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Evaporation is an effective cooling mechanism widely exploited in the thermal management of modern electronic devices, with a growing interest in the evaporation process in thin-film-based nanoporous membrane technologies. At such scales, classical approaches fail and one requires solutions of the Boltzmann equation; these are obtained here using the direct simulation Monte Carlo method. In particular, the evaporation from representative nanoporous meniscus shapes, corresponding to different operating conditions, has been investigated. Evaporation rates for the different conditions have been characterized as a function of a wide range of Knudsen numbers and free-stream Mach numbers. Additionally, the influence of porosity and evaporation coefficient on the nanoporous evaporation rates has been assessed. Investigations have also been carried out to consider cases where the meniscus has sunk within the pore, and cooling efficacy compared with cases where the meniscus is pinned to the top of the pore. This work demonstrates that the net evaporative mass flux is ultimately determined by the interplay between various physical effects, whose dominance is quantified by the Knudsen number, porosity, evaporation coefficient, and the meniscus shape. This work thus provides useful information for the design of nanoporous membrane-based cooling devices.