Transactions

566 TRANSACTIONS OF THE A.S.M.E. OCTOBER, 1941than the more theoretical ones, and suggest that further improvementsin the theory are possible.These data also verify the Nusselt data on gases in showing adeviation from the analogy between fluid friction and heat transfer.If this analogy (7) held, the heat-transfer and friction lines onthe plots would be coincident in the turbulent region. At lowReynolds’ numbers, the divergence may possibly be explained bythe presence of a greater “dip” region for heat transfer betweenviscous and turbulent flow than for friction. However, in thestrong turbulent region, the heat-transfer factors are still a good10 per cent below the friction factors. Above a Reynolds numberof 10,000 the slope of the line representing the heat-transfer data is—0.2 but at lower Reynolds’ numbers this slope becomes zeroand then of opposite direction in the “dip” region.There are a few results for the mixtures in the region of viscousflow, and while these seem to bear out the general shape ofcurves in the “dip” region and in the viscous region, there are notsufficient data to draw definite conclusions, other than that thePrandtl number appears as calculated.While the results of this study, together with those of Brunot(1), appear to, prove that the Prandtl number applies for gasesaccording to Equation [1], they show that further study of theanalogies between fluid friction and heat transfer is highly desirable.BIBLIOGRAPHY1 “Properties of Hydrogen M ixtures," by A. W. Brunot, Trans.A.S.M .E., October, 1940, pp. 613-616.2 “Engineering in the Service of Chem istry,” by Thomas H.Chilton, Industrial and Engineering Chemistry, vol. 32, January, 1940,pp. 23-31.3 “ Eine Beziehung zwischen W arm eaustausch und Stromupgswiderstandder Fliissigkeiten,” by L. Prandtl, Physikalische Zeitschrift,vol. 11, 1910, pp. 1072-1078.4 “ The Analogy Between Fluid Friction and H eat Transfer,” byT h. von Kdrmfin, Engineering, vol. 148, 1939, pp. 210-213.5 “ The Friction Factor for Clean Round Pipes,” by T . B. Drew,E. C. Koo, and W. H. McAdams, Trans. American Institute of ChemicalEngineers, vol. 28, 1932, pp. 56-72.6 “ Der W armeilbergang in Rohrleitungen,” by W. Nusselt,V.D .I. Mitteilungen uber Forschungsarbeiten, H eft 89, 1910, pp.1-38; also Zeit. V.D .I., vol. 53, 1909, pp. 1750-1755, 1808-1812.7 “A M ethod of Correlating Forced Convection H eat TransferD ata and a Comparison W ith Fluid Friction,” by A. P. Colburn,Trans. American Institute of Chemical Engineers, vol. 29, 1933, pp.174-209.D i s c u s s i o nR. H. N o r r i s . 4 It is of interest to compare the authors’ test resultsfor the region of viscous flow with theoretical results, eventhough, as the authors admit, their test data in this region are tooscanty to be conclusive.Fig. 13 of this discussion shows points representing the authors’test results compared with curves evaluated from a recentlypublished5 correlation of theoretical results, using the logarithmicmeantemperature difference basis. When the empirical correctionproposed by Colburn (7) for free convection is included, andthe possible range of error of the test results indicated by the heatbalancediscrepancy is allowed for, the agreement between testand theory is reasonably good (of the order of 10 per cent), belowReynolds’ number of 2200. For higher Reynolds’ numbers,transition to turbulent flow has presumably begun. The factthat the test values somewhat exceed the theoretical values mayindicate that the correction for free convection here applied to thelatter is not quite sufficient, or that the flow is not completelylaminar.4 General Engineering Laboratory, General Electric Company,Schenectady, N . Y. Jun. A.S.M.E.6 “Laminar-Flow Heat-Transfer Coefficients for D ucts,” by R. H.Norris and D. D. Streid, Trans. A.S.M.E., vol. 62, August, 1940, pp.525-533.