To compute parameters of heat and mass transfer in evaporating drops the emission-diffusion model is proposed. It is based on a dynamic balance between the vapor flow, obtained in the framework of the kinetic approach of Hertz-Knudsen, and diffusive flow of Maxwell. This approach allows taking into account characteristics of small droplet evaporation, where heat and mass transfer processes are not described by the regular diffusion model. The results of computations of the evaporation of free water droplets of different sizes according to regular diffusion and emission-diffusion models are compared. The effect of free convection flow and radiative heat transfer on droplets evaporation is determined. The suggested model is validated by comparison with experimental data obtained at the evaporation of water droplets suspended on polypropylene monofilaments. The form of droplet during evaporation is detected by microphotographing. The temperature of its surface is measured using infrared thermography. The numerical results and the experimental data show good agreement in time of evaporation and temperature of evaporating drops. (C) 2017 Elsevier Ltd. All rights reserved.