Microscale and Nanoscale Heat Transfer pp 107-131 | Cite as

# Radiative Transfer on Short Length Scales

- 6 Citations
- 1.6k Downloads

## **Abstract**

Heat transfer of radiative origin is treated classically by the transport equation of a phenomenological quantity called the specific intensity (see the Chapter on Radiative Transfer by *Carminati* in this volume). This quantity and its dynamical equation are based on a radiometric approach (incoherent addition of fluxes, geometrical optics). When the relevant distances become as small as the wavelength or less, such hypotheses are no longer valid. One must then go back to the more general ideas of electromagnetic theory.

The aim of this Chapter is to show how to calculate heat transfer of radiative origin from the equations governing the electromagnetic field. We begin by reviewing these equations. We then show how to calculate the quantities relevant to heat transfer, such as the radiative flux. We also review the theory of dipole radiation, which will prove helpful in the ensuing radiative transfer calculations.

In Sect. 2, we examine how a small dipolar sphere at temperature *T* will radiate in vacuum, and how transfer occurs between two such dipolar spheres at different temperatures. We then calculate the electromagnetic energy density near a surface at temperature *T* (Sect. 3). We shall see how this energy density is modified in the near field, particularly when the materials in place can carry surface waves. Finally, in Sect. 4, we investigate the near-field radiative transfer between two plane surfaces, bringing out the key role played once again by surface waves.

## Keywords

65.80.+n 82.53.Mj 81.16.-c 44.10.+i 44.40.+a 82.80.Kq## Preview

Unable to display preview. Download preview PDF.

## References

- J. D. Jackson:
*Classical Electrodynamics*, 2 ed. (John Wiley, New York 1975) zbMATHGoogle Scholar - Y. N. Obukhov, F. W. Hehl: Electromagnetic energy-momentum and forces in matter, Phys. Lett. A
**311**, 277–304 (2003) zbMATHCrossRefADSGoogle Scholar - S. M. Rytov, Y. A. Kravtsov, V. I. Tatarskii:
*Principles of Statistical Radiophysics*, vol. 3 (Springer, Berlin 1989) zbMATHGoogle Scholar - K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, J.-J. Greffet: Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field, Surf. Sci. Rep.
**57**, 59–112 (2005) CrossRefADSGoogle Scholar - J. Sipe: New Green-function formalism for surface optics, J. Opt. Soc. Am. B
**4**, 481 (1987) ADSCrossRefGoogle Scholar - K. Joulain, R. Carminati, J.-P. Mulet, J.-J. Greffet: Definition and measurement of the local density of electromagnetic states close to an interface, Phys. Rev. B
**68**, 245405 (2003) CrossRefADSGoogle Scholar - D. Polder, D. Van Hove: Theory of radiative heat transfer between closely spaced bodies, Phys. Rev. B
**4**, 3303 (1971) CrossRefADSGoogle Scholar - J. P. Mulet, K. Joulain, R. Carminati, J.-J. Greffet: Enhanced radiative heat transfer at nanometric distances, Microscale Thermophys. Eng.
**6**, 209–222 (2002) CrossRefGoogle Scholar