Asymptotic Theory of Nearly Free-Molecular Flows

An asymptotic theory for obtaining nearly free-molecular solutions which are uniformly valid throughout the flow field is proposed in the present study for the linearized Boltzmann equation. The theory is based on an integral-equation formulation of the linearized Boltzmann equation, using an inner-and-outer-expansion procedure. In the inner region the problem is simplified in that the collisional effects are only secondary. Outside of the inner region the angle subtended by the body is small so that the flow field is essentially that created by a source at the origin. The form of the source term is determined by the free-molecular solution to the problem. The drag force is obtained for two-dimensional flows. Three-dimensional flows and nonlinear problems are discussed.