Gravity-driven Poiseuille Flow in Dilute Gases. Elastic and Inelastic   Collisions
  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 
Andres Santos and Mohamed Tij