An Uniformly Valid Asymptotic Theory of Rarified Gas Flows Under the Nearly Free-Molecule Conditions (Classic Reprint)

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Excerpt from An Uniformly Valid Asymptotic Theory of Rarified Gas Flows Under the Nearly Free-Molecule Conditions For the flow of a rarefied gas of Infinite extent past an Immersed body at large Knudsen number, the description of the flow field by the free-molecule solution Is only valid in the Inner region, a region within a distance much larger than the body dimension but much less than a mean free path away from the body. Outside of this region the colllslonal effects cannot be considered as a perturbation even In the lowest order approximation. fb secure a systematic method of obtaining high order colllslonal corrections, It would be necessary to treat adequately the outer region, the flow field outside the Inner region. For this purpose an asymptotic theory for obtaining nearly free-molecule solutions which are uniformly valid throughout the flow field is proposed in the present study for the linearized Boltzmann equation with hard-sphere molecules. Power-law molecules can be treated in a like manner. The theory is based on a new Integral formulation of the linearized Boltzmann equation. An Inner-and-outer-expansion procedure is used. The simplification in the inner region is that the colllslonal effects are only secondary while 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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.