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Thermoviscous coating and rimming flow

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. 483-511. ISSN 0033-5614

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A comprehensive description is obtained of steady thermoviscous (i.e. with temperature-dependent 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 “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 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 constant-viscosity 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.