Models and solutions for isothermal and nonisothermal evaporation from a partially filled tube

Evaporation from a liquid pool which partially fills a circular tube into an otherwise quiescent ambient has been investigated by a succession of models and accompanying numerical solutions. The modeling included consideration of: (a) evaporation occurring under both isothermal and non-isothermal conditions as related to the absence or presence of depression of the temperature at the liquid surface, (b) interactions between the velocity, mass fraction, and temperature fields in the gas-vapor space in the tube and in the ambient, (c) natural convection in the gas-vapor space, (d) radiative interchange in the gasvapor space, (e) natural convection in the liquid pool, and (f) conduction in the insulation surrounding the tube, in the tube wall, and in the liner between the tube and the insulation. By using a special set of closure conditions at the open top of the tube, it was found that evaporation rates (i.e. Sherwood numbers) of acceptable accuracy can be obtained without having to extend the numerical solutions into the ambient. Another key finding was that the depression of the temperature at the liquid surface decreased the Sherwood number. When radiative transfer in the gas-liquid space was activated, the temperature depression diminished and the Sherwood number markedly increased. Natural convection in the liquid pool also acted to lessen the temperature depression and to increase the Sherwood number.