Radiation gray-body

Example 5 Radiation in a Furnace Chamber A furnace chamber of rectangular paraUelepipedal form is heated hy the combustion of gas inside vertical radiant tubes hningthe sidewalls. The tubes are of 0.127-m (5-in) outside diameter on 0.305-m (12-in) centers. The stock forms a continuous plane on the hearth. Roof and end walls are refractory. Dimensions are shown in Fig. 5-20. The radiant tubes and stock are gray bodies having emissivities of 0.8 and 0.9 respectively. What is the net rate of heat transmission to the stock by radiation when the mean temperature of the tube surface is SIG C (1500 F) and that of the stock is 649 C (1200 F) ... 

The fraction of black-body radiation actually emitted by flames is called emissivity. Emissivity is determined first by adsorption of radiation by combustion products (including soot) in flames and second by radiation wavelength. These factors make emissivity modeling complicated. By assuming that a fire radiates as a gray body, in other words, that extinction coefficients of the radiation adsorption are independent of the wavelength, a fire s emissivity can be written as... 

The models proposed to represent radiation transport process can be grouped into two classes. The first and simpler approach is to use some form of the Stefan-Boltzmann equation for radiant exchange between opaque gray bodies,... 

Applications of thermal radiation spectroscopy to expins and pyrots are readily apparent. As a consequence of the highly exothermic nature of explns and flares, significant thermal radiation is emitted which can serve to characterize the reaction processes. The photometric properties of pyrots have been treated in Vol 8, P505-R. In practice, thermal radiation characteristics of explns do not always closely approximate black body properties since the system is non-equilibrium in nature and is time dependent. In addition, some pyrotechnically related materials such as aluminum oxide and magnesium oxide behave as gray bodies with emissivities well below unity. For such systems the radiant emission is reduced as shown in Fig 4... 

Finally, we should mention Kirchhoff s law. The emissivity e expresses which fraction a body of temperature T emits to bodies of lower temperature. If e = 1, we speak of black-body radiation, otherwise of gray-body radiation. Kirchhoff s law compares the emissivity a with the absorptivity a of a body when exposed to incident radiation from a body with a higher temperature and states that... 

Accuracy of Pyrometers Most of the temperature estimation methods for pyrometers assume that the object is either a gray body or has known emissivity values. The emissivity of the non-black body depends on the internal state or the surface geometry of the objects. Also the medium through which the thermal 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. 

An element in a thermally radiative environment absorbs, reflects, refracts, diffracts, and transmits incoming radiative heat fluxes as well as emits its own radiative heat flux. Most solid materials in gas-solid flows, including particles and pipe walls, can be reasonably approximated as gray bodies so that absorption and emission can be readily calculated from Stefan-Boltzmann s law (Eq. (1.59)) for total thermal radiation or from Planck s formula (Eq. (1.62)) for monochromatic radiation. Other means of transport of radiative... 

If we are fortunate enough to have a gray body such that

It is quite apparent from Fig. 8-63 that solar radiation which arrives at the surface of the earth does not behave like the radiation from an ideal gray body, while outside the atmosphere the distribution of energy follows more of an ideal pattern. To determine an equivalent blackbody temperature for the solar radiation, we might employ the wavelength at which the maximum in the spectrum occurs (about 0.5 /im, according to Fig. 8-63) and Wien s displacement law [Eq. (8-13)]. This estimate gives... 

In this chapter v.e have examined several means for analyzing radiation heat transfer. The gray-body assumption, although not strictly correct, is a viable method for performing heat-transfer calculations. Assumptions of uniform ra-diosity and irradiation over surfaces are also not strictly correct but provide an approximation which is usually well within the accuracy of knowledge of surface proper , e. (n Table 8-6, we present a tabular summary of a few formulas which are ofte . used. 

Emissivity is numerically equal to absorptivity. As emissive power varies with wavelength, the ratio should be quoted at a particular wavelength for many materials. However, the emissive power is a constant fraction of the black body radiation, that is, the emissivity is constant. These materials are known as gray bodies. 

The net energy gained or lost by a body can be estimated by these laws. The simplest case is that of a gray body in black surroundings. These conditions, in which none of the energy emitted by the body is reflected back, are approximately those of a body radiating to atmosphere. If the absolute temperature of the body is Ti, the rate of heat loss is aeAT [Eq. (40)], where A is the area of the body and e its emissivity. Surroundings at a temperature emit radiation proportional to ctTI, and a fraction, determined by area and absorptivity a, is absorbed by the body this heat is aaAfi, and as absorptivity and emissivity are equal, Eq. (40) is valid. 

Plots of vs. X from Eq. (14.6) are shown as solid lines in Fig. 14.1 for blackbody radiation at temperatures of 1000, 1500, and 2000°F. The dotted line shows the monochromatic radiating power of a gray body of emissivity 0.9 at 2000. ... 

The absorptivity of a gray body, like the emissivity, is the same for all wavelengths. If the surface of the gray body gives diffuse radiation or refleption, its monochromatic absorptivity is also independent of the angle of incidence of the radiant beam. The total absorptivity equals the monochromatic absorptivity and is also independent of the angle of incidence. 

In fact, very few bodies behave as black bodies so a more realistic assumption would be to treat those as gray bodies. The net radiation between two gray bodies is then given by the following equation ... 

Gaseous radiation does not follow the 4th-power law because gases do not radiate in all wavelengths, as do solids (gray bodies). Each gas radiates only in a few narrow bands, as can be seen on a spectrograph in figures 2.17 and 2.18. 

Gray bodies do not exist in practice and the concept of a gray body is an idealized one. The absorptivity of a surface actually varies with the wavelength of the incident radiation. Engineering calculations can often be based on the assumption of a gray body... 

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