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The Diffusion of Passive Tracers in Laminar Shear Flow

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Published on: May 1, 2018

Higher-order effects in rarefied channel flows.

Henning Struchtrup¹, Manuel Torrilhon

¹Department of Mechanical Engineering, University of Victoria, Victoria BC, Canada V8W 2Y2. struchtr@uvic.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2008

Summary

This summary is machine-generated.

The regularized 13 moment (R13) equations model gas behavior in channel flows, showing a temperature profile dip. Reduced R13 equations lose Knudsen layer descriptions but predict a Knudsen number minimum for heated gas temperature.

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Area of Science:

Fluid dynamics
Kinetic theory of gases

Background:

The regularized 13 moment (R13) equations are a kinetic model for rarefied gas dynamics.
Understanding gas behavior in micro/nanochannels requires accurate modeling of rarefied effects.

Purpose of the Study:

To analyze the regularized 13 moment (R13) equations for plane channel flows.
To investigate the impact of Chapman-Enskog scaling on R13 equation solutions.
To examine the prediction of temperature profiles and Knudsen layers in rarefied gas flows.

Main Methods:

Applying Chapman-Enskog scaling to the R13 equations for Knudsen number-based reduction.
Analyzing the resulting second-order slip conditions.
Comparing solutions with and without Knudsen layers to direct Boltzmann equation solutions.

Main Results:

Reduced R13 equations capture the temperature profile dip in force-driven flow but lose Knudsen layer description.
Including Knudsen layers in R13 solutions improves agreement with Boltzmann equation results.
R13 equations predict a minimum in average gas temperature around Knudsen number 0.2 for radiatively heated gas.

Conclusions:

Chapman-Enskog scaling simplifies R13 equations but sacrifices Knudsen layer accuracy.
R13 equations with Knudsen layers offer better agreement with fundamental kinetic theory.
The predicted Knudsen minimum highlights the importance of rarefaction effects on gas temperature.