Thermoviscous Coating and Rimming Flow

Abstract

A comprehensive description is obtained of steady thermoviscous (that is, with temperature-dependent viscosity) coating and rimming flow of a thin film of fluid 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 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 for positive V and when M ≥ f-1/2 Mc0 for negative V, where is a monotonically decreasing function of V and M c0 ≃ 4.44272 is the critical load in the constant-viscosity case. It is also found that, for the exponential viscosity model, when the prescribed load satisfies M < 1.50315 there is a narrow region of the B-V parameter plane in which backflow occurs. © 2012 The Author. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oup.com.