Abstract
We present a mathematical model for the flow and temperature in a thin liquid film flow coating the inside of a cylinder driven at the surface by an air shear and distributed flux of liquid droplets with liquid removal through a region of the cylinder wall. Modelling is motivated by the industrial application of droplet-cooling of thin oil films in aero-engine bearing chambers where films may be fast-moving which involve significant inertia and heat convection. To account for these effects, we allow the Reynolds and Péclet numbers of the film to be sufficiently large that they persist at leading-order in the thin-film limit. We adopt a Karman–Pohlhausen integral approach of boundary layer theory to extend previous studies to include surface droplet impact and cooling. Example numerical results are presented to illustrate how inertial effects and the impacting droplets influence film dynamics. Thermal characteristics of a selection of flows subject to droplet cooling are investigated.
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