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The heat/mass transfer to a finite strip at small Péclet numbers

Published online by Cambridge University Press:  12 April 2006

R. C. Ackerberg ,
R. D. Patel  and
S. K. Gupta
R. C. Ackerberg
Affiliation:
Department of Chemical Engineering, Polytechnic Institute of New York, Brooklyn
R. D. Patel
Affiliation:
Department of Chemical Engineering, Polytechnic Institute of New York, Brooklyn
S. K. Gupta
Affiliation:
Department of Chemical Engineering, Polytechnic Institute of New York, Brooklyn
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Abstract

The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Péclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Péclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 1 , 15 May 1978 , pp. 49 - 65
Copyright
© 1978 Cambridge University Press

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References

Eisenberg, M., Tobias, C. W. & Wilke, C. R. 1954 Ionic mass transfer and concentration polarization at rotating electrodes. J. Electrochem. Soc. 101, 306.Google Scholar
Gordon, S. L., Newman, J. S. & Tobias, C. W. 1966 The role of ionic migration in electrolytic mass transport; diffusivities of [Fe(CN)6]3- and [Fe(CN)6]4- in KOH and NaOH solutions. Ber. Bunsenges. Phys. Chem. 70, 414.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Tables of Integrals, Series and Products. Academic Press.
Kaplun, S. 1957 Low Reynolds number flow past a circular cylinder. J. Math. Mech. 6, 595.Google Scholar
Lebedev, N. N. 1965 Special Functions and Their Applications. Dover.
Leveque, M. A. 1928 Transmission de chaleur par convection. Ann. Mines 13, 283.Google Scholar
Ling, S. C. 1963 Heat transfer from a small isothermal spanwise strip in an insulated boundary. J. Heat Transfer, Trans. A.S.M.E. C 85, 230.Google Scholar
Newman, J. 1973 The fundamental principles of current distribution and mass transport in electrochemical cells. In Electroanalytical Chemistry (ed. Allen J. Bard), vol. 6, p. 187. Marcel Dekker.
Patel, R. D., Mcfeeley, J. J. & Jolls, K. R. 1975 Wall mass transfer in laminar pulsatile flow in a tube. A.I.Ch.E. J. 21, 259.Google Scholar
Popov, D. A. 1975 Problems with discontinuous boundary conditions and the diffusion boundary-layer approximation. Prikl. Mat. Mekh. 39, 93 (English trans.).Google Scholar
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237.Google Scholar
Springer, S. G. 1974 The solution of heat transfer problems by the Wiener-Hopf technique. II. Trailing edge of a hot film. Proc. Roy. Soc. A 337, 395.Google Scholar
Springer, S. G. & Pedley, T. J. 1973 The solution of heat transfer problems by the Wiener–Hopf technique. I. Leading edge of a hot film. Proc. Roy. Soc. A 333, 347.Google Scholar