Near-field radiative heat transfer

Last updated May 13, 2024

Near-field radiative heat transfer (NFRHT) is a branch of radiative heat transfer which deals with situations for which the objects and/or distances separating objects are comparable or smaller in scale or to the dominant wavelength of thermal radiation exchanging thermal energy. In this regime, the assumptions of geometrical optics inherent to classical radiative heat transfer are not valid and the effects of diffraction, interference, and tunneling of electromagentic waves can dominate the net heat transfer. These "near-field effects" can result in heat transfer rates exceeding the blackbody limit of classical radiative heat transfer.

History

The origin of the field of NFRHT is commonly traced to the work of Sergei M. Rytov in the Soviet Union.^[1] Rytov examined the case of a semi-infinite absorbing body separated by a vacuum gap from a near-perfect mirror at zero temperature. He treated the source of thermal radiation as randomly fluctuating electromagnetic fields. Later in the United States, various groups theoretically examined the effects of wave interference and evanescent wave tunneling.^[2]^[3]^[4]^[5] In 1971, Dirk Polder and Michel Van Hove published the first fully correct formulation of NFRHT between arbitrary non-magnetic media.^[6] They examined the case of two half-spaces separated by a small vacuum gap. Polder and Van Hove used the fluctuation-dissipation theorem to determine the statistical properties of the randomly fluctuating currents responsible for thermal emission and demonstrated definitively that evanescent waves were responsible for super-Planckian (exceeding the blackbody limit) heat transfer across small gaps.

Since the work of Polder and Van Hove, significant progress has been made in predicting NFRHT. Theoretical formalisms involving trace formulas,^[7] fluctuating surface currents,^[8]^[9] and dyadic Green's functions,^[10]^[11] have all been developed. Though identical in result, each formalism can be more or less convenient when applied to different situations. Exact solutions for NFRHT between two spheres,^[12]^[13]^[14] ensembles of spheres,^[13]^[15] a sphere and a half-space,^[16]^[9] and concentric cylinders^[17] have all been determined using these various formalisms. NFRHT in other geometries has been addressed primarily through finite element methods. Meshed surface^[8] and volume^[18]^[19]^[20] methods have been developed which handle arbitrary geometries. Alternatively, curved surfaces can be discretized into pairs of flat surfaces and approximated to exchange energy like two semi-infinite half spaces using a thermal proximity approximation (sometimes referred to as the Derjaguin approximation). In systems of small particles, the discrete dipole approximation can be applied.

Theory

Fundamentals

Most modern works on NFRHT express results in the form of a Landauer formula.^[21] Specifically, the net heat power transferred from body 1 to body 2 is given by

P_{\mathrm {1\rightarrow 2,net} }=\int _{0}^{\infty }\left\{{\frac {\hbar \omega }{2\pi }}\left[n(\omega ,T_{1})-n(\omega ,T_{2})\right]{\mathcal {T}}(\omega )\right\}d\omega

,

where $\hbar$ is the reduced Planck constant, $\omega$ is the angular frequency, $T$ is the thermodynamic temperature, $n(\omega ,T)=\left(1/2\right)\left[\coth {\left(\hbar \omega /2k_{b}T\right)}-1\right]$ is the Bose function, $k_{b}$ is the Boltzmann constant, and

{\mathcal {T}}(\omega )=\sum _{\alpha }\tau _{\alpha }(\omega )

.

The Landauer approach writes the transmission of heat in terms discrete of thermal radiation channels, $\alpha$ . The individual channel probabilities, $\tau _{\alpha }$ , take values between 0 and 1.

NFRHT is sometimes alternatively reported as a linearized conductance, given by^[11]

G_{\mathrm {1\rightarrow 2,net} }(T)=\lim _{T_{1},T_{2}\rightarrow T}{\frac {P_{\mathrm {1\rightarrow 2,net} }}{T_{1}-T_{2}}}=\int _{0}^{\infty }\left[{\frac {\hbar \omega }{2\pi }}{\frac {\partial n}{\partial T}}{\mathcal {T}}(\omega )\right]d\omega

.

