The Mathematical Institute, University of Oxford, Eprints Archive

Thermoviscous Coating and Rimming Flow

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_{c0} divided by the square root of f for positive thermoviscosity number and when M is greater than M_{c0} for negative thermoviscosity number, where f is a monotonically decreasing function of the thermoviscosity number and M_{c0} = 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
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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