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To convert British thermal units per hoursquare footdegrees Fahrenheit to joules per metersecondkelvins, multiply by 1.7307; to convert British thermal units per cubic footdegrees Fahrenheit to joules per cubic meterkelvins, multiply by (6.707)(104); and to convert square feet per hour to square meters per second, multiply by (2.581)(10~5).
To convert British thermal units per hoursquare footdegrees Fahrenheit to joules per metersecondkelvins, multiply by 1.7307; to convert British thermal units per cubic footdegrees Fahrenheit to joules per cubic meterkelvins, multiply by (6.707)(104); and to convert square feet per hour to square meters per second, multiply by (2.581)(10~5).
bined conductive and convective modes. A discussion and explanation are given by Holt [Chem. Eng., 69(1), 110 (1962)]. Prediction of Uco by Eq. (1148) can be accomplished by replacing a by ae, the effective thermal diffusivity of the bed. To date so little work has been performed in evaluating the effect of mixing parameters that few predictions can be made. However, for agitated liquidphase devices Eq. (1819) is applicable. Holt (loc. cit.) shows that this equation can be converted for solids heat transfer to yield
where Dt = agitator or vessel diameter; N = turning speed, r/min; ffl = effective angle of repose of the burden; and a' is a proportionality constant. This is applicable for such devices as agitated pans, agitated kettles, spiral conveyors, and rotating shells.
The solids passage time through rotary devices is given by Saemann [Chem. Eng. Prog., 47,508, (1951)]:
and by Marshall and Friedman [Chem. Eng. Prog., 45, 482493, 573588 (1949)]:
where the second term of Eq. (1155b) is positive for counterflow of air, negative for concurrent flow, and zero for indirect rotary shells. From these equations a predictive equation is developed for rotaryshell devices, which is analogous to Eq. (1154):
(At)L sin ffl where 0 = solidsbed passage time through the shell, min; Sr = shell slope; L = shell length; Y = percent fill; and b is a proportionality constant.
Vibratory devices which constantly agitate the solids bed maintain a relatively constant value for Uco such that
with Uo having a nominal value of 114 J/(m2 s K) [20 Btu/(hft2 °F)].
Contactive (Direct) Heat Transfer Contactive heattransfer equipment is so constructed that the particulate burden in solid phase is directly exposed to and permeated by the heating or cooling medium (Sec. 20). The carrier may either heat or cool the solids. A large amount of the industrial heat processing of solids is effected by this mechanism. Physically, these can be classified into packed beds and various degrees of agitated beds from dilute to dense fluidized beds.
The temperature difference for heat transfer is the logmean temperature difference when the particles are large and/or the beds packed, or the difference between the inlet fluid temperature t3 and average exhausting fluid temperature t4, expressed A3f4, for small particles. The use of the log mean for packed beds has been confirmed by Thodos and Wilkins (Second American Institute of Chemical EngineersIIQPR Meeting, Paper 30D, Tampa, May 1968). When fluid and solid flow directions are axially concurrent and particle size is small, as in a verticalshell fluid bed, the temperature of the exiting solids t2 (which is also that of exiting gas t4) is used as A312, as shown by Levenspiel, Olson, and Walton [Ind. Eng. Chem., 44, 1478 (1952)], Marshall [Chem. Eng. Prog., 50, Monogr. Ser. 2, 77 (1954)], Leva (Fluidization, McGrawHill, New York, 1959), and Holt (Fourth Int. Heat Transfer Conf. Paper 11, American Institute of Chemical EngineersAmerican Society of Mechanical Engineers, Buffalo, 1960). This temperature difference is also applicable for wellfluidized beds of small particles in crossflow as in various vibratory carriers.
The packedbedtofluid heattransfer coefficient has been investigated by Baumeister and Bennett [Am. Inst. Chem. Eng. J., 4, 69 (1958)], who proposed the equation jH = (h/cG)(ci/ k)m = aNRe (1158)
where NRe is based on particle diameter and superficial fluid velocity. Values of a and m are as follows:
DJDV (dimensionless) 
a 
m 

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