Natural convection cooling of a hot vertical wall wet by a falling liquid film

The system studied is a plane channel delimited by two vertical walls, one of which is imposed an arbitrary temperature profile and may be partially or totally wet by a liquid film, while the other is adiabatic. Air from the environment flows along the channel, driven by buoyancy forces. Its mass flow rate depends on the hydraulic resistances and on the distribution of temperature and humidity (hence, density) along the channel, which, in turn, depends on the heat and mass transfer between hot wall and humid air. Due to evaporative or boiling mass transfer, the liquid film, if present, shrinks as it descends along the hot wall, and may be completely dried out at some height. A simplified computational model of the above system was developed and applied to the prediction of relevant quantities, such as the total energy subtracted to the hot wall, for a range of conditions (hot wall temperature and its distribution; film flow rate; ambient air temperature and humidity; channel height and thickness; localized hydraulic resistance).