Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures

Minh Tuan Ho, Lei Wu, Irina Graur, Yonghao Zhang, Jason Reese

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Abstract

We evaluate the accuracy of the McCormack model by comparing its solutions for Couette and Fourier flows of binary gaseous mixtures with results from the linearized Boltzmann equation. Numerical simulations of Ne-Ar and He-Xe gas mixtures are carried out from slip to near free-molecular flow regimes for different values of the molar concentration. Our numerical results show that while there are only small differences in the shear stress in Couette flow and the heat flux in Fourier flow, calculated from the two kinetic equations, differences in other macroscopic quantities can be very large, especially in free-molecular flow regime. Moreover, the difference between results from the two models increases with the molecular mass ratio and the molar concentration of the heavier species. Finally, the applicability of the McCormack model, which was derived for linearized flows only, is investigated by comparing its solutions with those from the Boltzmann equation for Fourier flow with large wall-temperature ratios.
Original languageEnglish
Pages (from-to)29-41
Number of pages13
JournalInternational Journal of Heat and Mass Transfer
Volume96
Early online date21 Jan 2016
DOIs
Publication statusPublished - 31 May 2016

Fingerprint

Couette flow
Boltzmann equation
free molecular flow
Molecular mass
Difference equations
Gas mixtures
temperature ratio
Heat flux
Shear stress
wall temperature
kinetic equations
mass ratios
shear stress
gas mixtures
heat flux
Kinetics
slip
Computer simulation
Temperature
simulation

Keywords

  • Boltzmann equations
  • McCormack equation
  • Couette flow
  • Fourier method
  • binary gaseous mixture

Cite this

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title = "Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures",
abstract = "We evaluate the accuracy of the McCormack model by comparing its solutions for Couette and Fourier flows of binary gaseous mixtures with results from the linearized Boltzmann equation. Numerical simulations of Ne-Ar and He-Xe gas mixtures are carried out from slip to near free-molecular flow regimes for different values of the molar concentration. Our numerical results show that while there are only small differences in the shear stress in Couette flow and the heat flux in Fourier flow, calculated from the two kinetic equations, differences in other macroscopic quantities can be very large, especially in free-molecular flow regime. Moreover, the difference between results from the two models increases with the molecular mass ratio and the molar concentration of the heavier species. Finally, the applicability of the McCormack model, which was derived for linearized flows only, is investigated by comparing its solutions with those from the Boltzmann equation for Fourier flow with large wall-temperature ratios.",
keywords = "Boltzmann equations, McCormack equation, Couette flow, Fourier method, binary gaseous mixture",
author = "Ho, {Minh Tuan} and Lei Wu and Irina Graur and Yonghao Zhang and Jason Reese",
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Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures. / Ho, Minh Tuan; Wu, Lei; Graur, Irina; Zhang, Yonghao; Reese, Jason.

In: International Journal of Heat and Mass Transfer, Vol. 96, 31.05.2016, p. 29-41.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures

AU - Ho, Minh Tuan

AU - Wu, Lei

AU - Graur, Irina

AU - Zhang, Yonghao

AU - Reese, Jason

PY - 2016/5/31

Y1 - 2016/5/31

N2 - We evaluate the accuracy of the McCormack model by comparing its solutions for Couette and Fourier flows of binary gaseous mixtures with results from the linearized Boltzmann equation. Numerical simulations of Ne-Ar and He-Xe gas mixtures are carried out from slip to near free-molecular flow regimes for different values of the molar concentration. Our numerical results show that while there are only small differences in the shear stress in Couette flow and the heat flux in Fourier flow, calculated from the two kinetic equations, differences in other macroscopic quantities can be very large, especially in free-molecular flow regime. Moreover, the difference between results from the two models increases with the molecular mass ratio and the molar concentration of the heavier species. Finally, the applicability of the McCormack model, which was derived for linearized flows only, is investigated by comparing its solutions with those from the Boltzmann equation for Fourier flow with large wall-temperature ratios.

AB - We evaluate the accuracy of the McCormack model by comparing its solutions for Couette and Fourier flows of binary gaseous mixtures with results from the linearized Boltzmann equation. Numerical simulations of Ne-Ar and He-Xe gas mixtures are carried out from slip to near free-molecular flow regimes for different values of the molar concentration. Our numerical results show that while there are only small differences in the shear stress in Couette flow and the heat flux in Fourier flow, calculated from the two kinetic equations, differences in other macroscopic quantities can be very large, especially in free-molecular flow regime. Moreover, the difference between results from the two models increases with the molecular mass ratio and the molar concentration of the heavier species. Finally, the applicability of the McCormack model, which was derived for linearized flows only, is investigated by comparing its solutions with those from the Boltzmann equation for Fourier flow with large wall-temperature ratios.

KW - Boltzmann equations

KW - McCormack equation

KW - Couette flow

KW - Fourier method

KW - binary gaseous mixture

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