Emissivity mean beam lengths

Note that these values are specific to the subject problem in which the mean beam length is L, , with gS evaluated from basic data, such as Table 5-8. (1 — in Eq. (5-165) represents the emissivity of a gray gas, which will be called Ec,i. For later use, note that,... 

Surface absorptivity or absorptance subscript 1 refers to the surface temperature while subscript 2 refers to the radiation source Gas absorptivity, emissivity, and transmissivity Dimensionless constant in mean beam length equation, LM = (5-LM0... 

Mean Beam Lengths It is always possible to represent the emissivity of an arbitrarily shaped volume of gray gas (and thus the corre-... 

Discussion This is the average emissivity for radiation emitted to ali surfaces of the cylindrical enclosure. For radiation emitted towards the center of the base, the mean beam length is 0.7ID jnstead of 0.60D, and the emissivity value WQuld e different. 

In Figure 8.23, the emissivity of such a gas is represented as a function of temperature and the product PL of the partial pressures of water and carbon dioxide and the path of travel defined by the mean beam length. Item 8 of Table 8.16 is a curve fit of such data. 

Use of the optically thin value of the mean beam length yields values of gas emissivities or exchange areas that are too high. It is thus necessary to introduce a dimensionless constant P < 1 and define some new average mean beam length such that KLm = P mo-For the case of parallel plates, we now require that the mean beam length exactly predict the gas emissivity for a third value of KL. In this example we find p = -An[2Es(KL)]/2KL and for KL = 0.193095 there results p = 0.880. The value p = 0.880 is not wholly arbitrary. It also happens to minimize the error defined by the so-called shape correction factor ( ) = [9(.s /dAi]/ l - for all KL > 0. The... 

Fig. 5.74 Hemispherical total emissivity co2 °f carbon dioxide at p = lbar as a function of temperature T with the product of the partial pressure pco2 and the mean beam length sm as a parameter. 1 bar = 100 kPa = 0.1 MPa...

The emission of gas radiation depends on the size and shape of the gas space it is described quantitatively by the irradiance, which the gas radiation generates at the surface of the gas space. The decisive equations (5.188) and (5.189) include the spectral emissivity e))(. and the emissivity integrated over all wavelengths q, which, according to (5.193) and (5.194), can be replaced by the emissivity of a gas hemisphere with a radius the same as the mean beam length. sni of any shaped gas space. 

In order to explain the determination of the mean beam length, we first have to look at the calculation of the spectral emissivity e G of a gas volume. We will then show how sm is determined and put together in Table 5.11 values of. sni that have been calculated for different geometries. In addition a simple approximation formula will be derived with which sm can be determined for gas spaces that are not covered in this collection. 

The emissivity of a gas also depends on the mean length an emitted radiation beam travels in the gas before reaching a bounding surface, and thus the shape and Ihe size of the gas body involved. During their experiments in the 1930s, Hotiel and his coworkers considered the emission of radiation from a hemispherical gas body to a small surface element located at the center of the base of Ihe hemisphere. Therefore, Ihe given charts represent emissivity... 

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