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
Mustafa Hadj-Nacer

Mechanical Engineering Department,
University of Nevada, Reno,
Reno, NV 89557
e-mail: mhadjnacer@unr.edu

Dilesh Maharjan

Mechanical Engineering Department,
University of Nevada, Reno,
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

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

Irina Graur

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

Miles Greiner

Fellow ASME
Mechanical Engineering Department,
University of Nevada, Reno,
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

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 R0.5; however, for large temperature ratio, a pronounced disagreement is observed.

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U.S. Dept. of Energy, Office of Civilian Radioactive Waste Management (OCRWM), 1987, “ Characteristics of Spent Nuclear Fuel, High-Level Waste, and Other Radioactive Wastes Which May Require Long-Term Isolation,” Report No. DOE/RW-0184.
Saling, J. H. , and Fentiman, A. , 2002, Radioactive Waste Management, 2nd ed., Taylor and Francis, New York.
Colmont, D. , and Roblin, P. , 2008, “ Improved Thermal Modeling of SNF Shipping Cask Drying Process Using Analytical and Statistical Approaches,” Packag. Transp. Storage Secur. Radioact. Mater., 19(3), pp. 160–164. [CrossRef]
USNRC staff, 2003, “ Cladding Considerations for the Transportation and Storage of Spent Fuel,” U.S. Nuclear Regulatory Commission, Memorandum No. 11, Revision No. 3. http://www.nrc.gov/reading-rm/doc-collections/isg/isg-11R3.pdf
Kennard, E. H. , 1938, Kitetic Theory of Gases, McGraw-Hill, New York.
Shakhov, E. M. , 1968, “ Generalization of the Krook Kinetic Relaxation Equation,” Fluid Dyn., 3(5), pp. 95–96. [CrossRef]
Graur, I. A. , and Polikarpov, A. , 2009, “ Comparison of Different Kinetic Models for the Heat Transfer Problem,” Heat Mass Transfer, 46(2), pp. 237–244. [CrossRef]
Graur, I. , Ho, M. T. , and Wuest, M. , 2013, “ Simulation of the Transient Heat Transfer Between Two Coaxial Cylinders,” J. Vac. Sci. Technol. A, 31(6), p. 061603. [CrossRef]
Bird, G. A. , 1994, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Science Publications, Oxford University Press, New York.
Cercignani, C. , 1990, Mathematical Methods in Kinetic Theory, Premuim Press, New York.
Kogan, M. N. , 1969, Rarefied Gas Dynamics, Plenum Press, New York.
Lin, J. T. , and Willis, D. R. , 1972, “ Kinetic Theory Analysis of Temperature Jump in a Polyatomic Gas,” Phys. Fluids, 15(1), pp. 31–38. [CrossRef]
Morse, T. F. , 1964, “ Kinetic Model for Gases With Internal Degrees of Freedom,” Phys. Fluids, 7(2), pp. 159–169. [CrossRef]
Holway, L. H. , 1966, “ New Statistical Models in Kinetic Theory: Methods of Construction,” Phys. Fluids, 9(9), pp. 1658–1673. [CrossRef]
Welander, P. , 1954, “ On the Temperature Jump in a Rarefied Gas,” Ark. Fys., 7(5), pp. 507–553.
Graur, I. , and Ho, M. T. , 2014, “ Rarefied Gas Flow Through a Long Rectangular Channel of Variable Cross Section,” Vacuum, 101, pp. 328–332. [CrossRef]
Sone, Y. , and Sugimoto, H. , 1995, “ Evaporation of a Rarefied Gas From a Cylindrical Condensed Phase Into a Vacuum,” Phys. Fluids, 7(8), p. 2072. [CrossRef]
Larina, I . N. , and Rykov, V . A. , 1998, “ A Numerical Method for Calculating Axisymmetric Rarefied Gas Flows,” Comput. Math. Math. Phys., 38(8), pp. 1335–1346.
Shakhov, E. M. , and Titarev, V . A. , 2009, “ Numerical Study of the Generalized Cylindrical Couette Flow of Rarefied Gas,” Eur. J. Mech. B/Fluids, 28(1), pp. 152–169. [CrossRef]
Hsu, S. K. , and Morse, T. F. , 1972, “ Kinetic Theory of Parallel Plate Heat Transfer in a Polyatomic Gas,” Phys. Fluids, 15(4), pp. 584–591. [CrossRef]
Stefanov, S. , Gospodinov, P. , and Cercignani, C. , 1998, “ Monte Carlo Simulation and Navier-Stokes Finite Difference Solution of Rarefied Gas Flow Problems,” Phys. Fluids, 10(1), pp. 289–300. [CrossRef]
Gallis, M. A. , Torczynski, J. R. , Rader, D. J. , and Bird, G. A. , 2009, “ Convergence Behavior of a New DSMC Algorithm,” J. Comput. Phys., 228(12), pp. 4532–4548. [CrossRef]
Stefanov, S. K. , 2011, “ On DSMC Calculations of Rarefied Gas Flows With Small Number of Particles in Cells,” SIAM J. Sci. Comp., 33(2), pp. 677–702. [CrossRef]
Hadjiconstantinou, N. G. , Garcia, A. L. , Bazant, M. Z. , and He, G. , 2003, “ Statistical Error in Particle Simulations of Hydrodynamic Phenomena,” J. Comput. Phys., 187(1), pp. 274–297. [CrossRef]
Schaaf, S. A. , and Chambre, P. L. , 1958, “ Flow of Rarefied Gases,” Fundamental of Gasdynamics, H. W. Edmmons , ed., Vol. III., Princeton University Press, Princeton, NJ, pp. 687–739.
Akhlaghi, H. , Roohi, E. , and Stefanov, S. , 2012, “ A Newiterative Wall Heat Flux Specifying Technique in DSMC for Heating/Cooling Simulations of MEMS/NEMS,” Int. J. Therm. Sci, 59, pp. 111–125. [CrossRef]
Meng, J. , Zhang, Y. , and M. R. J., 2015, “ Numerical Simulation of Rarefied Gas Flows With Specified Heat Flux Boundary Conditions,” Commun. Comput. Phys., 17(5), pp. 1185–1200. [CrossRef]


Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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



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