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An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries

Arlemark, E.J. and Dadzie, S.K. and Reese, J.M. (2010) An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries. Journal of Heat Transfer, 132 (4). 041006-1-041006-8. ISSN 0022-1481

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    Abstract

    We investigate a model for micro-gas-flows consisting of the Navier-Stokes equations extended to include a description of molecular collisions with solid boundaries, together with first and second order velocity slip boundary conditions. By considering molecular collisions affected by boundaries in gas flows we capture some of the near-wall effects that the conventional Navier-Stokes equations with a linear stress/strain-rate relationship are unable to describe. Our model is expressed through a geometry-dependent mean-free-path yielding a new viscosity expression, which makes the stress/strain-rate constitutive relationship non-linear. Test cases consisting of Couette and Poiseuille flows are solved using these extended Navier-Stokes equations, and we compare the resulting velocity profiles with conventional Navier-Stokes solutions and those from the BGK kinetic model. The Poiseuille mass flow-rate results are compared with results from the BGK-model and experimental data, for various degrees of rarefaction. We assess the range of applicability of our model and show that it can extend the applicability of conventional fluid dynamic techniques into the early continuum-transition regime. We also discuss the limitations of our model due to its various physical assumptions, and we outline ideas for further development.

    Item type: Article
    ID code: 13099
    Keywords: micro gas flows, navier stokes equations, mean free path, non linear constitutive relationships, velocity slip, knudsen layer, Mechanical engineering and machinery, Mechanical Engineering, Computational Mechanics
    Subjects: Technology > Mechanical engineering and machinery
    Department: Faculty of Engineering > Mechanical and Aerospace Engineering
    Related URLs:
    Depositing user: Ms Katrina May
    Date Deposited: 29 Sep 2009 13:56
    Last modified: 27 Mar 2014 21:11
    URI: http://strathprints.strath.ac.uk/id/eprint/13099

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