IXDUSTRIAL AND ENGINEERING CHEMISTRY
1104
viscous oils a t a high enough range of Reynolds numbers to insure the results being beyond the dip region. A. P. COLBURX E. I. DU POXTDE NEMOURS& COMPASY, IIC. RILMINGTON, DEL. December 28, 1934
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SIR: The source of argument bet,ween the writers (1, 3) is confined to the “transition zone” in a graph xhere a function of the heat transfer coefficient and other variables is plotted against Reynolds number. The Kaye and Furnas method of correlation makes no pretense of being applicable for viscous flow, and no data are available for both heating and cooling in the same apparatus for regions which are undoubtedly beyond the transition zone as fixed by Colburn (1). Since the transition zone is necessarily metastable, we might well expect certain variations in performance which could be “explained” by more than one line of reasoning. Qualitatively there is no argument. Heat transfer coefficient data, over a considerable range of velocity, viscosity, etc., show higher coefficients of heat transfer for cooling the liquid than for heating it, for the same value of Reynolds number, based on mean film conditions. Kaye and Furnas (3) offer an empirical correlation between heating and cooling data based on the ratio of the square root of the main-stream viscosity in the two cases. The method correlates the Morris and Whitman data (6) most satisfactorily and such other data as are available fairly well. The correlation is good enough to make the method useful for a simple prediction of a heating transfer coefficient if one for cooling is available, or vice versa. According to Colburn’s much more general theory ( I ) , summarized in his Figure 16, the ratio of hooolingto hheatingin the transition zone is dependent not only on the variables used by Kaye and Furnas but upon the ratio of pipe length to pipe diameter. Further, according to Colburn, there is no difference between heating and cooling beyond the transition zone, but no data are available to prove that definitely. Colburn’s placing of the curves through the transition region is based on data that are by no means complete, and in many cases are not consistent. The use of his curves for estimating film heat transfer coefficients, in the transition zone, without resort to experiment can lead to absurd results. Colburn’s curves of j vs. Reynolds number through the transition zone can be expressed roughly since j is proportional to the square of Reynolds number. In symbols then, approximately,
transposing,
tained on heat tramfer from gases to beds of broken solids ( 2 ) where the transfer for cooling the solids was higher than for heating, a t values of Reynolds number far beyond the transition zone. This is in keeping with the Kaye and Furnas hypothesis. Colburn contends that the differences between these heating and cooling coefficients are not great enough to be significant. However, these coefficients were not determined directly but were an integral effect of the temperature history of the beds of solids. The temperature histories, from which the coefficients were obtained, showed an unquestioned difference between heating and cooling. The Colburn hypothesis does not explain this. Unfortunately there are no complete heating and cooling data available for transfer involving gases in conduits. One point should be emphasized in this discussion of methods of correlation, and i t is seldom mentioned: The film coefficient of heat transfer refers to the film and only to the film of the fluid involved. Widely divergent experimental results are obtained by the unwitting introduction of minute layers of dirt, grease, gas, or a scale of some sort. The discussion is confined to that theoretical condition of a 100 per cent clean surface, a condition which is only approached and never completely realized. If scale or dirt is known to be present, it must be corrected for by an additional resistance factor. If it is pfesent but not accounted for they make themselves felt as inconsistent results. Hence the unsatisfactory state of heat transfer data a t the present time. C. C. FURNAS W. A. KAYE YALE U N I V E R S I T Y NEW HAVEN,CONS. June 29, 1935
Literature Cited (1) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29, 174-209 (1933). (2) Furnas, C. C., Bur. Mines, Bull. 361 (1932). (3) Kaye, W. H., and Furnas, C. C., ISD. ENG.CHEM.,26, 783-6 (1934). H., “Heat Transmission,” pp. 112-14, New Tork, (4) McAdams, Wr. McGraw-Hill Book Co., 1933. (5) Morris, F. H., and Whitman, W. G., IND. E s c . CHEM., 20, 234-40 (1928).
Correction SIR: I t has been called to my attention that the person holding the cylinder in No. 54 of the Alchemical and Historical Reproductions is not Liebig, although i t was so stated in a reliable source. After some research, I have been able to identify most of the persons shown in No. 54 (June, 1935,issue, p. 631)and No. 55 (July, 1935, issue, p. 758) as follows, reading left to right: KO.54: 1.
ha, then, is very sensitive to changes in d, G , and p . Thus if there is an error of 10 per cent each in d, G, and M/ and they all happen to be in the right direction, the error in the predicted h, would be 108 per cent. If the error in each of these three quantities was 20 per cent, the error in the estimated ha might be 237 per cent. These figures rather discourage the placing of complete reliance on the Colburn curves in the transition region and should tend to encourage further research. If either heating or cooling data are a t hand, the heat transfer coefficient for the other condition can be estimated either by the Kaye and Furnas method or the Colburn curves. I n general the data seem to fit the Kaye and Furnas predictions a little better than the Colburn curves. The discussion of the merits of the two methods cannot be continued into the region of very turbulent flow, for data are not available. Colburn contends that there should be no difference there between heating and cooling coefficients, Furnas and Kaye say there should be. If reliable data on gases were available, this matter might be settled. Data have been ob-
VOL. 27, NO. 9
Ortigosa, a Mexican.
2. Unknown. 3. Unknown. 4. Laboratory porter. 5. Wilhelm Keller, subsequently a practicing physician in
Philadelphia, Pa. 6 . Heinrich Will, assistant and successor to Liebig; died 1890.
7. Aubel, laboratory preparator, later Mayor of Winsaok, near
Giessen.
8. .inton Louis, later an architect. No. 55: 9 . Wydler, from Aarau. 10. Franz Varrentrapp, later director of the Mint, Braunschweig; died 1877. 11. W. Strecker, later professor of chemistry a t Wuerzburg. 12. Johann Josef Scherer, subsequently professor of medlcine in
Wueraburg. Emil Boeckmann, later director of the Fries Ultramarine Works, Heidelberg. 14. A. W.Hofmann, Liebig’s assistant until 1845, subsequently professor of chemistry, Berlin; died 1892. D. D. BEROLZHEIMER 50 EAST4 1 STREET ~ ~ NEW YORK,N. Y. 13.
June 21, 1935
