Abstract
A wide set of published mass and heat transfer data is reviewed in terms of the stochastic renewal theory. A simple model is then proposed describing the transfer in terms of the fluid bulk properties. Two expressions are presented and they enable us to evaluate the bulk transfer velocity as a function of the turbulence of the flow for smooth and fully-rough surfaces in large ranges of Schmidt (or Prandtl) and Reynolds numbers. The transfer over transitional surfaces can also be evaluated by using a simple criterion for the choice of the right expression. The proposed relationships agree satisfactorily with data from laboratory and atmospheric measurements, for both solid and liquid surfaces.
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Bird, R. B., Stewart, W. E., and Lightfoot, E. N.: 1960, Transport Phenomena, J. Wiley and Sons, New York, 780 pp.
Brutsaert, W.: 1965, ‘A Model for Evaporation as a Molecular Diffusion Process into a Turbulent Atmosphere’, J. Geophys. Res. 70, 5017–5024.
Brutsaert, W.: 1975, ‘A Theory for Local Evaporation (or Heat Transfer) from Rough and Smooth Surfaces at Ground Level’, Water Resour. Res. 11, 543–550.
Chamberlain, A. C.: 1966, ‘Transport of Gases to and from Grass and Grass-like Surfaces’, Proc. Roy. Soc. A290, 236–265.
Chamberlain, A. C.: 1968, ‘Transport of Gases to and from Surfaces with Bluff and Wave-like Roughness Elements’, Quart. J. Roy. Meteorol. Soc. 94, 318–332.
Corino, E. R. and Brodkey, R. S.: 1969, ‘A Visual Investigation of the Wall Region in Turbulent Flow’, J. Fluid Mech. 37, 1–30.
Danckwerts, P. V.: 1951, ‘Significance of Liquid-Film Coefficients in Gas Absorption’, Ind. Eng. Chem. 43, 1460–1467.
Dipprey, D. F. and Sabersky, R. H.: 1963, ‘Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers’, Int. J. Heat Mass Transfer 6, 329–352.
Fleagle, R. G., Deardorff, J. W., and Bradgley, F. I.: 1958, ‘Vertical Distribution of Wind Speed, Temperature and Humidity above a Water Surface’, J. Marine Res. 17, 141–157.
Fortescue, G. E. and Pearson, J. R. A.: 1967, ‘On Gas Absorption into a Turbulent Liquid’, Chem. Engng Sci. 22, 1163–1176.
Garratt, J. R. and Hicks, B. B.: 1973, ‘Momentum, Heat and Water Vapour Transfer to and from Natural and Artificial Surfaces’, Quart. J. Roy. Meteorol. Soc. 99, 680–687.
Grass, A. J.: 1971, ‘Structural Features of Turbulent Flow over Smooth and Rough Boundaries’, J. Fluid Mech. 50, 233–255.
Harriott, P.: 1962, ‘A Review of Mass Transfer to Interfaces’, Can. J. Chem. Eng. 40, 60–69.
Higbie, R.: 1935, ‘The Rate of Absorption of a Pure Gas into a Still Liquid During Short Periods of Exposure’, Trans. Am. Inst. Chem. Engrs. 35, 365–389.
Hinze, J. O.: 1959, Turbulence, An Introduction to Its Mechanisms and Theory, McGraw-Hill, New York, 586 pp.
Kader, B. A. and Yaglom, A. M.: 1972, ‘Heat and Mass Transfer Laws for Fully Turbulent Wall Flows’, Int. J. Heat Mass Transfer 15, 2329–2351.
Kays, W. M.: 1966, Convective Heat and Mass Transfer, McGraw-Hill, New York.
Kim, H. T., Kline, S. J., and Reynolds, W. C.: 1971, ‘The Production of Turbulence near a Smooth Wall in a Turbulent Boundary Layer’, J. Fluid Mech. 50, 133–160.
Kline, S. J., Reynolds, W. C., Schraub, F. A., and Rundstadler, P. W.: 1967, ‘The Structure of Turbulent Boundary Layers’, J. Fluid Mech. 30, 741–773.
Kolář, V.: 1965, ‘Heat Transfer in Turbulent Flow of Fluids through Smooth and Rough Tubes’, Int. J. Heat Mass Transfer 8, 639–653.
Kondo, J.: 1975, ‘Air-Sea Bulk Transfer Coefficients in Diabatic Conditions’, Boundary-Layer Meteorol. 9, 91–112.
Lamont, J. C. and Scott, D. S.: 1970, ‘An Eddy Cell Model of Mass Transfer into the Surface of a Turbulent Liquid’, AIChE J. 16, 513–519
Ling, S. C. and Kao, T. W.: 1976, ‘Parametrization of the Moisture and Heat Transfer Process over the Ocean under Whitecap Sea States’, J. Phys. Oceanogr. 6, 306–315.
Liss, P. S. and Slater, P. G.: 1974, ‘Flux of Gases Across the Air-Sea Interface’, Nature 247, 181–184.
MacCready, P. B.: 1953, ‘Structure of Atmospheric Turbulence’, J. Meteorol. 10, 434–449.
Möller, U. and Schumann, G.: 1970, ‘Mechanisms of Transport from the Atmosphere to the Earth's Surface’, J. Geophys. Res. 75, 3013–3019.
Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics: Mechanics of Turbulence, MIT Press, Cambridge, Mass., 769 pp.
Nunner, W.: 1956, ‘Wärmeübergang und Druckabfall in rauhen Rohren’, Ver. Deut. Ing. Forschungsh. 455(B), 22, 5–39.
Owen, P. R. and Thomson, W. R.: 1963, ‘Heat Transfer across Rough Surfaces’, J. Fluid Mech. 15, 321–334.
Pinkel, B.: 1954, ‘A Summary of NACA Research on Heat Transfer and Friction for Air Flowing through Tube with Large Temperature Difference’, Trans. A.S.M.E. 76, 305–317.
Roll, H. U.: 1965, Physics of the Marine Atmosphere, Academic Press, New York and London, 426 pp.
Sheppard, P. A., Tribble, D. T., and Garratt, J. R.: 1972, ‘Studies of Turbulence in the Surface Layer over Water (Lough Neagh). Part 1. Instrumentation, Programme, Profiles’, Quart. J. Roy. Meteorol. Soc. 98, 627–641.
Sverdrup, H. U.: 1937, ‘On the Evaporation from the Oceans’, J. Marine Res. 1, 3–14.
Takahashi, T.: 1958, ‘Micro-Meteorological Observations and Studies over the Sea’, Mem. Fac. Fish. Kagoshima Univ. 6, 1–46.
Verma, S. B. and Cermak, J. E.: 1974, ‘Wind-Tunnel Investigation of Mass Transfer from Soil Corrugations’, J. Appl. Meteorol. 13, 578–587.
Yaglom, A. M. and Kader, B. A.: 1974, ‘Heat and Mass Transfer Between a Rough Wall and Turbulent Fluid Flow at High Reynolds and Péclet Numbers’, J. Fluid Mech. 62, 601–623.
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Trombetti, F., Caporaloni, M. & Tampieri, F. Bulk transfer velocity to and from natural and artificial surfaces. Boundary-Layer Meteorol 14, 585–595 (1978). https://doi.org/10.1007/BF00121897
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DOI: https://doi.org/10.1007/BF00121897