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A mathematical model is provided for heat and mass transfer processes of a semi-transparent droplet. The model was validated by checking the calculated instantaneous evaporation rate of a large water droplet and comparing it with experimental data in the case of combined radiative-convective heating. The condensation, transitional and equilibrium evaporation regimes were modelled for droplets at a temperature of 40 °C. Flue gases were considered as hot and humid air flow in 150°C-1000 °C and humidity of 0.4 according to water vapour volumetric fraction, where droplets are slipping with initial velocity up to 60 m/s and their diameter is 50–1000 μm. In phase change regimes a detailed assessment is provided for heat and mass transfer parameters for droplets slipping in radiating high temperature humid gas flow. It was confirmed that the change in thermal and energy states of water droplets is dependent on their dispersity, flue gas temperature and humidity factors, which also define the droplet equilibrium evaporation temperature. The state and phase changes of droplets are influenced by the heat transfer regime change in them from radiative-convective to conductive, which is caused by rapidly decreasing droplet slipping velocity during transient phase change regime and radiation absorption weakening during their equilibrium evaporation. • Original software was used for the investigation. • Circulation inside droplet weakens when velocity is close to the flue gas velocity. • Radiation absorption weakens during droplet evaporation. • Droplet geometrical parameters in phase change regimes change individually. • Results define optimal waste heat recovery conditions in the humid flue gas. [ABSTRACT FROM AUTHOR]