  An overview of the hydrodynamic profiles derived by kinetic theory tools
(Boltzmann equation and kinetic models) for the gravity-driven Poiseuille flow
with particles colliding either elastically (planar and cylindrical geometries)
or inelastically (planar geometry) is presented. The results obtained through
second order in the gravity acceleration show that the Navier-Stokes
predictions are qualitatively incorrect over distances of the order of the mean
free path, especially in the case of the temperature profile