Two half-spaces

For two half-spaces, the radiation channels, $\alpha$ , are the s- and p- linearly polarized waves. The transmission probabilities are given by^[6]^[11]^[21]

\tau _{\alpha }(\omega )=\int _{0}^{\infty }\left[{\frac {k_{\rho }}{2\pi }}{\widehat {\tau }}_{\alpha }(\omega )\right]dk_{\rho },

where $k_{\rho }$ is the component of the wavevector parallel to the surface of the half-space. Further,

{\widehat {\tau }}_{\alpha }(\omega )={\begin{cases}{\frac {\left(1-\left|r_{0,1}^{\alpha }\right|^{2}\right)\left(1-\left|r_{0,2}^{\alpha }\right|^{2}\right)}{\left|1-r_{0,1}^{\alpha }r_{0,2}^{\alpha }\exp {\left(2ik_{z,0}l\right)}\right|^{2}}},&{\text{if }}k_{\rho }\leq \omega /c\\{\frac {4\Im {\left(r_{0,1}^{\alpha }\right)}\Im {\left(r_{0,2}^{\alpha }\right)}\exp {\left(-2\left|k_{z,0}\right|l\right)}}{\left|1-r_{0,1}^{\alpha }r_{0,2}^{\alpha }\exp {\left(-2\left|k_{z,0}\right|l\right)}\right|^{2}}},&{\text{if }}k_{\rho }>\omega /c,\end{cases}}

where:

$r_{0,j}^{\alpha }$ are the Fresnel reflection coefficients for $\alpha =s,p$ polarized waves between media 0 and $j=1,2$ ,
$k_{z,0}={\sqrt {(\omega /c)^{2}-k_{\rho }^{2}}}$ is the component of the wavevector in the region 0 perpendicular to the surface of the half-space,
$l$ is the separation distance between the two half-spaces, and
$c$ is the speed of light in vacuum.

Contributions to heat transfer for which $k_{\rho }\leq \omega /c$ arise from propagating waves whereas contributions from $k_{\rho }>\omega /c$ arise from evanescent waves.

Applications

Thermophotovoltaic energy conversion ^[22]
Thermal rectification ^[23]^[24]
Localized cooling ^[25]
Heat-assisted magnetic recording ^[26]^[27]

