Proximity effects in radiative heat transfer

We describe a fluctuating volume-current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume-integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associated matrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles.

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“…However, it is precisely at such small separations that approximate methods such as the proximity approximation become accurate. 41 …”

Section: A Low-rank Approximationsmentioning

confidence: 99%

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

et al. 2015

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“…The cross sections are parallel to the x-y plane and pass through the center of the spheres. The number of sub-volumes used in the simulations is selected such that the error associated with the T-DDA in the absence of sphere C is no more than 2% when compared to the exact solution for two spheres [30][31][32]. The sub-volume size leading to a converged T-DDA solution depends mostly on the dielectric function of the spheres  2 and the sphere diameter to gap ratio D/d [44].…”

Section: Near-field Radiative Heat Transfer Between Three Spheresmentioning

confidence: 99%

Near-field thermal electromagnetic transport: An overview

Edalatpour

DeSutter

Francoeur

2016

Journal of Quantitative Spectroscopy and Radiative Transfer

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A general near-field thermal electromagnetic transport formalism that is independent of the size, shape and number of heat sources is derived. The formalism is based on fluctuational electrodynamics, where fluctuating currents due to thermal agitation are added to Maxwell's curl equations, and is thus valid for heat sources in local thermodynamic equilibrium. Using a volume integral formulation, it is shown that the proposed formalism is a generalization of the classical electromagnetic scattering framework in which thermal emission is implicitly assumed to be negligible. The near-field thermal electromagnetic transport formalism is afterwards applied to a problem involving three spheres with size comparable to the wavelength, where all multipolar interactions are taken into account. Using the thermal discrete dipole approximation, it is shown that depending on the dielectric function, the presence of a third sphere slightly affects the spatial distribution of power absorbed compared to the two-sphere case. A transient analysis shows that despite a non-uniform spatial distribution of power absorbed, the sphere temperature remains spatially uniform at any instant due to the fact that the thermal resistance by conduction is much smaller than the resistance by radiation. The formalism proposed in this paper is general, and † Corresponding authors. Tel.: +1 801 581 5721, Fax: +1 801 585 9825 E-mail addresses: mfrancoeur@mech.utah.edu (M. Francoeur), sheila.edalatpour@utah.edu (S. Edalatpour) 2 could be used as a starting point for adapting solution methods employed in traditional electromagnetic scattering problems to near-field thermal electromagnetic transport.

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“…In addition to a variety of exact numerical techniques, there also exists a set of approximation methods for thermal transfer calculations. Among them, the most popular are the effective medium theory that is used for subwavelength periodic structures [19][20][21][22][23][24] , the proximity approximation and its modified version [25][26][27] , and the coupled mode theory 9,28,29 .…”

Section: Introductionmentioning

confidence: 99%

“…Here, we consider the thermal transfer between periodic array of finite-sized beams with three different beam shapes and a planar substrate in a wide range of distances from far-field to near-field regime. Moreover, for comparison purposes we have investigated the results of approximation methods such as the modified proximity approximation [25][26][27]44 and far-field approximation 27 that have been developed for thermal transfer calculations. The proximity approximation used here is called modified in the sense that it does consider the finite thickness of the beams and neglects part of the thermal transfer that transmits through the beams.…”

Section: Introductionmentioning

confidence: 99%

Effect of shape in near-field thermal transfer for periodic structures

2015

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In this paper, the effect of the geometrical shape on the radiative thermal transfer between a periodic array of beams and a planar substrate is investigated. Specifically, we analyze the changes in the thermal transfer that occur when the cross sectional shape of SiC beams is modified from rectangular to ellipsoidal and finally triangular. Numerical calculations are done based on the rigorous coupled wave analysis. These exact results from this analysis are compared to modified proximity and far-field approximations, which become valid for small and large spacings, respectively. Moreover, these results are also compared to effective medium theory, which becomes increasingly accurate in the limit of small periodicities. We show that a reduction in the periodicity will lead to a reduced thermal transfer for triangular and ellipsoidal shaped beams. Even though, in the limit of very small periodicity, thermal transfer for the case of rectangular shaped beams also decreases by decreasing the periodicity but this decrease is more slowly as compared to other cross sectional shapes. Finally, we show that even though changing periodicity will change the magnitude of thermal transfer, the scaling law for its variation with the beam to substrate spacing is primarily determined by the cross sectional shape rather than the periodicity. We analytically prove this fact by investigating the large and small periodicity regimes. INTRODUCTION:

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Proximity effects in radiative heat transfer

Cited by 46 publications

References 22 publications

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

Near-field thermal electromagnetic transport: An overview

Effect of shape in near-field thermal transfer for periodic structures

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