The importance of inertia in vertical film boiling stability*

In film boiling a continuous vapor thin-film forms between a liquid and a heated surface. For practical purposes it is of great interest to model the transient dynamics of this vapor film in order to predict the heat transfer coefficient. Such problems are typically handled in the framework of long-wave theory, where the disturbance aspect ratio (ε) is assumed to be small. Typically the Reynolds number (Re) is also assumed to be small, and this allows the removal of both ε² and εRe terms, which greatly simplifies the Navier-Stokes equations. While this is appropriate for horizontal cases, in vertical film boiling the Reynolds number quickly increases, giving rise to inertial effects that the classical approach fails to capture.

In the present work we resolve this issue by retaining the εRe terms. By applying an integral method we reduce the resulting set of governing equations to two coupled scalar PDEs, which include both inertial destabilization and evaporative stabilization. A linear stability analysis yields an estimate for the heat transfer coefficient for long plates, and this proves to be quite accurate for a variety of fluids.