# Electromagnetic waves and thermal radiation

In this chapter, the basic relations governing heat transfer by thermal radiation are presented. The material properties required for determining radiation exchange among surfaces are given, along with some methods for predicting these properties when measured values are unavailable. Finally, some applications of radiation in actual devices and processes and to contemporary micro- and nanoscale uses are presented.

## 9.1 Electromagnetic Waves and Thermal Radiation

Energy transfer by thermal radiation differs in fundamental ways from conduction and convection. Radiative energy is carried by electromagnetic waves, which require no medium for their propagation. Thus, unlike the other heat transfer modes, radiative energy can be transferred through a vacuum, for example allowing us to receive solar energy through the vacuum of space. Electromagnetic (EM) waves are described mathematically by Maxwell's Equations (Siegel and Howell, 2002; Modest, 2003; Bohren and Huffman, 1983), which formulate the propagation of the perpendicular amplitudes of the electric and magnetic components, E and H, of the waves (Figure 1). The energy carried by the wave is proportional to the square of the amplitude of the electrical component E of the wave. These equations can be used to predict the interaction of the waves with interfaces between differing materials, allowing prediction of the radiative properties of various materials in terms of electrical and magnetic properties. More details are in Section 9.5. The EM waves can be generated in various ways. Depending on the source of the EM waves, they may have differing wavelengths, extending from very short (nm) to very long (km) (Fig. 2). For radiative heat transfer, we are interested in EM waves originating from microscopic energy transitions that occur because of the internal energy state of a substance, which is in turn dependent on the absolute temperature of a material that is in thermodynamic equilibrium. EM waves originating from such a source are called thermal radiation, and this radiation is emitted by any substance that is above absolute zero temperature. This dependence means that all radiative transfer relations

Figure 1: Electromagnetic wave propagating in the x-direction with associated electric (Ey) and magnetic (Hz) components
Figure 2: The electromagnetic spectrum

must be in terms of absolute temperature. Thermal radiation is roughly in the range of 0.1 < λ< 1000 μm. The thermal radiation portion of the logarithmic wavelength scale of Fig. 2 is thus fairly small, and the visible portion of the spectrum is small indeed. Electromagnetic waves travel without attenuation (loss) through a vacuum and through perfectly transparent materials (ideal dielectrics). Some media will absorb wave energy, converting the radiation into internal energy. Air is generally transparent, although some gases such as carbon dioxide and water vapor can absorb radiation in certain ranges of the infrared portion of the spectrum as it travels. Solids, particularly metals, are very strong absorbers, and can completely absorb radiation over very short distances. Other solids (glass, for example) are quite transparent to radiation over wide ranges of wavelength. To provide the basis for computing energy transfer by thermal radiation, we must connect the temperature of a radiating surface to its rate of electromagnetic energy emission by radiation.

## References

Bohren, C.F. and Huffman D.R., 1983, Absorption and Scattering of Light by Small Particles, John Wiley & Sons, New York, NY.

Modest, M.F., 2003, Radiative Heat Transfer, 2nd ed., Academic Press, Sand Diego, CA.

Siegel, R. and Howell, J.R., 2002, Thermal Radiation Heat Transfer, 4th ed., Taylor and Francis, New York, NY.