Critique of the Classical Algebraic Analogies between Heat, Mass, and Momentum Transfer

Industrial and Engineering Chemistry Research

Volumn 36, Issue 9, 1997, Pages 3866-3878

  Churchill, Stuart W ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ERROR ANALYSIS; HEAT CONVECTION; HEAT FLUX; MASS TRANSFER; MOLECULAR DYNAMICS; PIPE FLOW; WALL FLOW;

MASS FLUX; MOMENTUM TRANSFER;

TURBULENT FLOW;

ANALOGY; HEAT TRANSFER; MASS TRANSFER; MOMENTUM TRANSFER; PRANDTL NUMBER;

EID: 0031231057     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie960750a     Document Type: Article

References (37)

1. Abbrecht, P. H.; Churchill, S. W. The Turbulent Entrance Region in Fully Developed Turbulent Flow. AIChE J. 1960, 6, 268.
2. Bejan, A. Convection Heat Transfer; John Wiley and Sons: New York, 1984.
3. Churchill, S. W. Comprehensive Correlating Equations for Heat, Mass and Momentum Transfer in Fully Developed Flow in Smooth Tubes. Ind. Eng. Chem. Fundam. 1977, 6, 109.
4. Churchill, S. W. Theoretically Based Expressions in Closed Form for the Local and Mean Coefficients of Skin Friction in Fully Turbulent Flow along Smooth and Rough Plates. Int. J. Heat Fluid Flow 1993, 14, 231.
5. Churchill, S. W. New, Simplified Models and Formulations for Turbulent Flow and Convection. AIChE J. 1997a, 43, 1125.
6. Churchill, S. W. The Prediction of Turbulent Convection without Explicit Empiricism. Thermal Science and Engineering, in press (1997b).
7. Churchill, S. W.; Balzhiser, R. E. The Radial Heat Flux. Chem. Eng. Prog. Symp. Ser. 1959, 55 (29), 127.
8. Churchill, S. W.; Chan, C. Improved Correlating Equations for the Friction Factor for Fully Turbulent Flow in Round Tubes and between Identical Parallel Plates, both Smooth and Naturally Rough. Ind. Eng. Chem. Res. 1994, 33, 2016.
9. Churchill, S. W.; Chan, C. Theoretically Based Correlating Equations for the Local Characteristics of Fully Turbulent Flow in Round Tubes and between Parallel Plates. Ind. Eng. Chem. Res. 1995a, 33, 1332.
10. Churchill, S. W.; Chan, C. Representation of the Time-Averaged Characteristics of Turbulent Flow in Channels in Terms of the Local Turbulent Shear and Normal Stresses. AIChE J. 1995b, 41, 2513.
11. Colburn, A. P. A Method of Correlating Forced Convection Heat Transfer Data and a Comparison with Fluid Friction. Trans. Am. Inst. Chem. Eng. 1933, 29, 174.
12. Danckwerts, P. V. Significance of Liquid Film Coefficients in Gas Absorption. AIChE J. 1957, 3, 1460.
13. Friend, W. L.; Metzner, A. B. Turbulent Heat Transfer Inside Tubes and the Analogy Among Heat, Mass and Momentum Transfer. AIChE J. 1958, 4, 393.
14. Heng, Ly; Chan, C.; Churchill, S. W. Exact Characteristics of Turbulent Convection. In preparation.
15. Higbie, R. The Rate of Absorption of Pure Gas into a Still Liquid During Short Periods of Exposure. Trans. Am. Inst. Chem. Eng. 1935, 31, 365.
16. Kadar, B. A.; Yaglom, A. M. Heat and Mass Transfer Laws for Fully Turbulent Wall Flows. Int. J. Heat Mass Transfer 1972, 15, 2229.
17. Knudsen, J. G.; Katz, D. L. Fluid Dynamics and Heat Transfer; McGraw-Hill Book Co.: New York, 1958; p 425.
