Fundamental Concepts

Consider a solid that is initially at a higher temperature T than that of its surroundi ngs T_sur, but around which there exists a vacuum (Figure 12.1). The presence of the vacuum precludes energy loss from the surface of the solid by conduction or convection. However, our intuition tells us that the solid will cool and eventually achieve thermal equilibrium with its surroundings. This cooling is associated with a reduction in the internal energy stored by the solid and is a direct consequence of the emission of thermal radiation from the surface. In turn, the surface will intercept and absorb radiation originating from the surroundings. However, if T_s > T_sur the net heat transfer rate by radiation q_rad, _net is from the surface, and the surface will cool until T, reaches T_sur. We associate thermal radiation with the rate at which energy is emitted by matter as a result of its finite temperature. At this moment thermal radiation is being emitted by all the matter that surrounds you: by the furniture and walls of the room,if you are indoors, or by the ground. buildings. and the atmosphere and sun if you are outdoors.

The mechanism of emission is related to energy released as a result of oscillations or transitions of the many electrons that constitute matter. These oscillations are, in turn, sustained by the internal energy, and therefore the temperature, of the matter.

Hence we associate the emission of thermal radiation with thermally excited conditions within the matter. All forms of matter emit radiation. For gases and for semitransparent solids, such as glass and salt crystals at elevated temperatures, emission is a volumetric phenoneizon, as illustrated in Figure 12.2. That is, radiation emerging from a finite volume of matter is the integrated effect of local emission throughout the volume. However, in this text we concentrate on situations for which radiation is a surface phenomenon. In most solids and liquids, radiation emitted from interior molecules is strongly absorbed by adjoining molecules. Accordingly, radiation that is emitted from a solid or a liquid originates from molecules that are within a distance of approximately 1 μm from the exposed surface. It is for this reason that emission from a solid or a liquid into an adjoining gas or a vacuum can be viewed as a surface phenomenon, except in situations involving nanoscale or microscale devices. We know that radiation originates due to emission by matter and that its subseq uent transport does not require the presence of any matter. But what is the nature of this transport? One theory views radiation as the propagation of a collection of particles termed photons or quanta. Alternatively, radiation may be viewed as the propag ation of electromagnetic waves. In any case we wish to attribute to radiation the standard wave properties of frequency v and wavelength A. For radiation propagating in a particular medium, the two properties are related by

 

where c is the speed of light in the medium. For propagation in a vacuum, c₀ = 2.998 x 10⁸ m/s. The unit of wavelength is commonly the micrometer (μm), where 1 μm = 10^-6 m.

The complete electromagnetic spectrum is delineated in Figure 12.3. The short wavelength gamma rays. X rays, and ultraviolet (UV) radiation are primarily of interest to the high-energy physicist and the nuclear engineer, while the long wavelength microwaves and radio waves (λ > 10⁵μm) are of concern to the electrical engineer.

It is the intermediate portion of the spectrum, which extends from approximately 0.1 to 100 μm and includes a portion of the UV and all of the visible and infrared (IR), that is termed thermal radiation because it is both caused by and affects the thermal state or  temperature of matter. For this reason, thermal radiation is pertinent to heat transfer. Thermal radiation emitted by a surface encompasses a range of wavelengths.

As shown in Figure 1 2.4a, the magnitude of the radiation varies with wavelength, and the term spectra! is used to refer to the nature of this dependence. As we will find, both the magnitude of the radiation at any wavelength and the spectral distribution vary with the nature and temperature of the emitting surface.

The spectral nature of thermal radiation is one of two features that complicates its description. The second feature relates to its directionality . As shown in Figure 1 2.4b, a surface may emit preferentially in certain directions, creating a directional distribution of the emitted radiation. To quantify the emission, absorption, reflection, and transmission concepts introduced in Chapter1, we must be able to treat both spectral and directional effects.