  We study unsteady internal flows in a sessile droplet of capillary size
evaporating in constant contact line mode on a heated substrate.
Three-dimensional simulations of internal flows in evaporating droplets of
ethanol and silicone oil have been carried out. For describing the Marangoni
flows we find it necessary to account for the diffusion of vapor in air, the
thermal conduction in all three phases and thermal radiation. The equations
have been solved numerically by finite element method using ANSYS Fluent. As a
result of the simulations, the nonstationary behavior of B\'enard-Marangoni
(BM) instabilities is obtained. At the first stage, a flower structure of BM
cells near the triple line emerge. For smaller contact angles, the cells grow
in size and occupy the central region of the droplet surface. Being closely
connected with recent experimental and theoretical studies, the results
obtained help to analyze and resolve the associated issues.
