Radiation from real surfaces

The emissivity of a material is defined as the ratio of the radiation per unit area emitted from a real or from a grey surface (one for which the emissitivity is independent of wavelength) to that emitted by a black body at the same temperature, Emissivities of real materials are always less than unity and they depend on die type, condition and roughness of the material, and possibly on the wavelength and direction of the emitted radiation as well. For diffuse surfaces where emissivities are independent of direction, the emissivity, which represents an average over all directions, is known as the hemispherical emissivity. For a particular wavelength X this is given by  

Equation 9.114 leads to Kirchoff s Law which states that the absorptivity, or fraction of incident radiation absorbed, and the emissivity of a surface are equal. If two bodies A and B of areas Ai and A2 are in a large enclosure from which no energy is lost, then the energy absorbed by A from the enclosure is Aia 7 where / is the rate at which energy is falling on unit area of A and ai is the absorptivity. The energy given out by A is 1 A] and, at equilibrium, these two quantities will be equal or  

For most industrial, non-metallic surfaces and for non-polished metals., e is usually about 0.9. although values as low as 0.03 are more usual for highly polished metals such 

This integration may be carried out numerically or graphically, though this approach, which has been considered in some detail by INCROPERA and DE can be 

From equation 9.117, it is seen that the rate of heat transfer by radiation from a hot body at temperature T to a. cooler one at temperature T2 is then given by  

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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. 

When an object is heated, it emits radiation—it glows. Even at room temperature, objects radiate at infrared frequencies. Imagine a hollow sphere whose inside surface is perfectly black. That is, the surface absorbs all radiation striking it. If the sphere is at constant temperature, it must emit as much radiation as it absorbs. If a small hole were made in the wall, we would observe that the escaping radiation has a continuous spectral distribution. The object is called a blackbody, and the radiation is called blackbody radiation. Emission from real objects such as the tungsten filament of a light bulb resembles that from an ideal blackbody. 

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. 

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... 

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. 

The relevance of contact resistances in SPS process has been simulated and confirmed, with the simulation shown in Fig. 6.15 as an example [4]. The system simulated is a Model 1050-Sumitomo SPS, where a solid graphitic cylinder is inserted into the die. The 2D cylindrical coordinate system of coupled thermal and electrical problems is numerically solved by using Abaqus (FEM). The heat losses due to radiation from all exposed surfaces, except those on the ends of the rams, have been considered, where a constant temperature of 25 °C is used for the simulation. Thermophysical parameters of all materials are available in that study. A proportional feedback controller based on the outer surface temperature of the die is modeled, in order to determine the voltage drop applied at two ends of the rams. This controller is used to imitate the actual proportional integral derivative (PID), which is observed in real SPS facilities. It is used to apply electric power input to the system when experiments are conducted in terms of temperature controlling. 

Strictly monochromatic radiation propagating in a unique direction (e.g., from a point source) is never realized. A monochromatic wave implies a periodic process of infinite duration. Such waves do not exist, although the signal from a stable, singlemode laser provides a fair approximation. Ordinary incoherent radiation emitted and reflected from real atmospheres and surfaces consists of individual wave packets of finite length and duration a few meters and 10 seconds are typical values. Similarly, point sources are replaced by extended sources in practice. Radiation from such sources tends to be incoherent and covers a range of frequencies and directions. Thus, it is more convenient to work with a distribution of plane waves and their associated Poynting vectors. 

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