Real surfaces, radiation

Emittanee and Absorptanee The ratio of the total radiating power of a real surface to that of a black surface at the same temperature is called the emittanee of the surface (for a perfectly plane surface, the emissivity), designated by . Subscripts X, 0, and n may be assigned to differentiate monochromatic, directional, and surface-normal values respectively from the total hemispherical value. If radi-... 

The heat flux radiated from a real surface is less than that from an ideal black body surface at the same temperature. The ratio of real to black body flux is the normal total emissivity. Emissivity, like thermal conductivity, is a property which must be determined experimentally. 

Figure 9.35. Comparison of black body, grey body and real surface radiation at 2000 K.<45 ...

Real surfaces, radiation 441,443 RbavblI.. B. N, 274, 302, 3 1 Reboilers 494, 495, 496 Reciprocal rule 448 Reciprocating piston compressor 347... 

The radiation emitted by a real surface is less than the radiation emitted by a blackbody, and the absorption of radiation by a real surface is incomplete. Many surfaces are excellent approximations to a blackbody, but some are not. Of the radiation incident upon a real surface, I(k, 9), a portion is reflected, some is... 

Consider a beam of radiant energy incident on a real surface. Part of this radiation is reflected, part of it is absorbed and the rest is... 

All the preceding discussions have considered radiation exchange between diffuse surfaces. In fact, the radiation shape factors defined by Eq. (8-21) hold only for diffuse radiation because the radiation was assumed to have no preferred direction in the derivation of this relation. In this section we extend the analysis to take into account some simple geometries containing surfaces that may have a specular type of reflection. No real surface is completely diffuse or completely specular. We shall assume, however, that all the surfaces to be considered emit radiation diffusely but that they may reflect radiation partly in a specular manner and partly in a diffuse manner. We therefore take the reflectivity to be the sum of a specular component and a diffuse component ... 

We have already described the radiation spectrum of the sun and noted that the major portion of solar energy is concentrated in the short-wavelength region. It was also noted that as a consequence of this spectrum, real surfaces may exhibit substantially different absorption properties for solar radiation than for long-wavelength earthbound radiation. 

If all surfaces emitted radiation uniformly in all directions, the emissive power would be sufficient to quantify radiation, and we would not need to deal with intensity. The radiation emitted by a blackbody pet unit nonnal area is the same in all directions, and thus there is no directional dependence. But this is not the case for real surfaces. Before we define intensity, wc need to quantify the size of an opening in space. 

In the preceding section, we defined a blackbody as a perfect emitter and absorber of radiation and said tliat no body can emit more radiation than a blackbody at the. same temperature. Therefore, a blackbody can serve as a convenient reference in describing the emission and absorption characteristics of real surfaces. 

The emissivity of a real surface is not a constant. Rather, it varies with the temperature of the surface as well as the wavelength and tlie direction of the emitted radiation. Therefore, different emissiviiies can be defined for a surface, depending on the effects considered. The most elemental emissivity of a surface at a given lemperature is the spectral directional emissivity, which is defined as the ratio of the intensity of radiation emitted by the suiface at a specified wavelength in a speeiOed direction to the intensit) of radiation emitted by a blackbody at the same temperature at the same wavelength. That is. 

A few comments about the validity of tlie diffuse approximation are in order. Although real surfaces do not emit radiation in a perfectly diffuse manner as a blackbody does, they often come close. The variation of emissivity with direction for both electrical conductors and nonconductors is given in Fig. 12 26. Here 0 is tlie angle measured from the normal of the surface, and thus 0 = 0 for radiation emitted in a direction normal to the surface. Note that Sg remains nearly constant for about 0 < d0° for conductors such as metals and for 6 < 70° for nonconductors such as plastics. Therefore, the directional emissivity of a sur face in the normal direction is representative of the hemispherical emissivity of the surface. In radiatioit analysis, it is common practice to assume the surfaces to be diffuse emitters with an emissivity equal to the value in the normal (6 = 0) direction. 

The effect of the gray approximation on emissivity and emissive power of a real surface is illustrated in Fig. 12 27. Note that the radiation emission from a real surface, in general, differs from the Planck distribution, and the emission curve may have several peaks and valleys. A gray surface should emit as much radiation as the real surface it represents at the. same temperature. Therefore, the areas under the emission curves of the real and gray surfaces must be equal. 

The reflectivity differs somewhat from the other properties in that it is bidirectional in nature. That is, the value of the reflectivity of a surface depends not only on the direction of the incident radiation but also the direction of reflection. Therefore, the reflected rays of a radiation beam incident on a real surface in a specified direction forms an irregular shape, as shown in Fig. 12-32. Such detailed reflectivity data do not exist for most surfaces, and even if they did, they would be of little value in radiation calculations since this would usually add more complication to the analysis. 

Real surfaces emit less radiation than a blackbody surface. One may define... 

The concept of hlackhody is determining the basis for describing the radiation properties of real surfaces. The black body denotes an ideal radiative surface which absorb all incident radiation, being a diffuse emitter and emit a maximum amount of energy as thermal radiation for a given wavelength and temperature. The black body can be considered as a perfect absorber and emitter. 

For real surfaces emissivity is defined as the ratio of the radiation emitted by the surface to the radiation emitted by a blackbody at the same temperature. So, the emissivity specifies how well a real body radiates energy as compared with a blackbody. The directional spectral emissivity ex,e X, 9, , T) of a surface at temperature T is defined as the ratio of the intensity of the radiation emitted at the wavelength A and the direction of 9 and to the intensity of the radiation emitted by a blackbody at the same values of T and... 

FIGURE 7.17 Radiation thermometry (a) calibration against a blackbody cavity (b) measurement of a real surface. 

For problems involving real surfaces it is useful to know the fraction of total energy radiated over a wavelength interval (0, A) or (Alt X2), which is to be designated by F(0 —> X) or AF(Ai X2), respectively. For an interval (0, A), from... 

So far, we have studied the radiation energy associated with black bodies. However, real surfaces do not behave like a black body. The next section is devoted to the surface properties of real surfaces. 

Here o is the Stefan-Boltzmann constant, with a value of 5.669 x 10 W/(m2-K4), or 1.714 x 1CT9 Btu/(h ft2 °R4). Engineering surfaces in general do not perform as ideal radiators, and for real surfaces the above law is modified to read... 

Exchange of radiation between distant parts of the same body is neglected q on the real surface of body is given as a boundary condition. Assuming the validity of such a balance for each part of the body, we use again the principle of solidification and again volume and surface densities pu, Q, q etc.) could be deduced from more plausible primitives. Cf. Rems. 7, 13 and 14. 

---