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Research Papers: Heat and Mass Transfer

# Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

[+] Author and Article Information

Mechanical Engineering Department,
Reno, NV 89557

Dilesh Maharjan

Mechanical Engineering Department,
Reno, NV 89557
e-mail: dileshz@gmail.com

Minh-Tuan Ho

Department of Mechanical and
Aerospace Engineering,
University of Strathclyde,
Glasgow G1 1XJ 5, UK
e-mail: minh-tuan.ho@strath.ac.uk

Stefan K. Stefanov

Professor
Institute of Mechanics,
Sofia 1113, Bulgaria
e-mail: stefanov@imbm.bas.bg

Irina Graur

Aix Marseille Université,
CNRS, IUSTI UMR 7343,
13453, Marseille, France
e-mail: irina.martin@univ-amu.fr

Miles Greiner

Professor,
Fellow ASME
Mechanical Engineering Department,
Reno, NV 89557
e-mail: greiner@unr.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 12, 2016; final manuscript received November 3, 2016; published online January 10, 2017. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 139(4), 042002 (Jan 10, 2017) (8 pages) Paper No: HT-16-1193; doi: 10.1115/1.4035172 History: Received April 12, 2016; Revised November 03, 2016

## 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 δ, ratios of hotter to cooler surface temperatures $T$, and inner to outer radii ratio $R$. The results of S-model kinetic 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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## Figures

Fig. 1

Cross section of (a) two coaxial cylinders and (b) two parallel plates configurations: dimensions (r, θ) in physical space; dimensions (υr, υθ) (or(υp,φ)) in molecular velocity space

Fig. 5

Percent deference of the dimensionless heat flux q between S-model and DSMC, and Numerical-continuum models as function of the rarefaction parameter δ obtained for all combinations of T and R and different values of thermal accommodation coefficient α

Fig. 2

Dimensionless temperature profiles between plates and cylinders for all combination of R and T and different values of rarefaction parameters δ = 100, 50, 10, and 3 in case α = 1

Fig. 3

Dimensionless heat flux as function of the rarefaction parameter δ obtained for all combination of R and T and different values of thermal accommodation coefficient α

Fig. 4

Dimensionless pressure profiles between plates and cylinders for all combination of R and T and different values of rarefaction parameters δ = 100, 50, 10, and 3 in case α = 1. l = r for R=0.5 and l = 1 − R1 + r for R=1 and 0.1.

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