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

The system studied is a plane channel in which one of the two vertical walls is kept at an arbitrary temperature profile and may be partially or completely wet by a falling liquid film, while the opposite wall is adiabatic. Air from the environment flows along the channel with a mass flow rate which depends on the balance between hydraulic resistances and buoyancy forces. These latter, in their turn, depend on the distribution of temperature and humidity (hence, density) along the channel and eventually on the heat and mass transferred from wall and film to the humid air. 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, as functions of the geometrical and physical quantities that characterize the problem (channel height and thickness, localized hydraulic resistance, hot wall temperature and its distribution, film flow rate, ambient air temperature and humidity). Conclusions were also drawn on the cooling strategy to be adopted in the case when only a limited amount of coolant is available.