Thin film flow inside a uniformly heated/cooled inclined rotating cylinder

Abstract

The present study investigates the flow of a thin film inside a uniformly heated/cooled cylinder rotating at various inclinations. The governing equations for mass, momentum, and energy are simplified using lubrication approximation and asymptotic analysis. The resulting spatiotemporal equation for film height evolution incorporates dimensionless parameters representing gravity, viscous drag, surface tension, and thermocapillary stress. Two-dimensional, steady-state solutions are derived, revealing that under the dominance of gravity over viscous drag, a liquid pool forms at the bottom of the horizontally rotating cylinder. This pool transforms into a more uniformly distributed thin film as the cylinder is rotated at slopes. Three-dimensional solutions show a ring structure for horizontally rotating cylinder, whereas it disappears for a cylinder rotating at slopes. Introducing infinitesimal axial perturbations to the steady solutions allows for the examination of their stability. The study finds that the thin film flow becomes unstable for a sloped cylinder. The gravitational force stabilizes (destabilizes) the flow for horizontal (vertical) cylinders. It is reported that thermocapillary stress has a stabilizing effect for a uniformly cooled cylinder. Additionally, the outcomes obtained through linear stability analysis have been corroborated through nonlinear computations.