Volumetric heat transfer coefficient

The thermal performance of cylindrical rotating shell units is based upon a volumetric heat-transfer coefficient... 

Employing wood chips, Cowan s drying studies indicated that the volumetric heat-transfer coefficient obtainable in a spouted bed is at least twice that in a direct-heat rotaiy diyer. By using 20- to 30-mesh Ottawa sand, fluidized and spouted beds were compared. The volumetric coefficients in the fluid bed were 4 times those obtained in a spouted bed. Mathur dried wheat continuously in a 12-in-diameter spouted bed, followed by a 9-in-diameter spouted-bed cooler. A diy-ing rate of roughly 100 Ib/h of water was obtained by using 450 K inlet air. Six hundred pounds per hour of wheat was reduced from 16 to 26 percent to 4 percent moisture. Evaporation occurred also in the cooler by using sensible heat present in the wheat. The maximum diy-ing-bed temperature was 118°F, and the overall thermal efficiency of the system was roughly 65 percent. Some aspec ts of the spouted-bed technique are covered by patent (U.S. Patent 2,786,280). 

One manner in which size may be computed, for estimating purposes, is by employing a volumetric heat-transfer concept as used for rotary diyers. It it is assumed that contacting efficiency is in the same order as that provided by efficient lifters in a rotaiy dryer and that the velocity difference between gas and solids controls, Eq. (12-52) may be employed to estimate a volumetric heat-transfer coefficient. By assuming a duct diameter of 0.3 m (D) and a gas velocity of 23 m/s, if the solids velocity is taken as 80 percent of this speed, the velocity difference between the two would be 4.6 m/s. If the exit gas has a density of 1 kg/m, the relative mass flow rate of the gas G becomes 4.8 kg/(s m the volumetric heat-transfer coefficient is 2235 J/(m s K). This is not far different from many coefficients found in commercial installations however, it is usually not possible to predict accurately the acdual difference in velocity between gas and soRds. Furthermore, the coefficient is influenced by the sohds-to-gas loading and particle size, which control the total solids surface exposed to the gas. Therefore, the figure given is only an approximation. 

A note of caution on the use of photo-etched channels has been offered by RAMSHAWfl3 ) who points out that the system is attractive in principle provided that severe practical problems such as fouling are not encountered. With laminar flow in matrices with a mean plate spacing of 0.3-1 mm, volumetric heat transfer coefficients of 7 MW/m3 K have been obtained with modest pressure drops. Such values compare with 0.2 MW/m3 K for shell and tube exchangers and 1.2 MW/m3 K for plate heat exchangers. 

Manufacturing and testing of compact micro heat exchangers with high volumetric heat transfer coefficients,... 

Figure 16.15. Correlation of volumetric heat-transfer coefficients with hold-up1 27)...

Bier, W., Keller, W., Linder, G., Seidel, D., Schubert, K., Manufacturing and testing of compact micro heat exchangers with high volumetric heat transfer coefficients, ASME, DSC-Microstructures, Sensors, and Actuators 1990, 19, 189-197. 

Hiraoka and Toei (H5) made experiments to study the volumetric heat-transfer coefficient. 

G- Flow rate per unit area or mass flux (kg m s" ) hv- Volumetric heat transfer coefficient (WWK) H- Enthalpy (J/kg)... 

The overall volumetric heat transfer coefficient is obtained by combining a gas and liquid coefficient. Woods provides a value of 3 kW/m °C for a typical volumetric overall heat transfer coefficient for a packed tower under the above conditions (see Table 3-18). For greater accuracy values for the individual gas and liquid volumetric heat transfer coefficient may be obtained using the relations... 

These values can be used to obtain the overall volumetric heat transfer coefficient. 

Note This problem was originally developed by H. Sawitstowski and W. Smith, Mass Transfer Process Calculations, p. 456, Interscience Publishers, New York (1963). In these calculations, they arrived at a total heat load of 405 kW, a calculated volumetric heat transfer coefficient of 2.4 kW/m °C, a diameter of 1.83 m and a height of 1.98 m. 

Dryer cost data were obtained from manufocturers as a function of dryer volume, the latter being calculated by the model assuming the volumetric heat transfer coefficient to be a function of mean biomass moisture content. The form of the function was derived from manufacturers data. 

Heat- and Mass-Transfer Estimates Many rotary dryer studies have correlated heat- and mass-transfer data in terms of an overall volumetric heat-transfer coefficient U a [W/(m K)], defined by... 

TABLE 12-30 Values of the Index n in Correlations for the Volumetric Heat-Transfer Coefficient (after Baker 1983)... 

McCormick (1962) reworked the data of Miller et al. (1942), Friedman and Marshall (1949), and Saeman and Mitchell (1954) with a view to obtaining a single correlation of the form of Eq. (12-101) for the volumetric heat-transfer coefficient. He demonstrated that all the data could be correlated with values of the exponent n from 0.46 to 0.67. Although the evidence was far from conclusive, he believed that a value of 0.67 for the exponent n was most reliable. Individual values of the constant K were obtained from the results of each of the workers cited above. He found that it was a function of the solids properties, the flight geometry, the rotational speed, and the dryer holdup, but that there was insufficient evidence available to relate K to these parameters. 

Friedman and Mahall, Studies in Rotary Drying. Part 1. Holdup and Dusting. Part 2. Heat and Mass Transfer, Chem. Eng. Progr, 45 482-493,573-588 (1949). Hirosue and Shinohara, Volumetric Heat Transfer Coefficient and Pressure Drop in Rotary Dryers and Coolers, 1st Int. Symp. on Drying, 8 (1978). Kamke and Wilson, Computer Simulation of a Rotary Dryer. Part 1. Retention Time. Part 2. Heat and Mass Transfer, A/C/iT/. 32 263-275 (1986). 

An alternative method of estimating dryer size very roughly is to estimate a volumetric heat-transfer coefficient [typical values are around 2000 I/(m s K)j and thus calculate dryer volume. 

Hirosue and Shinohara, Volumetric Heat Transfer Coefficient and Pressure Drop in Rotary Dryers and Coolers, 1st Int. Symp. on Drying, 8 (1978). 

For spherical particles the volumetric heat transfer coefficient is given as the product of the specific surface area and the interfaciai heat transfer coefficient (10.177). The volumetric interfaciai heat transfer coefficient is modeled by (10.178)... 

Spray dryer volumetric heat transfer coefficients = 0.13 to 0.18 kW/m -°C. 

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