Nonlocal heat conduction in silicon nanowires and carbon nanotubes
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ORIGINAL
Nonlocal heat conduction in silicon nanowires and carbon nanotubes Mingtian Xu 1 Received: 6 April 2020 / Accepted: 31 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Experimental results showed that the effective thermal conductivity of silicon nanowire is smaller than the bulk thermal conductivity, while that of carbon nanotube (CNT) is usually much larger than its bulk counterpart. In order to resolve this paradox, a nonlocal heat conduction model for one-dimensional materials is proposed. This nonlocal model indicates that the different heat conduction boundary conditions of silicon nanowire and CNT lead to the different behaviour of their thermal conductivities in comparison with their bulk counterparts. Furthermore, the nonlocal effect of heat flux on the surfaces of the CNT makes the thermal conductivity of the single-wall CNT more than seven orders of magnitude higher than its bulk thermal conductivity. The thermal conductivities of the single-wall and multi-wall CNTs obtained by using the nonlocal model show an agreement with the experimental ones.
1 Introduction The rapid development of nanotechnology has led to the emergence of one-dimensional materials, such as silicon nanowires and CNTs. Heat conduction in low-dimensional materials is not only an important fundamental scientific problem [1], but also has great application value [2]. The mechanism of heat conduction in low-dimensional materials is still an unsolved problem, which has attracted considerable attention. Lepri et al. studied the classical low-dimensional lattices, and found that the thermal conductivity diverges in the one and two dimension [1]. Narayan and Ramaswamy showed that for one-dimensional momentum-conserving systems the thermal conductivity generally diverges [3]. Basile et al. considered a system of harmonic oscillators perturbed by a nonlinear stochastic dynamics conserving momentum and energy, and found that its thermal conductivity diverges in one and two dimension, while it maintains a finite value in three and higher dimensions [4]. Yang et al. investigated the heat conduction of Femi-Pasta-Ulam lattice, and showed that the dimensional crossover phenomenon occurs when the size in transverse direction tends to zero and that in longitude direction tends to infinity [5]. Chang et al. experimentally found that the room temperature thermal conductivity of individual * Mingtian Xu [email protected] 1
Department of Engineering Mechanics, Shandong University, Jinan 250061, China
multiwalled carbon and boron-nitride nanotube is sizedependent even when the phonon mean free path is much shorter than the sample length [6]. Henry and Chen showed that the thermal conductivity of an individual polymer chain can be very high, even divergent in some cases [7]. Jou et al. found an explicit dependence of the second moments of the fluctuations of the total longitudinal heat flux in cylindrical nanowires on phonon boundary conditions [8]. Sellitto et al. explored the second-order boundary condit
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