Near-field radiative heat transfer

Prediction of radiative heat transfer between two spheres computed using near-field (NFRHT), classical (CRT), and discrete dipole (DDA) methods.

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.

## Contents

* 1 History
* 2 Theory
* 2.1 Fundamentals
* 2.2 Two half-spaces
* 3 Applications
* 4 References

## 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

P1->2,net=∫0∞{ℏω2π[n(ω,T1)−n(ω,T2)]𝒯(ω)}dω,

where ℏ is the reduced Planck constant, ω is the angular frequency, T is the thermodynamic temperature, n(ω,T)=(1/2)[coth⁡(ℏω/2kbT)−1] is the Bose function, kb is the Boltzmann constant, and

𝒯(ω)=∑ατα(ω).

The Landauer approach writes the transmission of heat in terms discrete of thermal radiation channels, α. The individual channel probabilities, τα, take values between 0 and 1.

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

G1->2,net(T)=limT1,T2->TP1->2,netT1−T2=∫0∞[ℏω2π∂n∂T𝒯(ω)]dω.

### Two half-spaces

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

τα(ω)=∫0∞[kρ2πτ^α(ω)]dkρ,

where kρ is the component of the wavevector parallel to the surface of the half-space. Further,

τ^α(ω)={(1−|r0,1α|2)(1−|r0,2α|2)|1−r0,1αr0,2αexp⁡(2ikz,0l)|2,if kρ≤ω/c4ℑ(r0,1α)ℑ(r0,2α)exp⁡(−2|kz,0|l)|1−r0,1αr0,2αexp⁡(−2|kz,0|l)|2,if kρ>ω/c,

where:

* r0,jα are the Fresnel reflection coefficients for α=s,p polarized waves between media 0 and j=1,2,
* kz,0=(ω/c)2−kρ2 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 kρ≤ω/c arise from propagating waves whereas contributions from kρ>ω/c arise from evanescent waves.

