SEPTEMBER. 1935
INDUSTRIAL A S D ENGINEERING CHEMISTRY
CORRESPONDENCE Heat Transfer Involving Turbulent Fluids SIR: I n the paper of the above title by Kaye and Furnas (S), the suggestion is made that heat transfer coefficients for heating can be predicted when those for cooling only have been measured, :ind vice versa, for the same mean film conditions, by applying ti function of the ratio of the viscosity of the fluid cooled at the main stream temperature t o that of the fluid heated. Kaye and Furnas gave consideration only to experiments in which the same investigat,or made runs in the same apparatus, at. the same average temperatures, for both heating and cooling; and of these runs, only those that were in turbulent flow (as judged on film conditions) were considered. I n effect, they vere limited t o the Morris and Khitman ( 6 ) gas oil data n-hich were considered by the writer to pass through the “transition zone” between turbulent and viscous flow and not applicable as a whole to either region separately. The explanation for the relative positions of the curves representing heating and cooling transfer coefficients, for this series of experiments when plotted against the Reynolds number based on the mean film conditions, was suggested by the writer (1) from a consideration of all the available data without regard to whether the flow was turbulent or viscous. 4 s regards friction i n pipes, it has been shon-n (4) that the t,ransition from one type to the other depends not on the film conditions but on of f l o ~ those of the main stream. It has also been shown that, regardless of what ordinate is used to include the heat transfer coefficient in a dimensionless grouping, correlation is obtained in viscous flow only by plotting against the group wclkL, Tvhere w is the weight flow and L the heated length. This group is proportional to (DT-/Z)(D/L)(cZlk). That is, in viscous flow the heat transfer coefficient is dependent not only on the Reynolds number :ind on c Z / k , but very decidedly on the ratio of length to diameter. Accordingly, n-hen heat transfer factors as defined by the writer are plotted against the Reynolds number it is found that in viscous flow the resulting curves may lie at any level, depending on ( D I L ) , the relative viscosity a t the film and main body temperatures, and on the Grashof group. Therefore, a t the critical velocity the heat transfer factors may lie far below, or even above, the extrapolated line XT-hich represents the data i n the far turbulent region (on water and on gases, mainly). The zone of transition was termed the “dip,” since there is a well-defined dip in the friction factor curves for flow in circular pipes. But the course follon-ed by the curve representing heat transfer factors may not parallel that for friction, since the starting point will be different for each set of experimental conditions. The situation is somewhat like that for flow in sections other than circular, for which I’oiseuille’s equation does not hold; the transition from viscous to turbulent flow in this case is represented by quite a different dip from that for circular pipes. The actual transition, occurring at Reynolds numbers on mainbody conditions of around 18.5 (in terms of DT,’Z, 2300 in consistent unite), will appear in plots based against film-condition Reynolds numbers a t different points, depending on the ratio of the film to the main-stream viscosity. Therefore, the blorris nnd R7hitm:in straw-oil heating data covering a range from 18 to 160 in values of DT7,/Z (2250 to 20,000 in Consistent units), represent a range of 6 to 106 (750 to 13,200 in consistent units on main-stream condition--that is, actually starting in viscous
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flow and passing through the critical velocit’y to a fair degree of turbulence. The cooling data, on the other hand, with a range (considered by Kaye and Furnas) of 18 to 150 (2250 to 18,600 in consistent units) represent a range on the main stream basis of about 50 to 365 (6200 to 45,000 in consistent units) ---that is, well into the turbulent region even at the start, and extending much farther. According to the considerations advanced above, it would seem reasonable that the heating data would (at the same film Reynolds number) be nearer to the lo^ values t,liat would be expected for this experimental apparatus at velocities just below the critical, Tvhile the cooling data would agree rather closely with the line representing other data in turbulent flow. This relationship is brought out in Figures 11 and 15 of the paper mentioned ( 1 ) . I t is therefore believed that the Morris and Whitman data do not furnish any satisfactory basis for methods of correlation applicable to turbulent flow generally. Other data available, including those of Furnas (2), do not show any significant difference, taken as a whole, between heating and cooling runs, when the transition zone has been passed. The comparison of coefficients presented by Kaye and Furrias calculated by means of the Dittus and Boelter equation is not significant, since this equation was likewise based principally on the same Morris and Whitman data. The attempted correlations of the Keevil data, and those of Clapp and Fitzsimons are not conclusive, since no experimental point,s were available as a check under the limitations imposed by Kaye and Furnas. The figure shows the actual trend of the experimental data of
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EXPERIMENTAL DATA O M I T T E D FROM ORIGINAL PLOT0 HEATING X - COOLING
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Clapp and Fitzsimons on heating (points marked by squares) a t low Reynolds numbers (in viscous flow on main-stream conditions, as any runs would almost necessarily be to compare with the cooling runs at’ the same film conditions). Some additional data on cooling (at higher film temperatures than the remainder, and a few at low Reynolds numbers) are also shown (points shown by X). These points fail to agree with the “predicted” curves. The same sets of data are shown on Figures 8 and 12 of the paper mentioned ( I ) , where the appearance of the “transition region” is well illustrated. As pointed out ( I ) , more data are needed 011 heat transfer for
IXDUSTRIAL AND ENGINEERING CHEMISTRY
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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
