On the Application of the Moment equations to the Thermally Induced Flows

Moment equations derived from the Boltzmann equation for the two-dimensional flows were formulated and generalized slip boundary conditions for the moments were derived. Fifty one moments relevant to the eigenfunctions included in the Chapman-Enskog solutions of the second order approximation were taking into account. These moment equations were applied to thermally induced flows in a two-dimensional vessel. The moment equations were solved using the MacCormack's difference scheme. Present results showed that the moment equations and the slip boundary conditions were applicable for the two-dimensional flows in the transition regime. Thermally induced slip flow adjacent to the solid wall decreased linearly in accordance with the decrease of the Knudsen number relevant to the size of the vessel. The values of obtained slip coefficient, velocity/(gradient of temperature along the solid wall), increased as the number of moment equations increased. Present results suggested that moments should be selected so as to decrease the number of equivalent equations in the moment equation system.