Theoretical andNumerical Study of Free-Molecular FlowProblems

By using two velocity direction-position relations, we investigate free-molecular effusion flows out of a twodimensional slit with a nonzero average exit velocity and a free-molecular effusion flow out of an annular slit with a zero average exit velocity. This study yields two sets of exact solutions and expressions for number density and velocity distributions in front of the exits. These solutions include the exact exit geometry parameters. Several properties of the solutions are discussed mathematically and physically. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical solutions. In general, the comparisons between analytical and numerical results are virtually identical. Besides the theoretical significance, the methodology used in this study can be further applied to study more realistic plume flows.