Thermoviscous Coating and Rimming Flow

Type
Article

Authors
Leslie, G. A.
Wilson, S. K.
DUFFY, B. R.

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2012-10-22

Print Publication Date
2012-11-01

Date
2012-10-22

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.

Acknowledgements
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).

Publisher
Oxford University Press (OUP)

Journal
The Quarterly Journal of Mechanics and Applied Mathematics

DOI
10.1093/qjmam/hbs013

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