A combined numerical and experimental study is carried out to estimate the interfacial evaporative mass flux of warm water in a partly filled rectangular enclosure. The top surface of the enclosure is at a cold reference condition. The study is carried out for a physical time of 30 s. In experiments, interferometry is used as a technique to visualize isotherms during flow induced in water, both during evaporation and with evaporation suppressed. At early time instants, the dominance of diffusive heat transport is observed, but as the cooling proceeds, weak convective currents appear in water. The recorded interferograms are analyzed to estimate the interfacial heat flux and then the interfacial mass flux of vapor. Experiments show that the evaporative heat flux is greater than the non-evaporative heat flux by a factor of six. An ab-initio model is developed in ANSYS-Fluent^® for evaporation, which incorporates two-layer natural convection in air and water and vapour transport in moist air. The model does not require specification of an explicit evaporation rate for the interface. The numerical model is validated against the interferometric experiments. Further, the mathematical model is extended to analyze convection-driven evaporation for two different initial temperatures of water. The initiation of free convection in air is seen to gradually increase the evaporative mass flux. This effect is more significant when the initial water temperature is higher.