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Start-up slip flow in a microchannel with a rectangular cross section

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Abstract

The paper outlines results of the theoretical study of an incompressible fluid flow in a rectangular microchannel subject to a sudden time-dependent pressure drop. The momentum equation together with the independent and dependent variables was reduced to a self-similar form by means of the symmetry analysis. The problem was solved using two analytical approaches, the Fourier method and the method of eigenfunction decomposition, as well as numerically by means of the lattice Boltzmann method. The unsteady two-dimensional velocity profiles in the microchannel were predicted using the infinite series and validated against the numerical solution. As expected, the flow pattern asymptotically attains the fully developed state, which is reached more rapidly for smaller Knudsen numbers. The analytical solution yielded expressions for the calculation of the hydraulic resistance coefficient.

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Authors and Affiliations

  1. Institute of Engineering Thermophysics, National Academy of Sciences, Kiev, 03057, Ukraine

    A. A. Avramenko & A. I. Tyrinov

  2. MBtech Group GmbH & Co. KGaA, 70736, Fellbach-Schmiden, Germany

    I. V. Shevchuk

Authors
  1. A. A. Avramenko
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  2. A. I. Tyrinov
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  3. I. V. Shevchuk
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Correspondence to I. V. Shevchuk.

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Communicated by Oleg Zikanov.

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Avramenko, A.A., Tyrinov, A.I. & Shevchuk, I.V. Start-up slip flow in a microchannel with a rectangular cross section. Theor. Comput. Fluid Dyn. 29, 351–371 (2015). https://doi.org/10.1007/s00162-015-0361-x

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  • DOI: https://doi.org/10.1007/s00162-015-0361-x

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