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RESEARCH PAPER

Finite Size Effects in Determination of Thermal Conductivities: Comparing Molecular Dynamics Results With Simple Models

[+] Author and Article Information
Patrice Chantrenne

Thermal Center of Lyon (CETHIL), UMR 5008 CNRS, INSA, Ba⁁t. S. Carnot, 20 Av. A. Einstein, 69621 Villeurbanne Cedex, France

Jean-Louis Barrat

Laboratoire de Physique de la Matière Condensée et Nanostructures, UMR 5586 CNRS, UCBL, Ba⁁t. L. Brillouin, 43 Bd. du 11 Nov. 1918, 69622 Villeurbanne Cedex, France

J. Heat Transfer 126(4), 577-585 (May 17, 2004) (9 pages) doi:10.1115/1.1777582 History: Received June 11, 2003; Revised May 17, 2004
Copyright © 2004 by ASME
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References

Figures

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Geometric configuration of the simulations: (a) for periodic boundary condition, the system and the simulation box have the same size; (b) for free surfaces, the size of the simulation box is larger than the system size
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Temperature profile in a system with thermostatted zones as a function of the nondimensional position in the direction of heat transfer. Periodic boundary conditions are used in all directions. The dots indicate the thermostatted zones.
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Velocity repartition function. Bold line: repartition function in the middle of the hot source. Thin line: repartition function in the middle of the intermediate bloc. In both cases, numerical and theoretical repartition functions are superimposed.
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Density of states D (in arbitrary units) versus angular frequency (Lennard-Jones units). Line: results for system at equilibrium; Diamonds: results for system with thermostatted zones.
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Thermal conductivity in LJ units as a function of the system size. Line with squares: periodic boundary conditions. Empty square: result for another thermostat dimension. Line with circles: free surfaces with dead atoms. Stars: free surfaces with phantom atoms. Empty circle: result for a system with really free surfaces.
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Inverse of thermal conductivity as a function of the inverse of the system size. The extrapolation of the regression line to an infinite system size gives the bulk thermal conductivity.
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Normalized thermal conductivity of a cube as a function of its characteristic length. Comparison between the WV model (full lines) with NEMD (dashed lines) for periodic boundary conditions (lines with squares) and fixed boundary surfaces (lines with circles).
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Normalized thermal conductivity of a film (a), as a function of L for two thicknesses (b), and as a function of its thickness for L=2000a0 (c)
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Normalized thermal conductivity of a wire (a), as a function of L for two values of 1 (b), and as a function of 1 for L=2000a0 (c)

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