  A theoretical framework is established to model the evaporation from
continuously fed droplets, promising tools in the thermal management of high
heat flux electronics. Using the framework, a comprehensive model is developed
for a hemispherical water droplet resting on a heated flat substrate
incorporating all of the relevant transport mechanisms: buoyant and
thermocapillary convection inside the droplet and diffusive and convective
transport of vapor in the gas domain. At the interface, mass, momentum, and
thermal coupling of the phases are also made accounting for all pertinent
physical aspects including several rarely considered interfacial phenomena such
as Stefan flow of gas and the radiative heat transfer from interface to the
surroundings. The model developed utilizes temperature dependent properties in
both phases including the density and accounts for all relevant physics
including Marangoni flow, which makes the model unprecedented. Moreover,
utilizing this comprehensive model, a nonmonotonic interfacial temperature
distribution with double temperature dips is discovered for a hemispherical
droplet having internal convection due to buoyancy in the case of high
substrate temperature. Proposed framework is also employed to construct several
simplified models adopting common assumptions of droplet evaporation and the
computational performance of these models, thereby the validity of commonly
applied simplifying assumptions, are assessed. Benchmark simulations reveal
that omission of gas flow, i.e. neglecting convective transport in gas phase,
results in the underestimation of evaporation rates by 23-54%. When gas flow is
considered but the effect of buoyancy is modeled using Boussinesq approximation
instead of assigning temperature dependent density throughout the gas domain,
evaporation rate can be underestimated by up to 16%.
