Gray body

Vanadium [7440-62-2] V, (at. no. 23, at. wt 50.942) is a member of Group 5 (VB) of the Periodic Table. It is a gray body-centered-cubic metal in the first transition series (electronic configuration When highly pure, it is very soft and dutile. Because of its high melting point, vanadium is referred to as a... 

Real or gray bodies deviate from these ideal blackbody values by the A-dependent emissivity, but the color sequence remains essentially the same. This mechanism explains the color of incandescent light sources such as flames in a candle, tungsten filament light bulb, flash bulb, carbon arc, limelight, lightning in part, and the incandescent part of pyrotechnics (qv). 

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,... 

This gray body approach, or some modified version, has been the more popular approach used by various authors, including Palchonok et al., (1995), Anderson and Lechner (1993), Mahalingan and Kolar (1990). 

The intensity versus wavelength distribution according to the Planck equation for the black-body emission is used to calculate the temperature (see Fig. 12). This calculation is based on two severe approximations. The first concerns with the assumption that the system is an ideal black body, which corresponds to assuming that the emissivity e equal to 1. On the contrary, real systems are gray bodies that possess emissivity values less than 1. In addition, the e dependence on the wavelength and on the pressure is generally neglected. 

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... 

Results of a comprehensive study of the absolute spectral radiance of the infrared emissions from methane—air expins have been reported (Ref 44). The spectral growth of these expanding flames was recorded with a time resolution of one msec in the spectral range 1.7— 5.0 microns. Time resolved spectra were obtained as a function of stoichiometry, nitrogen dilution and Halon dilution. Similar data are also available for coal dust-air explns. Additional applications of rapid scan IR spectroscopy are discussed in Ref 50. In this work, flare spectra (Mk45, LUU-2B and LUU-2B/B) in the 1.7-4.7 and 9—14 micron regions were studied. The Mk-45 and LUU-2B/B showed similar spectral character with Na and C02 emissions superimposed on a gray body continuum, while LUU-2B flares demonstrated variable emittance properties... 

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. 

Moreover, a solid is termed a gray body if its monochromatic emissivity ex is independent of the wavelength. The monochromatic-emissive power of a blackbody at a specific temperature and wavelength is given by Planck s formula... 

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... 

Radiative heat transfer plays an important part in many fluidized bed processes operated at high temperatures, such as coal combustion and gasification. When treating a fluidized bed as a whole solid gray body, the radiative heat transfer coefficient ht between the fluidized bed at temperature 7), and a heating surface at temperature Ts is defined as... 

A gray body is defined such that the monochromatic emissivity eA of the body is independent of wavelength. The monochromatic emissivity is defined as the ratio of the monochromatic-emissive power of the body to the monochromatic-emissive power of a blackbody at the same wavelength and temperature. Thus... 

Fig. 8-5 (a) Blackbody emissive power as a function of wavelength and temperature, (b) comparison of emissive power of ideal blackbodies and gray bodies with that of a real surface. 

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

Net heat lost by surface = energy emitted - energy absorbed or on a unit-area basis with the usual gray-body assumptions,... 

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. 

A 30 by 30 cm plate whose emissivity is 0.5 is attached to the side of a spaceship so that it is perfectly insulated from the inside of the ship. Assuming that outer space is a blackbody at 0 K, determine the equilibrium temperature for the plate at a point in space where the radiant heat flux from the sun is 1500 W/m2. Assume gray-body behavior. 

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