Convergence of vector spherical wave expansion method applied to near-field radiative transfer

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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“…The accuracy of the T-DDA is assessed by comparison against exact results for two spheres [23][24][25]. As shown in Fig.…”

Section: Accuracy Of the T-ddamentioning

confidence: 99%

“…In this work, the convergence of the T-DDA is studied by computing the relative error between the thermal conductance obtained using the exact solution for two spheres separated by a vacuum gap [23][24][25] and the thermal conductance from T-DDA simulations for the same configuration.…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of the thermal discrete dipole approximation

et al. 2015

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“…This condition is similar to the criterion for the convergence of the vector spherical wave expansion method of the near-field radiative transfer between two spheres which was shown in Ref. [49] to be of the form:…”

Section: Casementioning

confidence: 61%

“…(9) and (10) for radiative energy transfer calculations between two spheres has been derived in Ref. [49]. We will show in Sec.…”

Section: Translation Addition Theoremsmentioning

confidence: 99%

Near-field radiative transfer between two unequal sized spheres with large size disparities

Sasihithlu¹,

Narayanaswamy²

2014

Opt. Express

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We compute near-field radiative transfer between two spheres of unequal radii R1 and R2 such that R2 ≲ 40R1. For R2 = 40R1, the smallest gap to which we have been able to compute radiative transfer is d = 0.016R1. To accomplish these computations, we have had to modify existing methods for computing near-field radiative transfer between two spheres in the following ways: (1) exact calculations of coefficients of vector translation theorem are replaced by approximations valid for the limit d ≪ R1, and (2) recursion relations for a normalized form of translation coefficients are derived which enable us to replace computations of spherical Bessel and Hankel functions by computations of ratios of spherical Bessel or spherical Hankel functions. The results are then compared with the predictions of the modified proximity approximation.

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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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Convergence of vector spherical wave expansion method applied to near-field radiative transfer

Cited by 20 publications

References 46 publications

Convergence analysis of the thermal discrete dipole approximation

Convergence analysis of the thermal discrete dipole approximation

Near-field radiative transfer between two unequal sized spheres with large size disparities

Near-field thermal electromagnetic transport: An overview

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