Laminar-film condensation/evaporation on a vertically fluted surface

Abstract

Laminar-film flow with condensation or evaporation on a vertical fluted cylinder is examined. A kinematic wave equation describing the evolution of the film profile is obtained and solutions presented. The film profile evolves owing to axial, gravity-driven flow and transverse, surface-tension-driven flow from the crests to the valleys of the fluted cylinder. In the case of condensation the majority of the film reaches a uniform thickness and consequently there is a significant improvement in heat transfer compared with the classical unfluted result where the film thickens in an unbounded fashion. For evaporation a critical value of a parameter which involves the ratio of the Weber number and the gradient of the surface curvature is found below which the film totally drys out and above which the fluid funnels into tapering rivulets and only partially drys out. Typical dry-out lines are presented. For short cylinders the evaporative mass transfer for a fluted cylinder is slightly greater than that predicted for an unfluted case. However, when the cylinder is long the mass transfer is far less for a fluted cylinder owing to the reduction in film area associated with partial film dry out.