Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-29T17:03:56.443Z Has data issue: false hasContentIssue false
  • English
  • Français

The asymptotic form of the laminar boundary-layer mass-transfer rate for large interfacial velocities

Published online by Cambridge University Press:  28 March 2006

Andreas Acrivos
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

The convective diffusion of matter from a stationary object to a moving fluid stream is distinct from pure heat transfer because of the appearance of a finite interfacial velocity at the solid surface. This velocity is related to the rate of mass transfer by a dimensionless group B in such a way that for −1 < B < 0 the transfer is from the bulk to the surface while for 0 < B < ∞ the transfer is from the surface to the main stream. In this paper, asymptotic solutions to the two-dimensional laminar boundary-layer equations are developed for the case B [Gt ] 1, and for rather general systems. It is shown that in most instances the asymptotic expressions for the rate of mass transfer become accurate when B > 3 and that the transition region between the pure heat-transfer analogy (B ∼ 0) and the B [Gt ] 1 asymptote may be described by a simple graphical interpolation. These results may easily be extended to three-dimensional surfaces of revolution by the usual co-ordinate transformations of boundary-layer theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 12 , Issue 3 , March 1962 , pp. 337 - 357
Copyright
© 1962 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

Acrivos, A. 1960a A.I.Ch.E. J. 6, 410.
Acrivos, A. 1960b Phys. Fluids, 3, 657.
Acrivos, A. 1960c A.I.Ch.E. J. 6, 584.
Eckert, E. R. G. & Drake, R. M. 1959 Heat and Mass Transfer. New York: McGraw-Hill Book Co.
Eckert, E. R. G. & Hartnett, J. P. 1957 Trans. Amer. Soc. Mech. Engrs, 79, 247.
Eckert, E. R. G. & Lieblein, V. 1949 Forsch. Gebiete Ingenieurw. 16, 33.
Eichhorn, R. 1960 J. Heat Transf. C82, 250.
Emmons, H. W. & Leigh, D. C. 1953 Aero. Res. Counc., Lond., Rep. no. FM 1915.
ErdÉlyi, A. et al. 1953 Higher Transcendental Functions. New York: McGraw-Hill Book Co.
ErdÉlyi, A. et al. 1954 Tables of Integral Transforms, Vol. I. New York: McGraw-Hill Book Co.
Fage, A. & Falkner, V. M. 1931 Aero. Res. Counc., Lond., Rep. and Memo. no. 1408.
Görtler, H. 1957 J. Math. Mech. 6, 1.
Kaplun, S. & Lagerstrom, P. 1957 J. Math. Mech. 6, 585.
Lees, L. 1956 Jet. Prop. 26, 259.
Livingood, J. N. B. & Donoughe, P. L. 1955 NACA TN, no. 3588.
Meksyn, D. 1948 Proc. Roy. Soc. A, 192, 545.
Merk, H. J. 1959a J. Fluid Mech. 5, 460.
Merk, H. J. 1959b Appl. Sci. Res. A, 8, 237.
Mickley, H. S., Ross, R. C., Squyers, A. L. & Stewart, W. E. 1954 NACA TN, no. 3208.
Morgan, G. W. & Warner, H. W. 1956 J. Aero. Sci. 23, 937.
Morse, P. M. & Feshbach, H. 1953 Methods of Mathematical Physics. New York: McGraw-Hill Book Co.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 237.
Schlichting, H. 1960 Boundary Layer Theory, 4th ed. New York: McGraw-Hill Book Co.
Spalding, D. B. 1954 Proc. Roy. Soc. A, 221, 78.
Spalding, D. B. 1960 J. Heat Mass Transf. 1, 192.
Spalding, D. B. 1961 J. Heat Mass Transf. 2, 15.
Spalding, D. B. & Evans, H. L. 1961 J. Heat Mass Transf. 2, 199, 314.
Stewart, W. E. & Prober, R. 1961 Paper submitted to J. Heat Mass. Transf.Google Scholar