### Abstract

We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.

Original language | English |
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Title of host publication | Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels |

Pages | 95-102 |

Number of pages | 7 |

Publication status | Published - 23 Jul 2008 |

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### Keywords

- micro gas flows
- navier stokes equations
- mean free path
- non linear constitutive relationships
- velocity slip
- knudsen layer

### Cite this

*Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels*(pp. 95-102)

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*Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels.*pp. 95-102.

**An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries.** / Arlemark, E.J.; Dadzie, S.K.; Reese, J.M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries

AU - Arlemark, E.J.

AU - Dadzie, S.K.

AU - Reese, J.M.

PY - 2008/7/23

Y1 - 2008/7/23

N2 - In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers.We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.

AB - In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers.We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.

KW - micro gas flows

KW - navier stokes equations

KW - mean free path

KW - non linear constitutive relationships

KW - velocity slip

KW - knudsen layer

UR - http://www.asmeconferences.org/ICNMM08/pdfs/ICNMM08_FinalProgram.pdf

M3 - Conference contribution book

SN - 978-0-7918-4834-0

SP - 95

EP - 102

BT - Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels

ER -