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Heat Transfer Handbook part 64. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | RADIATIVE EXCHANGE WITHIN PARTICIPATING MEDIA 623 where ex s is the spectral emissivity of a homogeneous column sothermal and with constant concentrations of absorbing emitting material and tx 5 is its spectral transmissivity. For a homogeneous medium on a s irectral basis ex ax s 1 - Tx s 1 - e-x 8.96 where ax s is the spectral absorptivity of the medium. 8.5.1 Mean Beam Length Method Relatively accurate yet simple heat transfer calculations can be carried out if an isothermal absorbing-emitting but not scattering medium is contained in an isothermal black-walled enclosure. While these conditions are of course very restrictive they are met to some degree by conditions inside furnaces. For such cases the local heat flux on a point of the surface may be calculated by putting eq. 8.94 into eq. 8.20 which leads to q 1 - a Lm Ebw - e Lm Ebg 8.97 where Ebw and Ebg are blackbody emissive powers for the walls and medium gas and or particulates respectively and a Lm and e Lm are the total absorptivity and emissivity of the medium for a pata lengh Lm through the medium. The length Lm known as the mean beam length is a directional average of the thickness of the medium as seen from the point on the surface. On a spectral basis equation 8.97 is exact provided that the foregoing conditions are met and that an accurate value of the spectral mean beam length is known. It has been shown that spectral dependence of the mean beam length is weak generally less than 5 from the mean . Consequently total radiative heat flux at the surface may be calculated very accurately from eq. 8.97 provided that the emissivity and absorptivity of the medium are also known accurately. The mean beam lengths for many important geometries have been calculated and are collected in Table 8.5. In this table L0 is known as the geometric mean beam length which is the mean beam length for the optically thin limit kx 0 and Lm is a spectral average of the mean beam length. For geometries not listed in Table .