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References

↑ Rytov, Sergei Mikhailovich (1953). "[Theory of Electric Fluctuations and Thermal Radiation]". Academy of Sciences Press (in Russian).
↑ Emslie, A. G. (1961). "Radiation transfer by closely spaced shields". Archived from the original on August 2, 2021. Retrieved 2021-08-01.{{cite journal}}: Cite journal requires |journal= (help)
↑ Cravalho, E. G.; Tien, C. L.; Caren, R. P. (1967). "Effect of Small Spacings on Radiative Transfer Between Two Dielectrics". Journal of Heat Transfer. 89 (4): 351–358. doi:10.1115/1.3614396 . Retrieved 2021-08-01.
↑ Domoto, G. A.; Tien, C. L. (1970). "Thick Film Analysis of Radiative Transfer Between Parallel Metallic Surfaces" . Journal of Heat Transfer. 92 (3): 399–404. doi:10.1115/1.3449675 . Retrieved 2021-08-01.
↑ Boehm, R. F.; Tien, C. L. (1970). "Small Spacing Analysis of Radiative Transfer Between Parallel Metallic Surfaces" . Journal of Heat Transfer. 92 (3): 405–411. doi:10.1115/1.3449676 . Retrieved 2021-08-01.
1 2 Polder, Dirk; Van Hove, Michel A. (1971). "Theory of Radiative Heat Transfer between Closely Spaced Bodies". Physical Review B. 4 (10): 3303–3314. Bibcode:1971PhRvB...4.3303P. doi:10.1103/PhysRevB.4.3303 . Retrieved 2021-08-01.
↑ Krüger, Matthias; Bimonte, Giuseppe; Emig, Thorsten; Kardar, Mehran (2012). "Trace formulas for nonequilibrium Casimir interactions, heat radiation, and heat transfer for arbitrary objects". Physical Review B. 86 (11): 115423. arXiv: 1207.0374 . Bibcode:2012PhRvB..86k5423K. doi:10.1103/PhysRevB.86.115423. hdl: 1721.1/75443 . S2CID 15560455 . Retrieved 2021-08-01.
1 2 Rodriguez, Alejandro W.; Reid, M. T. H.; Johnson, Steven G. (2012). "Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries". Physical Review B. 86 (22): 220302. arXiv: 1206.1772 . Bibcode:2012PhRvB..86v0302R. doi:10.1103/PhysRevB.86.220302. hdl: 1721.1/80323 . S2CID 2089821 . Retrieved 2021-08-01.
1 2 Rodriguez, Alejandro W.; Reid, M. T. H.; Johnson, Steven G. (2013). "Fluctuating-surface-current formulation of radiative heat transfer: Theory and applications". Physical Review B. 88 (5): 054305. arXiv: 1304.1215 . Bibcode:2013PhRvB..88e4305R. doi:10.1103/PhysRevB.88.054305. hdl: 1721.1/88773 . S2CID 7331208 . Retrieved 2021-08-01.
↑ Volokitin, A. I.; Persson, B. N. J. (2001). "Radiative heat transfer between nanostructures". Physical Review B. 63 (20): 205404. arXiv: cond-mat/0605530 . Bibcode:2001PhRvB..63t5404V. doi:10.1103/PhysRevB.63.205404. S2CID 119363617 . Retrieved 2021-08-01.
1 2 3 Narayanaswamy, Arvind; Zheng, Yi (2014). "A Green's function formalism of energy and momentum transfer in fluctuational electrodynamics". Journal of Quantitative Spectroscopy and Radiative Transfer. 132: 12–21. arXiv: 1302.0545 . Bibcode:2014JQSRT.132...12N. doi:10.1016/j.jqsrt.2013.01.002. S2CID 54093246 . Retrieved 2021-08-01.
↑ Narayanaswamy, Arvind; Chen, Gang (2008). "Thermal near-field radiative transfer between two spheres". Physical Review B. 77 (7): 075125. arXiv: 0909.0765 . Bibcode:2008PhRvB..77g5125N. doi:10.1103/PhysRevB.77.075125. S2CID 56454063 . Retrieved 2021-08-01.
1 2 Mackowski, Daniel W.; Mishchenko, Michael I. (2008). "Prediction of Thermal Emission and Exchange Among Neighboring Wavelength-Sized Spheres". Journal of Heat Transfer. 130 (11). doi:10.1115/1.2957596 . Retrieved 2021-08-01.
↑ Czapla, Braden; Narayanaswamy, Arvind (2017). "Near-field thermal radiative transfer between two coated spheres". Physical Review B. 96 (12): 125404. arXiv: 1703.01320 . Bibcode:2017PhRvB..96l5404C. doi:10.1103/PhysRevB.96.125404. S2CID 119232589 . Retrieved 2021-08-01.
↑ Czapla, Braden; Narayanaswamy, Arvind (2019). "Thermal radiative energy exchange between a closely-spaced linear chain of spheres and its environment". Journal of Quantitative Spectroscopy and Radiative Transfer. 227: 4–11. arXiv: 1812.10769 . Bibcode:2019JQSRT.227....4C. doi:10.1016/j.jqsrt.2019.01.020. S2CID 119434620 . Retrieved 2021-08-01.
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↑ Xiao, Binghe; Zheng, Zhiheng; Gu, Changqing; Yimin, Xuan (2023). "Near-field heat transfer between concentric cylinders" . Journal of Quantitative Spectroscopy and Radiative Transfer. doi:10.1016/j.jqsrt.2023.108588 . Retrieved 2023-03-27.
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↑ Bhatt, Gaurang R.; Zhao, Bo; Roberts, Samantha; Datta, Ipshita; Mohanty, Aseema; Lin, Tong; Hartmann, Jean-Michel; St-Gelais, Raphael; Fan, Shanhui; Lipson, Michal (2020). "Integrated near-field thermo-photovoltaics for heat recycling". Nature Communications. 11 (1): 2545. arXiv: 1911.11137 . Bibcode:2020NatCo..11.2545B. doi:10.1038/s41467-020-16197-6. PMC 7242323 . PMID 32439917 . Retrieved 2021-08-01.
↑ Basu, Soumyadipta; Francoeur, Mathieu (2011). "Near-field radiative transfer based thermal rectification using doped silicon". Applied Physics Letters. 98 (11): 113106. Bibcode:2011ApPhL..98k3106B. doi:10.1063/1.3567026 . Retrieved 2021-08-01.
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[Rytov1953-1] Rytov, Sergei Mikhailovich (1953). "[Theory of Electric Fluctuations and Thermal Radiation]". Academy of Sciences Press (in Russian).

[Emslie1961-2] Emslie, A. G. (1961). "Radiation transfer by closely spaced shields". Archived from the original on August 2, 2021. Retrieved 2021-08-01.{{cite journal}}: Cite journal requires |journal= (help)

[Cravalho1967-3] Cravalho, E. G.; Tien, C. L.; Caren, R. P. (1967). "Effect of Small Spacings on Radiative Transfer Between Two Dielectrics". Journal of Heat Transfer. 89 (4): 351–358. doi:10.1115/1.3614396 . Retrieved 2021-08-01.

