Laminar Flow between Two Eccentric Tubes

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This Demonstration plots the contour lines of the dimensionless velocity of a fully developed laminar flow between two eccentric tubes. The dimensionless radius of the outer tube is 1. Using the sliders, you can specify the inner tube radius, eccentricity, the number of collocation points on the other radius, and the number of terms in the series solution.

Contributed by: Mikhail Dimitrov Mikhailov (March 2011)
Open content licensed under CC BY-NC-SA



Annular tubes are frequently used in double-pipe heat exchangers. The position of the internal tube has a big influence on the friction coefficient and heat transfer. White (1974) reported results about the annular channel developed by Piercy, Hooper and Winny (1933) on the basis of harmonic functions and conformal transformations. Sparrow, Loeffler, and Hubbard (1961) explored a hybrid method based on separation of variables and numerical collocation of one of the boundary conditions. This Demonstration explores similar methods to plot the velocity field of a fully developed laminar flow between two eccentric tubes.


N. A. V. Piercy, M. S. Hooper, and H. F. Winny, "Viscous Flow through Pipes with Cores," Phil. Mag., Series 7, 15, 1933 pp. 647-676.

E. M. Sparrow, A. L. Loeffler, and H. A. Hubbard, "Heat Transfer to Longitudinal Laminar Flow between Cylinders," J. Heat Transfer, 83, 1961 pp. 415-422.

F. M. White, Viscous Fluid Flow, New York: McGraw-Hill, Inc., 1974.

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