5.1 Dielectric heating

Dielectric heating usually takes place in the radio frequency, microwave or millimetre wave bands of the electromagnetic spectrum. Before World War II, there is little evidence of work on dielectric heating; however, Kassner [38] mentions industrial applications of microwave energy in two of his patents on spark-gap microwave generators [38–40]. Unfortunately early studies in radio frequency heating concluded that microwave heating of food stuffs would be most unlikely because the calculated electric field strength required to heat biological materials would approach the breakdown voltage of air [41].

A discovery that microwave energy could heat food by Spencer [42] lead to a series of patents for microwave cooking equipment [43–45]. Radiofrequencies and microwaves interact with all organic materials. The strength of this interaction depends on the dielectric properties of the materials. These dielectric properties are strongly influenced by the amount of water in the material. Absorption of radiofrequency or microwave energy by these dielectric materials generates heat in the material.

The major advantages of dielectric heating are its short start-up, precise control and volumetric heating [46]; however dielectric heating suffers from: uneven temperature distributions [10, 23]; unstable temperatures [47–50]; and rapid moisture movement [51]. The advantage of radio frequency and microwave heating is its volumetric interaction with the heated material as the electromagnetic energy is absorbed by the material and manifested as heat [52]. This means that the heating behaviour is not restricted by the thermal diffusivity of the heated material.

In industry, dielectric heating is used for drying [46, 53–55], oil extraction from tar sands, cross-linking of polymers, metal casting [46], medical applications [56], pest control [32], enhancing seed germination [57], and solvent free chemistry [58].

The temperature response of the material, other than on the surface, is limited by the coefficient of simultaneous heat and moisture movement [51]. If for any reason the local diffusion rate is much less than the electromagnetic power dissipation rate, the local temperature will increase rapidly. With increasing temperature, the properties of the material change. If such changes lead to the acceleration of electromagnetic power dissipation at this local point, the temperature will increase more rapidly. The result of such a positive feedback is the formation of a hot spot, which is a local thermal runaway [59].

Thermal runaway, which manifests itself as a sudden temperature rise due to small increases in the applied electromagnetic power, is very widely documented [48, 60]. It has also been reported after some time of steady heating at fixed power levels and is usually attributed to temperature dependent dielectric and thermal properties of the material [48, 60].

## 5.2 Hot body radiation energy transfer

Any object that is above zero degrees Kelvin will radiate energy in the form of electromagnetic photons. The German physicist, Max Planck (1858–1947), deduced that the radiation spectral density (ρ) given off from a hot object depended on the wavelength of interest and the temperature of the object. This spectral density can be described by:

$$\rho = \frac{2\text{hc}^2}{\lambda^5 \left\{ \mathbf{e}^{\frac{\text{bc}}{kT}} - \mathbf{1} \right\}} \tag{19}$$

where <sup>h</sup> is Planck'<sup>s</sup> constant (6.6256 � <sup>10</sup>�<sup>34</sup> <sup>J</sup> s), <sup>c</sup> is the speed of light, <sup>λ</sup> is the electromagnetic wavelength of interest, k is Boltzmann's constant (1.38054 � 10�<sup>23</sup> J K�<sup>1</sup> ), and T is the temperature in Kelvin. A typical set of spectral distributions for different temperatures is shown in Figure 9.

The wavelength at which peak radiation intensity occurs can be found by differentiating Planck's equation and setting the derivative equal to zero. Therefore, the wavelength of peak radiation is determined by:

$$
\lambda\_{\rm p} \approx \frac{\text{hc}}{\text{5kT}} \tag{20}
$$

where λ<sup>p</sup> is the peak radiation wavelength (m). At room temperature, or above, the wavelength of peak radiation will be in the micrometre range (�10 μm), which is in the long-wavelength infrared band (Table 3). The penetration of electromagnetic energy into materials is limited by the wavelength and the dielectric properties of the material [61], as pointed out in Eq. (17). The penetration depth of any radiation from objects at room temperature, or above, will be in the nanometre

Figure 9. Radiative spectral density at different temperatures as a function of temperature and wavelength.


#### Table 3.

A commonly used sub-division scheme for the infrared part of the electromagnetic spectrum.

Energy Transfer from Electromagnetic Fields to Materials DOI: http://dx.doi.org/10.5772/intechopen.83420

range; therefore, this form of radiative energy transfer must be regarded as a surface phenomenon, where further energy transfer from the surface into the material occurs via internal conduction and convection.

The total radiated power can be determined by integrating Planck's equation across all wavelengths for a temperature to yield the Stefan-Boltzmann equation. The power transferred from an object at one temperature to another object at a lower temperature is given by [62]:

$$q = \epsilon \sigma A \left( T\_A^4 - T\_\text{p}^4 \right) \tag{21}$$

where q is the radiation power transferred (W); ε is the surface emissivity of the radiator material; <sup>σ</sup> is the Stefan-Boltzmann constant (5.6704 � <sup>10</sup>�<sup>8</sup> J s�<sup>1</sup> <sup>m</sup>�<sup>2</sup> <sup>K</sup>�<sup>4</sup> ); A isthe surface area ofthe heated object (m2 ); TA isthe temperature ofthe infrared source (K); and Tp is the temperature of the material being heated (K). In the case of a normal object the power transfer is reduced by a factor ε, which depends on the properties of the object's surface. This factor is referred to as the emissivity of the surface.

#### 5.3 Thermal imaging

Brightness temperature is the temperature that a black body, in thermal equilibrium with its surroundings, would need to have in order to duplicate the observed electromagnetic wave intensity, at a known wavelength. The brightness temperature of a body can be determined by rearranging Planck's equation to find Tb for a given spectral density value, at a wavelength λ:

$$T\_b = \frac{\text{hc}^2}{\lambda k \bullet \ln\left(\frac{2\text{hc}}{\rho \lambda^5} + 1\right)}\tag{22}$$

Figure 10. Thermal image of a microwave heated sample of biosolids.

The real surface temperature of an object can be determined by dividing the brightness temperature by the surface emissivity of the object being assessed. Since the emissivity is a value between 0 and 1, the real temperature will be greater than or equal to the brightness temperature. This is effectively how remote thermal sensors and thermal imaging systems operate (Figure 10).