[Domoto1970-4] Domoto, G. A.; Tien, C. L. (1970). "Thick Film Analysis of Radiative Transfer Between Parallel Metallic Surfaces" . Journal of Heat Transfer. 92 (3): 399–404. doi:10.1115/1.3449675 . Retrieved 2021-08-01.

[Boehm1970-5] Boehm, R. F.; Tien, C. L. (1970). "Small Spacing Analysis of Radiative Transfer Between Parallel Metallic Surfaces" . Journal of Heat Transfer. 92 (3): 405–411. doi:10.1115/1.3449676 . Retrieved 2021-08-01.

[Polder1971-6] 1 2 Polder, Dirk; Van Hove, Michel A. (1971). "Theory of Radiative Heat Transfer between Closely Spaced Bodies". Physical Review B. 4 (10): 3303–3314. Bibcode:1971PhRvB...4.3303P. doi:10.1103/PhysRevB.4.3303 . Retrieved 2021-08-01.

[Kruger2012-7] Krüger, Matthias; Bimonte, Giuseppe; Emig, Thorsten; Kardar, Mehran (2012). "Trace formulas for nonequilibrium Casimir interactions, heat radiation, and heat transfer for arbitrary objects". Physical Review B. 86 (11): 115423. arXiv: 1207.0374 . Bibcode:2012PhRvB..86k5423K. doi:10.1103/PhysRevB.86.115423. hdl: 1721.1/75443 . S2CID 15560455 . Retrieved 2021-08-01.

[Rodriguez2012-8] 1 2 Rodriguez, Alejandro W.; Reid, M. T. H.; Johnson, Steven G. (2012). "Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries". Physical Review B. 86 (22): 220302. arXiv: 1206.1772 . Bibcode:2012PhRvB..86v0302R. doi:10.1103/PhysRevB.86.220302. hdl: 1721.1/80323 . S2CID 2089821 . Retrieved 2021-08-01.

[Rodriguez2013-9] 1 2 Rodriguez, Alejandro W.; Reid, M. T. H.; Johnson, Steven G. (2013). "Fluctuating-surface-current formulation of radiative heat transfer: Theory and applications". Physical Review B. 88 (5): 054305. arXiv: 1304.1215 . Bibcode:2013PhRvB..88e4305R. doi:10.1103/PhysRevB.88.054305. hdl: 1721.1/88773 . S2CID 7331208 . Retrieved 2021-08-01.

[Volokitin2001-10] Volokitin, A. I.; Persson, B. N. J. (2001). "Radiative heat transfer between nanostructures". Physical Review B. 63 (20): 205404. arXiv: cond-mat/0605530 . Bibcode:2001PhRvB..63t5404V. doi:10.1103/PhysRevB.63.205404. S2CID 119363617 . Retrieved 2021-08-01.

[Narayanaswamy2014-11] 1 2 3 Narayanaswamy, Arvind; Zheng, Yi (2014). "A Green's function formalism of energy and momentum transfer in fluctuational electrodynamics". Journal of Quantitative Spectroscopy and Radiative Transfer. 132: 12–21. arXiv: 1302.0545 . Bibcode:2014JQSRT.132...12N. doi:10.1016/j.jqsrt.2013.01.002. S2CID 54093246 . Retrieved 2021-08-01.

[Narayanaswamy2008-12] Narayanaswamy, Arvind; Chen, Gang (2008). "Thermal near-field radiative transfer between two spheres". Physical Review B. 77 (7): 075125. arXiv: 0909.0765 . Bibcode:2008PhRvB..77g5125N. doi:10.1103/PhysRevB.77.075125. S2CID 56454063 . Retrieved 2021-08-01.

[Mackowski2008-13] 1 2 Mackowski, Daniel W.; Mishchenko, Michael I. (2008). "Prediction of Thermal Emission and Exchange Among Neighboring Wavelength-Sized Spheres". Journal of Heat Transfer. 130 (11). doi:10.1115/1.2957596 . Retrieved 2021-08-01.

[Czapla2017-14] Czapla, Braden; Narayanaswamy, Arvind (2017). "Near-field thermal radiative transfer between two coated spheres". Physical Review B. 96 (12): 125404. arXiv: 1703.01320 . Bibcode:2017PhRvB..96l5404C. doi:10.1103/PhysRevB.96.125404. S2CID 119232589 . Retrieved 2021-08-01.

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