The literature to date offers practically no such values. However, enough proprietary work has been performed to present a reliable evaluation for the comparison of mechanisms (see "Introduction: Modes of Heat Transfer").
For the radiative mechanism of heat transfer to solids, the rate equation for parallel-surface operations is qra = b(T4 - T4)if (11-70)
where b = (5.67)(10~8)(SI) or (0.172)(10~8)(U.S. customary), qra = radiative heat flux, and if = an interchange factor which is evaluated from
where es = coefficient of emissivity of the source and er = "emissivity" (or "absorptivity") of the receiver, which is the divided-solids bed. For the emissivity values, particularly of the heat source es, an important consideration is the wavelength at which the radiant source emits as well as the flux density of the emission. Data for these values are available from Polentz [Chem. Eng., 65(7), 137; (8), 151 (1958)] and Adlam (Radiant Heating, Industrial Press, New York, p. 40). Both give radiated flux density versus wavelength at varying temperatures. Often, the seemingly cooler but longer wavelength source is the better selection.
Emitting sources are (1) pipes, tubes, and platters carrying steam, 2100 kPa (300 lbf/in2); (2) electrical-conducting glass plates, 150 to 315°C (300 to 600°F) range; (3) light-bulb type (tungsten-filament resistance heater); (4) modules of refractory brick for gas burning at high temperatures and high fluxes; and (5) modules of quartz tubes, also operable at high temperatures and fluxes. For some emissivity values see Table 11-10.
For predictive work, where Ura is desired for sizing, this can be obtained by dividing the flux rate qra by At:
where b = (5.67)(10"8) (SI) or (0.172)(1Cr8) (U.S. customary). Hence:
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