engineering and Physical Sciences Research Council (EPSRC) via a Doctoral Training Account (DTA) research studentship. Part of this work was undertaken while the corresponding author (S. K. W.) was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, Princeton University, USA, and it was completed while he was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM), Mathematical Institute, University of Oxford, UK. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherOxford University Press (OUP)en
dc.titleThermoviscous Coating and Rimming Flowen
dc.typeArticleen
dc.identifier.journalThe Quarterly Journal of Mechanics and Applied Mathematicsen
dc.contributor.institutionUniversity of Strathclyde, Glasgow, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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