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The usefulness of higher-order constitutive relations for describing the Knudsen layer

Lockerby, Duncan A. and Reese, J.M. and Gallis, Michael A. (2005) The usefulness of higher-order constitutive relations for describing the Knudsen layer. Physics of Fluids, 17 (10). p. 100609. ISSN 1070-6631

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    Abstract

    The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight.

    Item type: Article
    ID code: 5019
    Keywords: knudsen flow, slip flow, flow simulation, fluid dynamics, mechanical engineering, kinetic theory, Mechanical engineering and machinery
    Subjects: Technology > Mechanical engineering and machinery
    Department: Faculty of Engineering > Mechanical and Aerospace Engineering
    Related URLs:
      Depositing user: Strathprints Administrator
      Date Deposited: 20 Dec 2007
      Last modified: 11 Jun 2014 05:30
      URI: http://strathprints.strath.ac.uk/id/eprint/5019

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