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Research Papers: Micro/Nanoscale Heat Transfer

Phonon Boundary Effects and Thermal Conductivity of Rough Concentric Nanowires

[+] Author and Article Information
F. X. Alvarez1

Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spainxavier.alvarez@uab.cat

D. Jou

Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain; Institut d’Estudis Catalans, Carme 47, 08001 Barcelona, Catalonia, Spaindavid.jou@uab.cat

A. Sellitto

Department of Mathematics and Computer Science, University of Basilicata, Campus Macchia Romana, 85100 Potenza, Italyant.sellitto@gmail.com

1

Corresponding author.

J. Heat Transfer 133(2), 022402 (Nov 02, 2010) (7 pages) doi:10.1115/1.4002439 History: Received December 13, 2009; Revised August 20, 2010; Published November 02, 2010; Online November 02, 2010

By using a phonon hydrodynamics model for heat flow complemented with boundary conditions for smooth or rough boundaries, we study the influence of boundary conditions on the longitudinal thermal conductivity for several kinds of nanowires (single, tubular, and core-shell). The effects of the boundaries are seen to be extremely important.

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Figures

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Figure 2

Cylindrical and concentric nanowires with a longitudinal heat flow. The inner core may be made either by different material with respect to the outer shell (core-shell nanowire) or it may be vacuum (tubular nanowire).

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Figure 3

Comparison between the behavior of the effective thermal conductivity of a Si–Ge core-shell composite nanowire and that of a Ge tubular nanowire in terms of the ratio Φ=Ric/Ros at 100 K (κSi(0)=884 W m−1 K−1, κGe(0)=232 W m−1 K−1, lSi=557 nm, and lGe=130 nm). Only specular and diffusive scattering has been supposed on the walls, i.e., Δ=0 nm both in the silicon and in the germanium.

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Figure 4

Comparison between the behavior of the effective thermal conductivity of a Si–Ge core-shell composite nanowire and that of a Ge tubular nanowire in terms of the ratio Φ=Ric/Ros at 100 K. The presence of backscattering on both walls has been supposed (Δ=3 nm and L=6 nm).

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Figure 5

Behavior of the effective thermal conductivity of a Si–Ge core-shell composite nanowire at 100 K in terms of the ratio Φ=Ric/Ros in the case of backscattering only in the outer shell (Fig. 5) and in the case of backscattering only in the inner core (Fig. 5). The inset in Fig. 5, plotting the results in a shorter length scale, allows to show the behavior of κnw(eff) around the value Φ=0.85 clearer. The friction parameters characterizing backscattering are Δ=3 nm and L=6 nm.

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Figure 1

Different degree of roughness of a wall described by the parameters Δ (height of the roughness peaks) and L (separation of neighboring roughness peaks). When the ratio Δ/L→0 (or in the limit case when Δ=0), only specular and diffusive scattering is expected (Fig. 1). Otherwise, backscattering is expected (Fig. 1). Furthermore, when L=2Δ, the surface has no flat regions but it is completely rough in which case C=0 is expected.

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