Radiation nonblack surfaces

The analysis of radiation transfer in enclosures consisting of black surfaces is relatively easy, as we have seen, but most enclosures encountered in practice involve nonblack surfaces, which allow multiple reflections to occur. Radiation analysis of such enclosures becoroe.s very complicated unless some simplifying assumptions are made. 

NONBLACK SURFACES. The treatment of radiation between nonblack surfaces, in the general case where absorptivity and emissivity are unequal and both depend upon wavelength and angle of incidence, is obviously complicated. Several important special cases can, however, be treated simply. 

Clouds of Nonblack Particles The correction for nonblackness of the particles is complicated by multiple scatter of the radiation reflected by each particle. The emissivity . of a cloud of gray particles of individual surface emissivity 1 can be estimated by the use of Eq. (5-151), with its exponent multiplied by 1, if the optical thickness alv)L does not exceed about 2. Modified Eq. (5-151) would predict an approach of . to 1 as L 0°, an impossibihty in a scattering system the asymptotic value of . can be read from Fig. 5-14 as /, with albedo (0 given by particle-surface refleclance 1 — 1. Particles with a perimeter lying between 0.5 and 5 times the wavelength of interest can be handledwith difficulty by use of the Mie equations (see Hottel and Sarofim, op. cit., chaps. 12 and 13). 

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. 

The absorptivity, a, reflectivity, p, and transmissivity, r, are the key radiation properties of a material. The magnitudes of a, p, and r depend on the type of material, its thickness and its surface finish, and also on the wavelength of the radiation. Absorption characteristics are defined in a similar manner to emission characteristics (see Section 10.2). The absorptivity for a nonblack body is the ratio of the nonblack absorption to the black absorption at the same surface temperature. Only the absorbed portion causes heating however, as very few bodies behave as black bodies a more realistic assumption would be to treat those as gray bodies, which have the same absorptivity over the entire wavelength spectrum. 

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