Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-17T05:10:12.854Z Has data issue: false hasContentIssue false
  • English
  • Français

Heat and mass transfer between a rough wall and turbulent fluid flow at high Reynolds and Péclet numbers

Published online by Cambridge University Press:  29 March 2006

A. M. Yaglom  and
B. A. Kader
A. M. Yaglom
Affiliation:
Institute of Atmospheric Physics, Academy of Sciences of USSR, Moscow
B. A. Kader
Affiliation:
Moscow Institute of Mechanical Engineering for Chemical Industry
Get access Rights & Permissions [Opens in a new window]

Abstract

General dimensional and similarity arguments are applied to derive a heat and mass transfer law for fully turbulent flow along a rough wall. The derivation is quite analogous to Millikan's (1939) derivation of a skin-friction law for smooth-and rough-wall flows and to the derivation of the heat and mass transfer law for smooth-wall flows by Fortier (1968a, b) and Kader & Yaglom (1970, 1972).

The equations derived for the heat or mass transfer coefficient (Stanton number) Ch and Nusselt number Nu include the constant term β of the logarithmic equation for the mean temperature or concentration of a diffusing substance. This term is a function of the Prandtl number, the dimensionless height of wall protrusions and of the parameters describing the shapes and spatial distribution of the protrusions. The general form of the function β is roughly estimated by a simplified analysis of the eddy-diffusivity behaviour in the proximity of the wall (in the gaps between the wall protrusions). Approximate values of the numerical coefficients of the equation for β are found from measurements of the mean velocity and temperature (or concentration) above rough walls. The equation agrees satisfactorily with all the available experimental data. It is noted that the results obtained indicate that roughness affects heat and mass transfer in two ways: it produces the additional disturbances augmenting the heat and mass transfer and simultaneously retards the fluid flow in the proximity of the wall. This second effect leads in some cases to deterioration of heat and mass transfer from a rough wall as compared with the case of a smooth wall at the same values of the Reynolds and Prandtl numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 3 , 11 February 1974 , pp. 601 - 623
Copyright
© 1974 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Afzal, N. & Yajnik, K. S. 1971 Asymptotic theory of heat transfer in two-dimensional boundary layers Z. angew. Math. Phys. 22, 899–906.Google Scholar
Antuf'Ev, V. M. 1966 Effectiveness of Convective Heating Surfaces of Various Shapes. Moscow: Publ. House ‘Energiya
Becirspahic, S. 1969 Velocity and temperature distribution near rough walls. Paper presented at Int. Sem. on Heat Mass Transfer in Flows with Separated Regions including Measurements Tech., Herceg Novi, Yugoslavia.
Becirspahic, S. 1971 Etude expérimental de l’écoulement près des parois régueuses. Therm. et Aéraul. 1, 261–286.Google Scholar
Bergles, A. E. 1969 Survey and evaluation of techniques to augment convective heat and mass transfer Prog. Heat Mass Transfer, 1, 331–424.Google Scholar
Blackadar, A. R. & Tennekes, H. 1968 Asymptotic similarity in neutral barotropic planetary boundary layers J. Atmos. Sci. 25, 1015–1020.Google Scholar
Chamberlain, A. C. 1968 Transport of gases to and from surfaces with bluff and wavelike roughness elements Quart. J. Roy. Met. Soc. 94, 318–332.Google Scholar
Csanady, G. T. 1967 On the ‘resistance law’ of a turbulent Ekman layer. J. Atmos. Sci. 24, 467–471.Google Scholar
Dawson, D. A. & Trass, O. 1972 Mass transfer at rough surfaces Int. J. Heat Mass Transfer, 15, 1317–1336.Google Scholar
Dipprey, D. F. & Sabersky, R. H. 1963 Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers Int. J. Heat Mass Transfer, 6, 329–353.Google Scholar
Fortier, A. 1968a Transfer problems in turbulent flows Ann. N. Y. Acad. Sci. 154, 704–727.Google Scholar
Fortier, A. 1968b Théorie asymptotique de la couche limite turbulente. Paper presented at Int. Summer School on Heat Mass Transfer in Turbulent Boundary Layer, Herceg Novi, Yugoslavia.
Galin, N. M. 1966 Heat exchange in turbulent fluid flow along rought walls. Candidate dissertation, Moscow Energetics Institute.
Gill, A. E. 1967 The turbulent Ekman layer. Unpublished manuscript, Dept. Appl. Math. & Theo. Phys., University of Cambridge.Google Scholar
