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: [email protected].
| Original language | English (US) |
|---|---|
| Pages (from-to) | 483-511 |
| Number of pages | 29 |
| Journal | The Quarterly Journal of Mechanics and Applied Mathematics |
| Volume | 65 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 22 2012 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.