Leslie, G. A. and Wilson, S. K. and Duffy, B. R. (2012) *Thermoviscous Coating and Rimming Flow.* The Quarterly Journal of Mechanics and Applied Mathematics . (Submitted)

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## Abstract

A comprehensive description is obtained of steady thermoviscous (i.e. with temperature-dependent viscosity) coating and rimming flow 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 and the thermoviscosity number) 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 the Biot number when M is greater than or equal to M_ divided by the square root of f for positive thermoviscosity number and when M is greater than M_ for negative thermoviscosity number, where f is a monotonically decreasing function of the thermoviscosity number and M_ = 4.44272 is the critical load in the constant-viscosity case. It is also found that when the prescribed load M is less than 1.50315 there is a narrow region of the Biot number - thermoviscosity number parameter plane in which backflow occurs.

Item Type: | Article |
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Subjects: | D - G > General |

Research Groups: | Oxford Centre for Collaborative Applied Mathematics |

ID Code: | 1556 |

Deposited By: | Peter Hudston |

Deposited On: | 12 Jul 2012 07:37 |

Last Modified: | 12 Jul 2012 07:37 |

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