Evaporation is a crucial step for producing clean water in technologies such as solar desalination. While the configuration of a low-temperature solar still for water production is well-known, its productivity in terms of the mass of liquid water produced per unit area and unit time is quite low. In order to assess acceleration techniques for water production, the evaporation rate from a warm body of water needs to be first established. In the present study, warm water is evaporated in a circular cavity with an air gap and condensed over a colder surface. In the two-fluid system, buoyancy-driven convection appears in air, evaporative cooling and buoyancy-driven flow are seen in the water body. The evaporation-induced buoyant flow in water is studied experimentally using a Mach-Zehnder interferometer in the wedge fringe setting. The relevant interfacial heat flux, including the important contribution from evaporation, is determined by evaluating the interferograms. Numerical simulations of convection in the air-water system have been conducted using commercial software by solving the mass, momentum, energy, and moisture transport equations with Stefan flow and jump conditions in heat flux at the interface. This ab initio approach tracks flow transition in air and water and its influence on the instantaneous evaporation mass flux. The interfacial heat flux determined numerically is compared with experimentally derived values for two temperature differences and three water depths at various time instants. The comparison is found to be good, thus validating the ab initio modelling approach for determining evaporation rates. Further simulations show that a higher temperature difference across the air gap increases the strength of convection in air and hence, the interfacial heat flux. A larger water depth and a consequent reduction of air gap within the cavity delays flow transition in air from diffusion to convection while increased thermal inertia of water results in a quasi-steady state. Interfacial Nusselt numbers have been further compared for circular and cuboidal cavities. For a given Rayleigh number, the circular enclosure shows higher Nusselt number, the difference being attributed to stronger convection in air, sustained by the axisymmetric geometry.