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Mass transfer from small capillaries with wall resistance in the laminar flow regime

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Abstract

The Graetz problem in heat transfer is extended to the analysis of mass transfer in circular ducts for the cases where wall resistance is included and where non-Newtonian fluids that obey Casson's equation are considered. The eigenvalues and fluid bulk coefficients are presented for the fluid between the extremes of Newtonian and slug flow. It is found that for fluids which are only slightly non-Newtonian, such as blood, which is closely approximated by Casson's equation, the mass transfer rate can be predicted by Newtonian fluid analysis without appreciable error. Some experimental results give support to the theory.

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Abbreviations

A :

constant

c :

concentration

D :

capillary diameter

h :

mass transfer coefficient

p :

pressure

Pe :

U m D/D, Péclet number

P :

wall permeability

r :

radius

Sh ξ :

local Sherwood number, 1/2hD/D

Sh o :

overall Sherwood number, 1/2h 0 D/D

Sh w :

wall Sherwood number, 1/2PD/D

u :

velocity

U m :

average velocity

x :

length

D :

diffusivity

τ :

shear stress

η :

viscosity coefficient in Casson's equation

d:

outside

m:

mean

o:

overall

in:

inlet

References

  1. Sideman, S., D. Luss, and R. E. Peck, Appl. Sci. Res. A 14 (1954) 157.

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  2. Hamming, R. W., Numerical Methods for Scientists and Engineers, pp. 183–222, McGraw-Hill, New York 1962.

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  3. Copley, A. L. and G. Stainsby (edit.), Flow Properties of Blood and Other Biological Systems, (Proceedings of Discussion), Pergamon, Oxford 1960.

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  4. Wolf Jr., L. and S. Zaltzman, Optimum Geometry for Artificial Kidney Dialyzers, Chem. Eng. Progr. Symp. Ser. 84 (1968), Vol. 64.

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, University of British Columbia, Vancouver, Canada

    H. R. Davis & G. V. Parkinson

Authors
  1. H. R. Davis
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  2. G. V. Parkinson
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Davis, H.R., Parkinson, G.V. Mass transfer from small capillaries with wall resistance in the laminar flow regime. Appl. Sci. Res. 22, 20–30 (1970). https://doi.org/10.1007/BF00400512

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  • DOI: https://doi.org/10.1007/BF00400512

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