The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries

Edalatpour, Sheila; Francoeur, Mathieu

doi:10.1016/j.jqsrt.2013.08.021

Cited by 104 publications

(68 citation statements)

References 72 publications

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“…The T-DDA described in Ref. [35] has been slightly modified, such that the main steps and equations of the updated formulation are provided in Section II. The approximations made in the T-DDA are listed in Section III.…”

Section: Ddamentioning

confidence: 99%

“…(3) is the source function for the scattered field [35]. The incident field is generated by an external source and satisfies the homogenous vector…”

Section: Description Of the T-dda Formalismmentioning

confidence: 99%

“…So far, a few numerical methods have been proposed for solving the thermal stochastic Maxwell equations [28][29][30][31][32][33][34]. Edalatpour and Francoeur [35] presented a relatively simple approach called the thermal discrete dipole approximation (T-DDA). The T-DDA is based on the discrete dipole approximation (DDA), which is a well-known method for modeling light absorption and scattering by particles with size comparable to, or smaller than, the wavelength [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

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Convergence analysis of the thermal discrete dipole approximation

et al. 2015

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The thermal discrete dipole approximation (T-DDA) is a numerical approach for modeling nearfield radiative heat transfer in complex three-dimensional geometries. In this work, the convergence of the T-DDA is investigated by comparison against the exact results for two spheres separated by a vacuum gap. The error associated with the T-DDA is reported for various sphere sizes, refractive indices and vacuum gap thicknesses. The results reveal that for a fixed number of subvolumes, the accuracy of the T-DDA degrades as the refractive index and the sphere diameter to gap ratio increase. A converging trend is observed as the number of subvolumes increases. The large computational requirements associated with increasing the number of subvolumes, and the shape error induced by large sphere diameter to gap ratios, are mitigated by using a nonuniform discretization scheme. Nonuniform discretization is shown to significantly accelerate the convergence of the T-DDA, and is thus recommended for near-field thermal radiation simulations. Errors less than 5% are obtained in 74% of the cases studied by using up to 82712 subvolumes. Additionally, the convergence analysis demonstrates that the T- † 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 DDA is very accurate when dealing with surface polariton resonant modes dominating radiative heat transfer in the near field.

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Section: Ddamentioning

confidence: 99%

“…(3) is the source function for the scattered field [35]. The incident field is generated by an external source and satisfies the homogenous vector…”

Section: Description Of the T-dda Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convergence analysis of the thermal discrete dipole approximation

et al. 2015

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“…145 DDA has been recently employed and suggested as an efficient approach for computing radiative heat transfer 146 as well as fluorescence 3,145 from arbitrary geometries, but unfortunately suffers from a number of important limitations. Technically, DDA belongs to the general class of volume integral equations traditionally solved numerically via the method of weighted residuals 147 (or method of moments as it is conventionally known when applied to computational electromagnetics 148 ), by which integral equations are converted into a solvable and finite set of linear systems of equations.…”

Section: Introductionmentioning

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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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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“…In terms of modeling, closed-form solutions of near-field thermal electromagnetic transport have been derived for special geometries such as one-dimensional layered media [28,29], two large spheres [30][31][32], a sphere and a surface [33,34] and an arbitrary number of nanoparticles modeled as electric point dipoles [35,36] using the method of dyadic Green's function. Moreover, a number of numerical methods have been adapted to near-field thermal radiation: the finite-difference time-domain method [37][38][39], the finite-difference frequencydomain method [40], the boundary element method [41], the method of moments [42] and the discrete dipole approximation, which has been referred to as the thermal discrete dipole approximation (T-DDA) [43,44]. Additional information about near-field thermal radiation modeling and its potential engineering applications can be found in the numerous review papers published during the past decade [28,[45][46][47][48][49][50][51][52].…”

Section: Introductionmentioning

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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The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries

Cited by 104 publications

References 72 publications

Convergence analysis of the thermal discrete dipole approximation

Convergence analysis of the thermal discrete dipole approximation

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

Near-field thermal electromagnetic transport: An overview

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