Modelling planar film boiling of arbitrary inclination with the lubrication approximation

Abstract

A model for inclined planar film boiling using the lubrication approximation is derived. A dimensionless form of this model is presented, and it is shown that for a given plane orientation, the dynamics of the film thickness are governed by two dimensionless parameters: The Bond number and the evaporation number. The resulting scalar thin film equation is parabolic, fourth order, and highly nonlinear. A semi-implicit finitevolume method is derived in order to avoid having to satisfy the time step limitations required by explicit methods for the fourth order diffusion term. It is demonstrated how this model can be used to study transient vapor film growth, and the travelling wave instabilities which may occur under certain conditions