Abstract
Radiative heat transfer across nanoscale-thick layers attracts considerable attention because of its importance for modern technology, and also because of the evidence that conventional methods of radiative heat transfer fail at such small scales. This paper analyzes several approaches to this problem that have been proposed since the late 1960s when the first adaptations of the classical Stefan–Boltzmann law of radiative heat transfer to smaller scales were presented. It is shown that while all authors agree that thermal radiation is described by Maxwell’s equations for electrodynamics, the methods of these studies drifted from deductive reasoning based on these equations toward heuristic guesses. This paper identifies critical points of several of these previous studies that are responsible for the lack of a suitable theory of radiative heat transfer across nanoscale layers despite almost 50 years of effort. Among these points are: (1) attempts to describe heat transfer using statistical distributions that are limited to equilibrium systems that cannot produce any heat flux; (2) application of the so-called fluctuation–dissipation theorem when its conditions are not satisfied; (3) the failure to distinguish between different kinds of evanescent fields; (4) an unjustified assumption that resonant surface waves can transfer heat by tunneling.
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Domoto, G.A., Boehm, R.F., Tien, C.L.: Experimental investigation of radiative transfer between metallic surfaces at cryogenic temperatures. J. Heat Transf. 92(3), 412–416 (1970). https://doi.org/10.1115/1.3449677
Loomis, J.J., Maris, H.J.: Theory of heat transfer by evanescent electromagnetic waves. Phys. Rev. B 50(24), 18517–18524 (1994)
Narayanaswamy, A., Shen, S., Hu, L., Chen, X., Chen, G.: Breakdown of the planck blackbody radiation law at nanoscale gaps. Appl. Phys. A 96, 357–362 (2009). https://doi.org/10.1007/s00339-009-5203-5
Cravalho, E.G., Tien, C.L., Caren, R.P.: Effect of small spacing on radiative transfer between two dielectrics. J. Heat Transf. 89(3), 351–358 (1967). https://doi.org/10.1115/1.3614396
Polder, D., van Hove, N.: Theory of radiative heat transfer between closely spaced bodies. Phys. Rev. B 4(10), 3303–3314 (1971)
Israelachvili, J.: Intermolecular and Surface Forces, 2nd edn. Academic Press, London (1991)
Abrikosov, A.A., Gorkov, L.P., Dzialoshinskii, I.E.: Quantum Field Theoretical Methods in Statistical Physics. Pergamon Press, Oxford (1965)
Rytov, S.M.: Theory of Electric Fluctuations and Thermal Radiation. Air Force Cambridge Research Center, Bedford (1959)
Nyquist, H.: Thermal agitation of electric charge in conductors. Phys. Rev. 32(1), 110–113 (1928)
Johnson, J.B.: Thermal agitation of electricity in conductors. Phys. Rev. 32(1), 97–109 (1928)
Shchegrov, A.V., Joulain, K., Carminati, R., Greffet, J.-J.: Near-field spectral effects due to electromagnetic surface excitations. Phys. Rev. Lett. 85(7), 1548–1551 (2000)
Khalatnikov, I.M.: Heat exchange between solid and Helium-II. JETP 22(6), 687–704 (1952)
Kapitsa, P.L.: Viscosity of liquid helium below the \(\lambda \)-point. C. R. Acad. Sci. URSS 18, 21 (1938). (Also in ‘Nature’, v. 141 (1938) and in ‘Collected papers of P. L. Kapitsa’, v. 2, Ed. D. ter Haar, Pergamon, Oxford, 1965)
Rytov, S.M., Kravtsov, Y.A., Tatarskii, V.I.: Principles of Statistical Radiophysics. 3. Elements of Random Fields. Springer, Berlin (1987)
Leontovich, M.A., Rytov, S.M.: About a differential law for the intensity of electric fluctuations and their dependence on the skin-effect. Zhurnal eksperementalnoj i Teoreticheskoj fiziki 23, 246–252 (1952). (In Russian )
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Course of Theoretical Physics, vol. 2, 4th edn. Pergamon Press, Oxford (2000)
Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media. Course of Theoretical Physics, vol. 8. Pergamon Press, Oxford (1960)
Feynman, R.P., Leighton, R.B., Sands, M.L.: The Feynman Lectures on Physics, vol. 2, 3rd edn. Pearson/Addison-Wesley, San Francisco (2006)
Landau, L.D., Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics, Part 1. Course of Theoretical Physics, vol. 5, 3rd edn. Elsevier/Butterworth-Heinemann, Amsterdam (2007)
Mulet, J., Joulain, K., Carminati, R., Greffet, J.-J.: Enhanced radiative heat transfer at nanomentric distances. Microsc. Thermophys. Eng. 6(3), 209–222 (2002). https://doi.org/10.1080/10893950290053321
Lord Rayleigh, D.C.L.: On waves propagated along the plane surface of an elastic solid. Proc. Lond. Math. Soc. s1–17(1), 4–11 (1885). https://doi.org/10.1063/1.1745338
Brekhovskikh, L.M.: Waves in Layered Media. Applied Mathematics and Mechanics, vol. 16. Academic Press, New York (1960)
Pendry, J.B.: Radiative exchange of heat between nanostructures. J. Phys. Condens. Matter 11(35), 6621–6633 (1999)
Wurfel, P.: The chemical potential of radiation. J. Phys. C 15, 3967–3985 (1982)
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Budaev, B.V., Bogy, D.B. A critical review of published approaches to nanoscale thermal radiation. Z. Angew. Math. Phys. 71, 69 (2020). https://doi.org/10.1007/s00033-020-1288-7
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DOI: https://doi.org/10.1007/s00033-020-1288-7