## A

where Kcv = drying rate, for constant-rate period, kg/(m2 s) [lb/(h ft2)]; Td and Tw = respective dry-bulb and wet-bulb temperatures of the air; and A = latent heat of evaporation at temperature Tw. Note here that the temperature-difference determination of the operation is a simple linear one and of a steady-state nature. Also note that the operation is a function of the airflow rate. Further, the solids are granular with a fairly uniform size, have reasonable capillary voids, are of a firm texture, and have the particle surface wetted.

The coefficient h is also used to predict (in the constant-rate period) the total overall air-to-solids heat-transfer coefficient Ucv by

where k = solids thermal conductivity and x is evaluated from z(Xc - Xo) x =--

Xc — Xe where z = bed (or slab) thickness and is the total thickness when drying and/or heat transfer is from one side only but is one-half of the thickness when drying and/or heat transfer is simultaneously from both sides; Xo, Xc, and Xe are respectively the initial (or feed-stock), critical, and equilibrium (with the drying air) moisture contents of the solids, all in kg H2O/kg dry solids (lb H2O/lb dry solids). This coefficient is used to predict the instantaneous drying rate

By rearrangement, this can be made into a design equation as follows:

where W = weight of dry solids in the equipment, A = latent heat of evaporation, and 0 = drying time. The reader should refer to the full reference article by Tsao and Wheelock (loc. cit.) for other solids conditions qualifying the use of these equations.

Radiative Heat Transfer Heat-transfer equipment using the radiative mechanism for divided solids is constructed as a "table" which is stationary, as with trays, or moving, as with a belt, and/or agitated, as with a vibrated pan, to distribute and expose the burden in a plane parallel to (but not in contact with) the plane of the radiant-heat sources. Presence of air is not necessary (see Sec. 12 for vacuum-shelf dryers and Sec. 22 for resublimation). In fact, if air in the intervening space has a high humidity or CO2 content, it acts as an energy absorber, thereby depressing the performance.

For the radiative mechanism, the temperature difference is evaluated as

where Te = absolute temperature of the radiant-heat source, K (°R); and Tr = absolute temperature of the bed of divided solids, K (°R).

Numerical values for Ura for use in the general design equation may be calculated from experimental data by

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

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)(10—8) (U.S. customary). Hence:

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