Continuum and kinetic simulations of heat transfer through rarefied gas in annular and planar geometries in the slip regime

Mustafa Hadj-Nacer, Dilesh Maharjan, Minh-Tuan Ho, Stefan K. Stefanov, Irina Graur, Miles Greiner

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter d, ratios of hotter to cooler surface temperatures T , and inner to outer radii ratio R. The results of S-modelkinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T = 1.1 and large radius ratios R > 0.5; however, for large temperature ratio, a pronounced disagreement is observed.
LanguageEnglish
Article number042002
Number of pages8
JournalJournal of Heat Transfer
Volume139
Issue number4
Early online date10 Jan 2017
DOIs
Publication statusPublished - 30 Apr 2017

Fingerprint

rarefied gases
slip
Gases
heat transfer
Heat transfer
continuums
Kinetics
Geometry
kinetics
heat flux
geometry
temperature ratio
simulation
Temperature
temperature
Heat flux
cold surfaces
hot surfaces
accommodation coefficient
rarefaction

Keywords

  • heat transfer
  • rarefied gas
  • parallel plates
  • coaxial cylinders
  • nonlinear Shakhov model
  • direct simulation Monte Carlo
  • temperature-jump boundary condition
  • heat flux

Cite this

Hadj-Nacer, Mustafa ; Maharjan, Dilesh ; Ho, Minh-Tuan ; Stefanov, Stefan K. ; Graur, Irina ; Greiner, Miles. / Continuum and kinetic simulations of heat transfer through rarefied gas in annular and planar geometries in the slip regime. In: Journal of Heat Transfer. 2017 ; Vol. 139, No. 4.
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abstract = "Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter d, ratios of hotter to cooler surface temperatures T , and inner to outer radii ratio R. The results of S-modelkinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T = 1.1 and large radius ratios R > 0.5; however, for large temperature ratio, a pronounced disagreement is observed.",
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Continuum and kinetic simulations of heat transfer through rarefied gas in annular and planar geometries in the slip regime. / Hadj-Nacer, Mustafa; Maharjan, Dilesh; Ho, Minh-Tuan; Stefanov, Stefan K.; Graur, Irina; Greiner, Miles.

In: Journal of Heat Transfer, Vol. 139, No. 4, 042002, 30.04.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Continuum and kinetic simulations of heat transfer through rarefied gas in annular and planar geometries in the slip regime

AU - Hadj-Nacer, Mustafa

AU - Maharjan, Dilesh

AU - Ho, Minh-Tuan

AU - Stefanov, Stefan K.

AU - Graur, Irina

AU - Greiner, Miles

N1 - © ASME

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N2 - Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter d, ratios of hotter to cooler surface temperatures T , and inner to outer radii ratio R. The results of S-modelkinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T = 1.1 and large radius ratios R > 0.5; however, for large temperature ratio, a pronounced disagreement is observed.

AB - Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter d, ratios of hotter to cooler surface temperatures T , and inner to outer radii ratio R. The results of S-modelkinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T = 1.1 and large radius ratios R > 0.5; however, for large temperature ratio, a pronounced disagreement is observed.

KW - heat transfer

KW - rarefied gas

KW - parallel plates

KW - coaxial cylinders

KW - nonlinear Shakhov model

KW - direct simulation Monte Carlo

KW - temperature-jump boundary condition

KW - heat flux

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