Isachenko, V. P., Agababov, S. G. & Galin, N. M. 1965 Experimental investigation of heat transfer and hydraulic resistance in turbulent water flow in pipes with artificial roughness. In Heat Transfer and Hydraulic Resistance (Works of Moscow Energetics Institute, no. 63), pp. 27–37.Google Scholar
Izakson, A. A. 1937 On the formula for the velocity distribution near walls Tech. Phys. USSR, 4, 155–162.Google Scholar
Jayatilleke, C. L. V. 1969 The influence of Prandtl number and surface roughness on the resistance of the laminar sub-layer to momentum and heat transfer Prog. Heat Mass Transfer, 1, 193–329.Google Scholar
Kader, B. A. 1966 On the structure of the viscous sublayer of an incompressible fluid. Izv. AN SSRS, Ser. Mekh. Zhidk. i Gaza. (Ser. Mech. Liquid & Gas), no. 6, pp. 157–164.Google Scholar
Kader, B. A. & Aronov, A. R. 1970 Statistical analysis of the experimental works on heat and mass transfer at high Prandtl numbers Teor. Osnovy Khim. Tekh. (Theor. Found. Chem. Engng), 4, 637–652.Google Scholar
Kader, B. A. & Yaglom, A. M. 1970 Universal law of turbulent heat and mass transfer at large Reynolds and Péclet numbers Dokl. Akad. Nauk SSSR, 190, 65–68.Google Scholar
Kader, B. A. & Yaglom, A. M. 1972 Heat and mass transfer laws for fully turbulent wall flows Int. J. Heat Mass Transfer, 15, 2329–2353.Google Scholar
Kays, W. M. 1966 Convective Heat and Mass Transfer. McGraw-Hill.
Kolác, V. 1965 Heat transfer in turbulent flow of fluids through smooth and rough tubes Int. J. Heat Mass Transfer, 8, 639–653.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Millikan, C. B. 1939 A critical discussion of turbulent flows in channels and circular tubes. Proc. 5th Int. Cong. Appl. Mech., Cambridge, Mass., pp. 386–392.Google Scholar
Millonshchikov, M. D. 1971 Turbulent heat and mass transfer in pipes with smooth and rough walls Atomnaya Energiya (Atomic Energy), 31, 199–204.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. 1. M.I.T. Press.
Nunner, W. 1956 Wärmeübergang und Druckabfall in rauhen Rohren. VDI-Forschungsheft, Nr. 455.Google Scholar
Owen, P. R. & Thomson, W. R. 1963 Heat transfer across rough surfaces. J. Fluid Mech. 15, 321–334.Google Scholar
Pinkel, B. 1954 A summary of NACA research on heat transfer and friction for air flowing through tubes with large temperature differences Trans. A.S.M.E. 76, 305–317.Google Scholar
Seleznev, A. A. 1955 Roughness effects on heat transfer at forced air flows in pipes. Teploenergetika, no. 7, pp. 45–47.Google Scholar
Seleznev, A. A. 1956 Roughness effects on heat transfer at forced fluid flows in pipes. Candidate dissertation, Kazan Institute of Aircraft Industry, Kazan, USSR.
Siegel, R. & Sparrow, E. M. 1960 Comparison of turbulent heat transfer results for uniform wall heat flux and uniform wall temperature Trans. A.S.M.E. 82, 152–153.Google Scholar
šLanČIauskas, A. & Drižius, M.-R. 1971 Wall temperature profiles in turbulent boundary layers of various fluids. Trudy Akad. Nauk Lithuanian SSR, B 1 (64), 189–203.Google Scholar
šlančiauskas, A., Pedišius, A. & Žukauskas, A. 1971 Universal temperature profiles and turbulent Prandtl number at various fluid flows in a flat plate boundary layer. Trudy Akad. Nauk. Lithuanian SSR, B 2 (65), 131–142.Google Scholar
Smith, J. W. & Gowen, R. A. 1965 Heat transfer efficiency in rough pipes at high Prandtl number A.I.Ch.E. J. 11, 941–943.Google Scholar
Squire, H. B. 1951 The friction temperature: a useful parameter in heat-transfer analysis. Proc. Gen. Discus. Heat Transfer, Inst. Mech. Engng & A.S.M.E., London, pp. 185–186.Google Scholar
Squire, W. 1959 An extended Reynolds analogy. Proc. 6th Midwestern Conf. Fluid Mech., University of Texas, Austin, pp. 16–33.Google Scholar
Tennekes, H. 1968 Outline of a second-order theory of turbulent pipe flow A.I.A.A. J. 6, 1735–1740.Google Scholar
Teverovskii, B. M. 1956 Influence of surface roughness on hydraulic resistance and convective heat transfer. Candidate dissertation, Kuibyshev Industrial Institute, Kuibyshev, USSR.
Teverovskii, B. M. 1958 On the influence of surface roughness on hydraulic resistance and convective heat transfer. Izv. Vysch. Uchebn. Zaved. SSSR, Energetika (Proc. Universities & Colleges USSR, Ser. Energetics), 7, 84–89.Google Scholar
Watson, J. S. & Thomas, D. G. 1967 Forced convection mass transfer: Part IV. A.I.Ch.E. J. 13, 676–677.Google Scholar
Webb, R. L., Eckert, E. R. G. & Goldstein, R. J. 1971 Heat transfer and friction in tubes with repeated-rib roughness Int. J. Heat Mass Transfer, 14, 601–617.Google Scholar
Yajnik, K. S. 1970 Asymptotic theory of turbulent shear flows. J. Fluid Mech. 42, 411–427.Google Scholar