Grey body radiation

The intensity of a flare is largely determined by its temp, which in turn depends on the stability of the reaction products. In order to generate grey body radiation which encompasses the spectral sensitivity of the human eye (0.4— 0.74pm), 3000°K should be exceeded. Whereas this is possible using nitrates and perchlorates with alkaline earth metals as well as Zr, Ti and Hf (Ref 34) (H, C, B, Si and P form oxides which dissociate at high temps), in practice Mg and A1 are found to be best in terms of heat output, cost, and transparency to visible radiation... 

On the other hand, for molecules, the electronic transitions result in bands lO SOnm in width due to the changes in vibrational energy levels which also occur. A third type of radiation emitted by stars in the near-UV visible near-IR region is a continuum emission originating from hot particles e.g. hot AI2O3 particles) but this is considered to be grey body radiation and does not contribute to the colour of the star. 

Accuracy of Pyrometers Most of the temperature estimation methods for pyrometers assume that the objec t is either a grey body or has known emissivity values. The emissivity of the nonblack body depends on the internal state or the surface geometry of the objects. Also, the medium through which the therm radiation passes is not always transparent. These inherent uncertainties of the emissivity values make the accurate estimation of the temperature of the target objects difficult. Proper selection of the pyrometer and accurate emissivity values can provide a high level of accuracy. 

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

In this way, ihe emissive power of a grey body is a constant proportion of the power-emitted by the black body, resulting in the curve shown in Figure 9.35 where, for example, e = 0.6. The assumption that the surface behaves as a grey body is valid for most engineering calculations if the value of emissivity is taken as that for the dominant temperature of the radiation. 

For a grey body, the emissivity and the absorptivity are, by definition, independent of temperature and hence equation 9.115 may be applied more generally showing that, where one radiation property (a, r or e) is specified for an opaque body, the other two may be obtained from equations 9.115 and 9.124. KirchofPs Law explains why a cavity with a small aperture approximates to a black body in that radiation entering is subjected to repeated internal absorption and reflection so that only a negligible amount of the incident radiation escapes through the aperture. In this way, a - e = 1 and, at T K, the emissive power of the aperture is aT4. 

For grey bodies, the emissivity, e, must be included and the net radiation per unit area is then... 

To calibrate the pixel sensitivities black body radiation is usually measured at different temperatures. Since a black body has an emissivity of 1 at every position, variations in detector pixel sensitivities are eliminated by a calibration function. As this IRT-method should be used here to quantify very small heat signals on combinatorial libraries with diverse materials, differences in emissivities have to be considered. Most materials are grey bodies with individual emissivities less than 1. Therefore, the calibration was not performed with a black body but with the library, as described before, a procedure that corrects not only for pixel sensitivity but also for emissivity differences across the library plate [5]. For additional temperature calibration, the IR-emission of the library is recorded at several temperatures in a narrow temperature window around the planned reaction temperature. By this procedure, emissivity changes, temperature dependence and individual sensitivities of the detector pixels can be calibrated in one step. After this... 

The most common radiation sources are thermal ones. In the NIR region quartz-halogen lamps are mainly used. These emit the radiation of a tungsten wire, which is a grey body at about 3000 K, the emissivity of which has been studied by De Vos, 1954, Rutgers and De Vos, 1954, 1973. 

In the following sections we will look at the radiation properties of real bodies, which, with respect to the directional dependence and the spectral distribution of the radiated energy, are vastly different from the properties of the black body. In order to record these deviations the emissivity of a real radiator is defined. Kirch-hoff s law links the emissivity with the absorptivity and suggests the introduction of a semi-ideal radiator, the diffuse radiating grey body, that is frequently used as an approximation in radiative transfer calculations. In the treatment of the emissivities of real radiators we will use the results from the classical electromagnetic theory of radiation. In the last section the properties of transparent bodies, (e.g. glass) will be dealt with. 

The directional spectral emissivity is independent of the wavelength A sA = s x(f3,cp,T). A body with this property is called a grey body or a grey radiator. 

In radiative exchange calculations, it is preferable to use the model, described in the previous section, of a grey, diffuse radiating body as a simple approximation for the radiative behaviour of real bodies. As Lambert s cosine law is valid for this model, we denote these bodies as grey Lambert radiators. The energy radiated from them is distributed like that from a black body over the directions in... 

If the bodies participating in radiative exchange cannot be assumed to be black bodies, then the reflected radiation flows also have to be considered. In hollow enclosures, multiple reflection combined with partial absorption of the incident radiation takes place. A general solution for radiative exchange problems without simplifying assumptions is only possible in exceptional cases. If the boundary walls of the hollow enclosure are divided into isothermal zones, like in 5.5.2, then a relatively simple solution is obtained, if these zones behave like grey Lambert radiators. Each zone is characterised purely by its hemispherical total emissivity si — whilst at = is valid for its absorptivity, and for the reflectivity... 

Merely from the fact that even a true black body would yield less than half this amount (Table 7) at an estimated flame temperature of about 2500it becomes obvious that in intense pyrotechnic radiation thermal grey-body emission is heavily augmented by selective radiation and luminescent phenomena. This can be experimentally demonstrated by a comparison of light emission from binary mixtures where various alkali salts act as oxidizers. Table 9 (from Table 13.7, Shidlovsky ) shows these relations. He uses a fixed ratio of 40 % metal fuel and 60% of the nitrates of sodium, potassium, or barium. It is of course not... 

Black (grey) body—An ideal concept of a solid radiating substance. 

For a grey body (any non-blackbody object), the radiation energy per unit time can be calculated by the equation... 

The Stefan-Boltzmann law describes heat flow for a grey body (1) radiating into a large enclosed space (2) ... 

A perfect black-body that absorbs all of the radiation that is incident on it and does not reflect any light has a = 1. In general a grey-body has 0<8<1, white paint has 8 = 0.95, and polished steel has e = 0.07. The Stephen-Boltzmann constant a is given by... 

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 the 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 ... 

The difference between the fourth power of the temperature of the emitter and that of the body which receives the radiation, is characteristic of radiative exchange. This temperature dependence is found in numerous radiative heat transfer problems involving grey radiators. 

Gases only absorb and emit radiation in narrow wavelength regions, so-called bands. Their spectral emissivities show a complex dependency on the wavelength, in complete contrast to solid bodies. This means that gases cannot be idealised as grey radiators without a loss of accuracy. 

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