Limitations of kinetic theory to describe near-field heat exchanges in many-body systems

Kathmann, Christoph; Messina, Riccardo; Ben‐Abdallah, Philippe; Biehs, Svend‐Age

doi:10.1103/physrevb.98.115434

Cited by 32 publications

(21 citation statements)

References 45 publications

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“…We obtained FED results which differ from our previous work by a factor of 2/ , which was due to the use of an inappropriate form of the fluctuation dissipation theorem and has been corrected here. Our results in Figure 3(b) match those of Kathmann et al [29] for FED and for KT with ̃ when their results are appropriately scaled by / for the difference in temperature and Fourier's law is used to calculate thermal conductivity. For the SiC case, there is generally good agreement between KT with ̃ and FED, with an average absolute error of 10.5% for KT where it is nonzero.…”

Section: Radiative Thermal Conductivitysupporting

confidence: 84%

Validity of Kinetic Theory for Radiative Heat Transfer in Nanoparticle Chains

Tervo¹,

Cola²,

Zhang³

2019

Proceeding of Proceedings of the 9th International Symposium on Radiative Transfer, RAD-19

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In chains of closely-spaced nanoparticles supporting surface polaritons, near-field electromagnetic coupling leads to collective effects and super-Planckian thermal radiation exchange. Researchers have primarily used two analytical approaches to calculate radiative heat transfer in these systems: fluctuational electrodynamics, which directly incorporates fluctuating thermal currents into Maxwell's equations, and a kinetic approach where the dispersion relation provides modes and propagation lengths for the Boltzmann transport equation. Here, we compare results from the two approaches in order to identify regimes in which kinetic theory is valid and to explain differing results in the literature on its validity. Using both methods, we calculate the diffusive radiative thermal conductivity of nanoparticle chains. We show that kinetic theory is valid and matches predictions by fluctuational electrodynamics when the propagation lengths are greater than the particle spacing.

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Section: Radiative Thermal Conductivitysupporting

confidence: 84%

Validity of Kinetic Theory for Radiative Heat Transfer in Nanoparticle Chains

Tervo¹,

Cola²,

Zhang³

2019

Proceeding of Proceedings of the 9th International Symposium on Radiative Transfer, RAD-19

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“…Then, a similar heat superdiffusion was found in the periodically arranged planar SiC plates [41]. Recently, a new method was developed to calculate the diffusive radiative thermal conductivity of arbitrary collections of nanoparticles [42], which is an important progress relative to the kinetic method used to calculate the effective radiative thermal conductivity of 1D nanoparticle chain [43][44][45]. Also, the radiative thermal energy (RTE) emitted in the near field by a set of interacting nanoparticles has been the object of investigations, and has been recently predicted to focus the field in spots that are much smaller than those obtained with a single thermal source [46].…”

Section: Introductionmentioning

confidence: 86%

Radiative heat transfer and radiative thermal energy for two-dimensional nanoparticle ensembles

et al. 2020

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Radiative heat transfer (RHT) and radiative thermal energy (RTE) for two-dimensional (2D) nanoparticle ensembles are investigated in the framework of many-body radiative heat transfer theory. We consider nanoparticles made of different materials: metals (Ag), polar dielectrics (SiC), or insulator-metallic phase-change materials (VO 2 ). We start by investigating the RHT between two parallel 2D finite-size square-lattice nanoparticle ensembles, with particular attention to many-body interactions (MBI) effects. We fix the particle radius (a) as the smallest length scale, and we describe the electromagnetic scattering from particles within the dipole approximation. Depending on the minimal distance between the in-plane particles (the lattice spacing p for periodic systems), on the separation d between the two lattice and on the thermal wavelength λ T =hc/k B T , we systematically analyze the different physical regimes characterizing the RHT. Four regimes are identified, rarefied regime, dense regime, non-MBI regime, and MBI regime, respectively. When p λ T , a multiple scattering of the electromagnetic field inside the systems gives rise to a MBI regime. MBI effects manifest themselves in different ways, depending on the separation d: (a) If d > λ T , due to the pure intra-ensemble MBI inside each 2D ensemble, the total heat conductance is less affected, and the thermal conductance spectrum manifests a single peak which is nonetheless shifted with respect to the one typical of two isolated nanoparticles. (b) If d < λ T , there is a strong simultaneous intra-ensemble and inter-ensemble MBI. In this regime there is a direct quantitative effect on the heat conductance, in addition to a qualitative effect on the thermal conductance spectrum, which now manifests a new second peak. As for the RTE, to correctly describe the radiation emitted by metallic nanoparticles, we derive an expression of the Poynting vector including also magnetic contribution, in addition to the electric one. By analyzing both periodic and nonperiodic ensembles, we show that the RTE emitted by a single 2D nanoparticle ensemble is sensitive to the particle distribution. As instance, we see that the RTE emitted by 2D concentric-ring-configuration ensemble has an inhibition feature near the center of the ensemble.

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“…Taking into account that SPhPs can be treated like bosonic particles [20,25], q can be determined by means of the BTE under the relaxation time approximation in the intensity representation [26,27]. The validity of BTE for describing the energy transport by SPhPs still remains under debate as its predictions showed mixed results with respect to the fluctuational electrodynamic theory [28,29]. In thin films, the predictions of the BTE for the SPhP thermal conductivity showed a good agreement with the corresponding ones of this theory [28] and, therefore, in this work, we assume its validity for describing the propagation of SPhPs along a nanowire.…”

Section: Theoretical Modelsmentioning

confidence: 99%

Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire

et al. 2021

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Heat transport guided by the combined dynamics of surface phonon-polaritons (SPhPs) and phonons propagating in a polar nanowire is theoretically modeled and analyzed. This is achieved by solving numerically and analytically the Boltzmann transport equation for SPhPs and the Fourier’s heat diffusion equation for phonons. An explicit expression for the SPhP thermal conductance is derived and its predictions are found to be in excellent agreement with its numerical counterparts obtained for a SiN nanowire at different lengths and temperatures. It is shown that the SPhP heat transport is characterized by two fingerprints: (i) The characteristic quantum of SPhP thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 μm supporting the ballistic propagation of SPhPs. (ii) The deviation of the temperature profile from its typical linear behavior predicted by the Fourier’s law in absence of heat sources. For a 150 μm-long SiN nanowire maintaining a quasi-ballistic SPhP propagation, this deviation can be as large as 1 K, which is measurable by the current state-of-the-art infrared thermometers.

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Limitations of kinetic theory to describe near-field heat exchanges in many-body systems

Cited by 32 publications

References 45 publications

Validity of Kinetic Theory for Radiative Heat Transfer in Nanoparticle Chains

Validity of Kinetic Theory for Radiative Heat Transfer in Nanoparticle Chains

Radiative heat transfer and radiative thermal energy for two-dimensional nanoparticle ensembles

Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire

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