A Mathematical Model of Condensation Heat and Mass Transfer to a Moving Droplet in its Own Vapor

Abstract

A mathematical model appropriate for predicting condensation heat and mass transfer rates along the surface of a droplet moving in pure vapor is developed. A Karman-Pohlhansen type of integral approach was adopted for the solution of vapor-phase boundary layer equations. The diffusion-dominated internal core was solved using a finite difference numerical scheme. The rate-controlling mechanism of pure vapor condensing on a droplet was found in the thermal core region of the liquid phase where the streamlines correspond to the isotherms and diffusion is the primary transport mechanism. The total rate of heat transfer is found to be inversely proportional to the droplet radius. The condensation velocity at the vapor-liquid interface reduces the boundary layer thickness and moves the separation point toward the rear stagnation point. The internal motion also helps increase the transport rates by reducing both the boundary layer thickness and thermal resistance in the liquid phase. The results predicted by this model compare favorably with available experimental values.