18. Lyson, R. E. Liquid Metal Heat Transfer Coefficients. Chem. Eng. Prog. 1951, 47, 75.
19. Martinelli, R. C. Heat Transfer of Molten Metals. Trans. ASME 1947, 69, 947.
20. McAdams, W. H. Heat Transmission, 3rd ed.; McGraw-Hill Book Co.: New York, 1954; p 212.
21. Metzner, A. B.; Friend, W. L. Theoretical Analogies between Heat, Mass, and Momentum Transfer and Modifications for Fluids of High Prandtl or Schmidt Numbers. Can. J. Chem. Eng. 1958, 36, 235.
22. Notter, R. H.; Sleicher, C. A. A Solution to the Turbulent Graetz Problem-III. Fully Developed and Entry Region Heat Transfer Rates. Chem. Eng. Sci. 1972, 27, 2073.
23. Page, F., Jr.; Schlinger, W. G.; Breaux, D, K.; Sage, B. H. Point Values of Eddy Conductivity and Eddy Viscosity in Uniform Flow between Parallel Plates. Ind. Eng. Chem. 1952, 44, 424.
24. Papavassiliou, D. V.; Hanratty, T. J. Transport of a Passive Scalar in a Turbulent Channel Flow. Int. J. Heat Mass Transfer 1997, 40, 1303. 196.
25. Petukhov, B. S. Heat Transfer and Friction in Turbulent Pipe Flow with Variable Physical Properties. Adv. Heat Transfer 1970, 6, 503.
26. Petukhov, B. S.; Popov, V. N. Theoretical Calculations of Heat Exchange and Frictional Resistance in Tubes of an Incompressible Fluid with Variable Physical Properties. High Temperature 1963, 1, 69.
27. Prandtl, L. Eine Beziehung zwischen Wärmeaustausch und Strömungswiderstand der Flüssigkeit. Phys. Z 1910, 11, 1072.
28. Reichardt, H. Die Grundlagen des turbulenten Wärmeübertraganges. Archiv. Wärmetechnik 1951, 2, 129; English transl. The Principles of Turbulent Heat Transfer. Nat. Adv. Comm. Aeronaut. TM1408, Washington, D.C., Sept. 1957.
29. Reichardt, H. Die Grundlagen des turbulenten Wärmeübertraganges. Archiv. Wärmetechnik 1951, 2, 129; English transl. The Principles of Turbulent Heat Transfer. Nat. Adv. Comm. Aeronaut. TM1408, Washington, D.C., Sept. 1957.
30. Reynolds, O. On the Extent and Action of the Heating Surface on Steam Boilers. Proc. Lit. Philos. Soc. Manchester 1874, 14, 7; Papers on Mechanical and Physical Subjects; Cambridge University Press: Cambridge, 1901; Vol. I, Paper 14, p 81.
31. Reynolds, O. On the Extent and Action of the Heating Surface on Steam Boilers. Proc. Lit. Philos. Soc. Manchester 1874, 14, 7; Papers on Mechanical and Physical Subjects; Cambridge University Press: Cambridge, 1901; Vol. I, Paper 14, p 81.
32. Sherwood, T. K.; Ryan, J. M. Mass Transfer to a Turbulent Fluid with and without Chemical Reaction. Chem. Eng. Sci. 1959, 11, 81.
33. Sleicher, C. A.; Tribus, M. Heat Transfer in a Pipe with Turbulent Flow and Arbitrary Wall-Temperature Distribution. Trans. ASME 1957, 79, 789.
34. Taylor, G. I. Conditions at the Surface of a Hot Body Exposed to the Wind. British Adivsory Committee Aeronautical Reports and Memoranda, No. 272, 1916.
35. Thomas, L. C.; Fan, L. T. Heat and Momentum Transfer Analogy for Incompressible Boundary Layer Flow. Int. J. Heat Mass Transfer 1971, 14, 715.
36. von Kármán, Th. The Analogy Between Fluid Friction and Heat Transfer. Trans. ASME 1939, 61, 705.
37. Yahkot, V.; Orszag, S. A.; Yahkot, A. Heat Transfer in Turbulent Fluids-1. Pipe Flow. Int. J. Heat Mass Transfer 1987, 30, 15.