from Figure 6 that this is approximatel>-true for the smallest particles a t the shallo\\-er depths. From Table I. one can see that the heat transfer coefficient is usually greater at higher temperatures when all other. parameters are the same. \.ariatiom \\-ith temperature are zignificant compared to the experimental error only \\-hen large parrs of the data are considered. 'They may be due in part to the increased thermal conductivity of the gas. and in part to the greater degree of fluidization a t higher temperature which causes a breakup of aggregates and. therefore. less gas bypassing. Acknowledgment
'The authors are indebted to P. M. Giles and N. hl. Schnurr for their contributions. They also thank G. M. Grover. E. \Y. Snlmi, and Joseph I>.Smith, J r . , for their advice and encouragement. Nomenclature
surface area of solid per unit volume of bed, sq. cm. cc. heat capacity of gas. joules g. C. D = static bed depth. cm. D , = average particle diameter, cm. G = superficial gas flow rate: g.,'sq. cm.-sec. h = particle to gas heat transfer coefficient, wattsjsq. cm.u
=
C',
=
t o
Nu = Nusselt number = hD, k R e = R e p o l d s number = GD, p to = temperature of solids. ' C. t , = temperature of gas. O C . to = temperature of gas a t bed exit, O C. t i = remperature of gas at bed inlet, O C p = gas viscosity, poises Literature Cited (1) .4nton. .J. K . . thesis. University of Iowa. 1953. (2) Lichorn. J.. \Vhite. K. R.; Chem. En?. Proqr. Symp. Ser.. 48, No. 4. 11 (1952). (3) Frantz. J . F., Chem. En,?. P r o ~ r .5 7 , N o . 7,35 (1961). (4) Heertjes. P. M,, McKibbins, S. I V , : Chrm. En:. Scz. 5 , 161 (1 956). (5)' .Johkstone. H. F., Pigford. K.L.. Chapin, J. H.!Trans. .4m. Inst. Cheni. Engrs. 37, 95 (1941). (6) Ketternrinp. K. N.. Mand?rfield. E. L.:Smith. J. M . , Cheni. Etlg. P70g7. 46, 139 (1950). ( 7 ) Kramers. H.. Phvszca 12. 61 11946). ( 8 ) Richardson. .J. P.. Aver's. P . . ~Tran's. Inst. Chem. Eners. (London) 37. 314 11959) (9) may have changed from 0.36 at one extreme to 0.38 a t the other extreme, resulting in a curvature which is so slight as to be covered by the scattering of the data. This interpretation is confirmed by the fact that the confidence limits are generally higher when 2p p ' values, and hence A values, are higher. From Equations 28 a n d 29 it can be seen that, when A = 0: p can be really constant; the higher the value of A ? the more inaccurate is the hypothesis of a constant p (or p ' ) , and therefore higher confidence limits are expected to be shown by a regression analysis based on a constant value ofp or p'. T h e explanation offered for the results obtained can be tested by considering the order of magnitude of u p . Both p and p ' may be assumed again to be 0.37 at the "average" experimental conditions. For Q = 4 cc. per second and CY = 6.5', 6 is on the average 0.31 cm., and T O = 35 dynes per sq. cm. From the average value A = 0.35. the order of magnitude of ut,can be estimated from Equation 7 at 0.7cm. per second, 338
- du/dy , Figure 8.
X
x
10-4cm.
microns is consistent with the hypothesis that
