Non-isothermal flow of a thin film of fluid with temperature-dependent viscosity on a stationary horizontal cylinder

Abstract

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A depth-averaged model for non-isothermal thin-film rimming flow

“…Temperature profiles in rimming and coating flows have been extensively studied using lubrication theory with inertia and heat convection typically negligible, for example [6], and good reviews of work on this is available in the recent publications [7,8]. Our paper aims to extend the thin film analysis by including these effects which may become important in the aero-engine application.…”

Thermoviscous Coating and Rimming Flow

“…as used by many previous authors, for example (3,15,16,21,27,39,46). As, for example, Leslie, Wilson and Duffy (27) describe, physically realistic values of V vary over several orders of magnitude from arbitrarily small values (when the viscosity is effectively independent of temperature and/or when the magnitude of the heating or cooling is small) to reasonably large values (when the viscosity is strongly dependent on temperature and/or when the magnitude of the heating or cooling is large).…”

“…As, for example, Leslie, Wilson and Duffy (27) describe, physically realistic values of V vary over several orders of magnitude from arbitrarily small values (when the viscosity is effectively independent of temperature and/or when the magnitude of the heating or cooling is small) to reasonably large values (when the viscosity is strongly dependent on temperature and/or when the magnitude of the heating or cooling is large). Referred to polar coordinates r = a ± Y (with origin at the cylinder's axis) and θ (measured counter-clockwise from the horizontal), as shown in Figure 1 (drawn for coating flow), we take the free surface of the fluid to be at r = a+h for coating flow and r = a−h for rimming flow, the film thickness being denoted by h = h(θ).…”

“…However, relatively little work has been done on thermoviscous coating and rimming flow on a heated or cooled horizontal cylinder. Duffy and Wilson (12) used lubrication theory to study steady flow on both a stationary and a uniformly rotating cylinder in the rather special case in which the free surface is at the same uniform temperature as the surrounding atmosphere and found that the film thickness (and hence the load, but not the temperature or the velocity) can be obtained by a simple re-scaling of the isothermal solution, and recently Leslie, Wilson and Duffy (27) analysed steady thermoviscous flow with prescribed flux on a stationary cylinder. In the present work we obtain a comprehensive description of steady thermoviscous coating and rimming flow on a uniformly rotating horizontal cylinder.…”

Effects of Viscosity and Magnetic Field on a Non-Isothermal Cylindrical Channel Flow

“…Such flow has its applications in heat transfer, convection and radiation in solid, porous and surface to surface media. Activities associated to a non-isothermal flow are industrial processes, heat exchangers and coating activities [1]. Several studies have addressed problem on a non-isothermal channel flow [2,3].…”