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

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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.
Original languageEnglish
Article number042002
Number of pages8
JournalJournal of Heat Transfer
Issue number4
Early online date10 Jan 2017
Publication statusPublished - 30 Apr 2017



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

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