Modeling of Navier-Stokes equations for high Knudsen number gas flows

Nishanth Dongari, Anupam Agrawal

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39 Citations (Scopus)


The possibility of modeling the Navier–Stokes equations and together with the conventional second order slip boundary condition at high Knudsen numbers is explored in this paper by incorporating the Knudsen diffusion phenomenon in rarefied gases. An effective mean free path (MFP) model is augmented to the
governing equation and the slip boundary condition, as gas transport properties can be related to the MFP. This simple modification is shown to implicitly take care of the complexities associated in the transitional flow regime, without necessitating dependency of the slip coefficients on the Knudsen number. Unique analytical model with fixed values of slip coefficients is proposed and rigorous comparisons with the experimental and simulation data for pressure driven and thermally driven rarefied gas flows support
this conjecture. First and second order slip coefficients have been proposed as 1.1466 and 0.9756 for rectangular channels and 1.1466 and 0.14 for the capillaries, from the continuum to the transition flow regime. The current work is significant from the numerical simulation point of view because simulation
tools are better developed for Navier–Stokes equations.
Original languageEnglish
Pages (from-to)4352-4358
JournalInternational Journal of Heat and Mass Transfer
Issue number15-16
Early online date9 May 2012
Publication statusPublished - Jun 2012


  • Knudsen diffusion
  • microchannels
  • micro-capillary flow
  • thermal transpiration
  • Navier-Stokes
  • gas flows


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