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 temperaturedependent 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 ``fullfilm'' 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 fullfilm solution with a prescribed load is described. In particular, there are no fullfilm 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 constantviscosity 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 06:37 
Last Modified:  29 May 2015 19:15 
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