Rivulet formulation in the flow of film down a uniformly heated vertical substrate

Three-dimensional regularized weighted residuals model is developed to study vertical falling film on a uniformly substrate with constant heat flux. The model is verified through linear stability analyses in both the stream and the span directions. It is shown that rivulet formation is due to the dominance of the thermocapillary Marangoni effect in the span direction, i.e., the component in the span direction of the surface temperature gradient is much larger than the component in the stream direction, which results from the different heat transfer modes in the stream and the span directions. Four types of initial disturbance are separately imposed on the film flow. It is shown that the initial disturbance does have an influence on the rivulet formation process, but it has no effect on the eventual film structure. Rivulet formation on the film enhances the heat transfer on a wavy film surface, which is attributed for the most part to the increase in the surface area of the film. On the effect of the Reynolds and the Marangoni numbers on rivulet formation, an increase in the former results in an increase in rivulet width, while an increase in the latter causes an advance in the film rupture.