Leslie, George Adam and Wilson, Stephen and Duffy, Brian (2012) Thermoviscous coating and rimming flow. Quarterly Journal of Mechanics and Applied Mathematics, 65 (4). pp. 483511. ISSN 00335614

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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 which 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 “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 B when M ¸ ˆ f−1/2Mc0 for positive V and when M > Mc0 for negative V , where ˆ f is a monotonically decreasing function of V and Mc0 ' 4.44272 is the critical load in the constantviscosity case. It is also found that when the prescribed load satisfies M < 1.50315 there is a narrow region of the B–V parameter plane in which backflow occurs.
Item type:  Article 

ID code:  42214 
Keywords:  thermoviscous coating , rimming flow, temperaturedependent viscosity, Mathematics, Mechanics of Materials, Mechanical Engineering, Applied Mathematics, Condensed Matter Physics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date Deposited:  27 Nov 2012 15:05 
Last modified:  27 Mar 2015 00:41 
URI:  http://strathprints.strath.ac.uk/id/eprint/42214 
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