## Applications

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

## References

1. ↑ Rytov, Sergei Mikhailovich (1953). "[Theory of Electric Fluctuations and Thermal Radiation]" (in Russian). Academy of Sciences Press.
2. ↑ Emslie, A. G. (1961). Radiation transfer by closely spaced shields. https://apps.dtic.mil/sti/citations/AD0257466. Retrieved 2021-08-01.
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. https://doi.org/10.1115/1.3614396. Retrieved 2021-08-01.
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. https://doi.org/10.1115/1.3449675. Retrieved 2021-08-01.
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. https://doi.org/10.1115/1.3449676. Retrieved 2021-08-01.
6. ↑ 6.0 6.1 Polder, Dirk; Van Hove, Michel A. (1971). "Theory of Radiative Heat Transfer between Closely Spaced Bodies". Physical Review B 4 (10): 3303–3314. doi:10.1103/PhysRevB.4.3303. Bibcode: 1971PhRvB...4.3303P. https://link.aps.org/doi/10.1103/PhysRevB.4.3303. Retrieved 2021-08-01.
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. doi:10.1103/PhysRevB.86.115423. Bibcode: 2012PhRvB..86k5423K. https://link.aps.org/doi/10.1103/PhysRevB.86.115423. Retrieved 2021-08-01.
8. ↑ 8.0 8.1 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. doi:10.1103/PhysRevB.86.220302. Bibcode: 2012PhRvB..86v0302R. https://link.aps.org/doi/10.1103/PhysRevB.86.220302. Retrieved 2021-08-01.
9. ↑ 9.0 9.1 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. doi:10.1103/PhysRevB.88.054305. Bibcode: 2013PhRvB..88e4305R. https://link.aps.org/doi/10.1103/PhysRevB.88.054305. Retrieved 2021-08-01.
10. ↑ Volokitin, A. I.; Persson, B. N. J. (2001). "Radiative heat transfer between nanostructures". Physical Review B 63 (20): 205404. doi:10.1103/PhysRevB.63.205404. Bibcode: 2001PhRvB..63t5404V. https://link.aps.org/doi/10.1103/PhysRevB.63.205404. Retrieved 2021-08-01.
11. ↑ 11.0 11.1 11.2 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. doi:10.1016/j.jqsrt.2013.01.002. Bibcode: 2014JQSRT.132...12N. https://www.sciencedirect.com/science/article/pii/S0022407313000101. Retrieved 2021-08-01.
12. ↑ Narayanaswamy, Arvind; Chen, Gang (2008). "Thermal near-field radiative transfer between two spheres". Physical Review B 77 (7): 075125. doi:10.1103/PhysRevB.77.075125. Bibcode: 2008PhRvB..77g5125N. https://academiccommons.columbia.edu/doi/10.7916/D8FX7MCD/download. Retrieved 2021-08-01.
13. ↑ 13.0 13.1 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. https://doi.org/10.1115/1.2957596. Retrieved 2021-08-01.
14. ↑ Czapla, Braden; Narayanaswamy, Arvind (2017). "Near-field thermal radiative transfer between two coated spheres". Physical Review B 96 (12): 125404. doi:10.1103/PhysRevB.96.125404. Bibcode: 2017PhRvB..96l5404C. https://link.aps.org/doi/10.1103/PhysRevB.96.125404. Retrieved 2021-08-01.
15. ↑ 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. doi:10.1016/j.jqsrt.2019.01.020. Bibcode: 2019JQSRT.227....4C. https://www.sciencedirect.com/science/article/pii/S0022407318309270. Retrieved 2021-08-01.
16. ↑ Otey, Clayton; Fan, Shanhui (2011). "Numerically exact calculation of electromagnetic heat transfer between a dielectric sphere and plate". Physical Review B 84 (24): 245431. doi:10.1103/PhysRevB.84.245431. Bibcode: 2011PhRvB..84x5431O. https://link.aps.org/doi/10.1103/PhysRevB.84.245431. Retrieved 2021-08-01.
17. ↑ 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. https://www.sciencedirect.com/science/article/pii/S0022407323001061. Retrieved 2023-03-27.
18. ↑ Edalatpour, Sheila; Francoeur, Mathieu (2014). "The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries". Journal of Quantitative Spectroscopy and Radiative Transfer 133: 364–373. doi:10.1016/j.jqsrt.2013.08.021. Bibcode: 2014JQSRT.133..364E. https://www.sciencedirect.com/science/article/pii/S0022407313003543. Retrieved 2021-08-01.
19. ↑ Edalatpour, Sheila; Francoeur, Mathieu (2016). "Near-field radiative heat transfer between arbitrarily shaped objects and a surface". Physical Review B 94 (4): 045406. doi:10.1103/PhysRevB.94.045406. Bibcode: 2016PhRvB..94d5406E. https://link.aps.org/doi/10.1103/PhysRevB.94.045406. Retrieved 2021-08-01.
20. ↑ Walter, Lindsay P.; Tervo, Eric J.; Francoeur, Mathieu (2022). "Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method". Physical Review B 106 (19): 195417. doi:10.1103/PhysRevB.106.195417. https://link.aps.org/doi/10.1103/PhysRevB.106.195417. Retrieved 2023-02-28.
21. ↑ 21.0 21.1 Biehs, S.-A.; Messina, R.; Venkataram, P. S.; Rodriguez, A. W.; Cuevas, J. C.; Ben-Abdallah, P. (2021). "Near-field radiative heat transfer in many-body systems". Reviews of Modern Physics 93 (2): 025009. doi:10.1103/RevModPhys.93.025009. Bibcode: 2021RvMP...93b5009B. https://link.aps.org/doi/10.1103/RevModPhys.93.025009. Retrieved 2021-08-01.
22. ↑ Bhatt, Gaurang R.; Zhao, Bo; Roberts, Samantha; Datta, Ipshita; Mohanty, Aseema; Lin, Tong; Hartmann, Jean-Michel; St-Gelais, Raphael et al. (2020). "Integrated near-field thermo-photovoltaics for heat recycling". Nature Communications 11 (1): 2545. doi:10.1038/s41467-020-16197-6. PMID 32439917. PMC 7242323. Bibcode: 2020NatCo..11.2545B. https://doi.org/10.1038/s41467-020-16197-6. Retrieved 2021-08-01.
23. ↑ Basu, Soumyadipta; Francoeur, Mathieu (2011). "Near-field radiative transfer based thermal rectification using doped silicon". Applied Physics Letters 98 (11): 113106. doi:10.1063/1.3567026. Bibcode: 2011ApPhL..98k3106B. https://doi.org/10.1063/1.3567026. Retrieved 2021-08-01.
24. ↑ Yang, Yue; Basu, Soumyadipta; Francoeur, Mathieu (2013). "Radiation-based near-field thermal rectification with phase transition materials". Applied Physics Letters 103 (16): 163101. doi:10.1063/1.4825168. Bibcode: 2013ApPhL.103p3101Y. https://doi.org/10.1063/1.4825168. Retrieved 2021-08-01.
25. ↑ Guha, Biswajeet; Otey, Clayton; Poitras, Carl B.; Fan, Shanhui; Lipson, Michal (2012). "Near-Field Radiative Cooling of Nanostructures". Nano Letters 12 (9): 4546–4550. doi:10.1021/nl301708e. PMID 22891815. Bibcode: 2012NanoL..12.4546G. https://doi.org/10.1021/nl301708e. Retrieved 2021-08-01.
26. ↑ Challener, W. A.; Peng, Chubing; Itagi, A. V.; Karns, D.; Peng, Wei; Peng, Yingguo; Yang, XiaoMin; Zhu, Xiaobin et al. (2009). "Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer". Nature Photonics 3 (4): 220–224. doi:10.1038/nphoton.2009.26. Bibcode: 2009NaPho...3..220C. https://doi.org/10.1038/nphoton.2009.26. Retrieved 2021-08-01.
27. ↑ Stipe, Barry C.; Strand, Timothy C.; Poon, Chie C.; Balamane, Hamid; Boone, Thomas D.; Katine, Jordan A.; Li, Jui-Lung; Rawat, Vijay et al. (2010). "Magnetic recording at 1.5 Pb m−2 using an integrated plasmonic antenna". Nature Photonics 4 (7): 484–488. doi:10.1038/nphoton.2010.90. Bibcode: 2010NaPho...4..484S. https://doi.org/10.1038/nphoton.2010.90. Retrieved 2021-08-01.

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