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Modelling micro mass and heat transfer for gases using extended continuum equations

by M. Torrilhon and H. Struchtrup

(Report number 2008-13)

Abstract
This paper presents recent contributions to the development of macroscopic continuum transport equations for micro gas flows. Within kinetic theory of gases a combination of the Chapman-Enskog expansion and Grad's moment method yields the regularized 13 moment equations (R13 equations) which are of high approximation order. In addition, a complete set of boundary conditions can be derived from the boundary conditions of the Boltzmann equations. The R13 equations are linearly stable and their results for moderate Knudsen numbers stand in excellent agreement to DSMC simulations. We give analytical expressions for heat and mass transfer in micro-channels. These expressions help to understand the complex interaction of fluid variables in micro-scale systems. In particular, the R13 model is capable to predict and explain the Knudsen minimum of mass flow rate in Poiseuille flows.

Keywords:

@Techreport{TS08_378,
  author = {M. Torrilhon and H. Struchtrup},
  title = {Modelling micro mass and heat transfer for gases using extended continuum equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-13.pdf },
  year = {2008}
}

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