  Interaction of particles of dust with vortex convective flows is under
theoretical consideration. It is assumed that the volume fraction of solid
phase is small, variations of density due to nonuniform distribution of
particles and those caused by temperature nonisothermality of medium are
comparable. Equations for the description of thermal buoyancy convection of a
dusty medium are developed in the framework of the generalized Boussinesq
approximation taking into account finite velocity of particle sedimentation.
The capture of a cloud of dust particles by a vortex convective flow is
considered, general criterion for the formation of such a cloud is obtained.
The peculiarities of a steady state in the form of a dust cloud and backward
influence of the solid phase on the carrier flow are studied in detail for a
vertical layer heated from the sidewalls. It is shown that in the case, when
this backward influence is essential, a hysteresis behavior is possible. The
stability analysis of the steady state is performed. It turns out that there is
a narrow range of governing parameters, in which such a steady state is stable.
