Evaporation from an open-topped vertical tube which is partially filled with a liquid has been investigated analytically and numerically. The space above the liquid surface is occupied by a binary mixture consisting of the evaporating vapor and a gas. Spatial variations of the concentrations of the vapor and the gas give rise to density variations which induce natural convection motions. The numerical solutions were carried out for water as the evaporating vapor and air as the gas. It was found that the presence of natural convection can lead to significant increases in the rate of evaporation-up to a factor of five for the investigated parameter ranges. The enhancement is favored by a relatively high concentration of vapor at the liquid surface, a dry ambient, and a relatively large tube diameter. The flow pattern consists of a U-shaped loop, with fluid drawn downward into the tube from the ambient through an annular region adjacent to the tube wall. The upstreaming flow in the core of the tube forms the other leg of the loop.