Application of conformal mapping to viscous flow between moving circular cylinders
Author:
Lee A. Segel
Journal:
Quart. Appl. Math. 18 (1961), 335-353
MSC:
Primary 76.00; Secondary 82.00
DOI:
https://doi.org/10.1090/qam/120969
MathSciNet review:
120969
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Abstract: This work shows that conformal mapping provides an effective way to solve certain unsteady two-dimensional perturbation problems involving the flow of a viscous incompressible fluid, in particular flow between moving circular cylinders. If the outer cylinder is considered fixed, the principal motions treated are the slow rotation of a slightly eccentric inner cylinder, and the vibration of an inner cylinder about a slightly eccentric point. Mapping the given circular boundaries (of a cross-section) into concentric circles enables one to solve for the stream function by means of a series.
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G. Kirchoff, Pogg. Ann. 94 (1845), as in Ges. Abhandl. 1, Leipzig, 1882
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H. Martin, Über Tonhöhe und Dämpfung der Schwingungen von Saiten in verschiedenen Flüssigkeiten, Ann. Phys. (4) 77, 627-57 (1925)
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- Lee Aaron Segel, APPLICATIONS OF CONFORMAL MAPPING TO BOUNDARY PERTURBATION PROBLEMS, ProQuest LLC, Ann Arbor, MI, 1960. Thesis (Ph.D.)–Massachusetts Institute of Technology. MR 2939170
L. A. Segel, Application of conformal mapping to boundary perturbation problems for the membrane equation, to be published
G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums, Math, and Phys. Papers 3, The University Press, Cambridge, 1901, pp. 38-54
J. T. Stuart, Chap. VII of Laminar boundary layers, to be published by the Clarendon Press, Oxford, 1960/61
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E. Whittaker and G. Watson, Modern analysis, The University Press, Cambridge, 1952
J. Andres and U. Ingard, Acoustic streaming at low Reynold’s numbers, J. Acoust. Soc. Amer. 25, 932-8(1953)
S. Goldstein, Ed., Modern developments in fluid dynamics, Clarendon Press, Oxford, 1938
G. Kirchoff, Pogg. Ann. 94 (1845), as in Ges. Abhandl. 1, Leipzig, 1882
H. Kober, Dictionary of conformal representation, Dover, N. Y., 1952
C. C. Lin, On a perturbation theory based on the method of characteristics, J. Math. Phys. 33, 132-3 (1954)
H. Martin, Über Tonhöhe und Dämpfung der Schwingungen von Saiten in verschiedenen Flüssigkeiten, Ann. Phys. (4) 77, 627-57 (1925)
P. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill, N. Y., 1953
A. Nikitin, O dviženii vyazkoľ židkosti meždu ščipom i podšipnikom, (On the flow of a viscous fluid between pin and bearing), In ženernyľ Sbornik 23, 173-85 (1956)
L. A. Segel, Applications of conformal mapping to boundary perturbation problems, Ph.D. Thesis, M. I. T. Math. Dept., 1959
L. A. Segel, Application of conformal mapping to boundary perturbation problems for the membrane equation, to be published
G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums, Math, and Phys. Papers 3, The University Press, Cambridge, 1901, pp. 38-54
J. T. Stuart, Chap. VII of Laminar boundary layers, to be published by the Clarendon Press, Oxford, 1960/61
J. T. Stuart and L. Woodgate, Experimental determination of the aerodynamic damping on a vibrating circular cylinder, Phil. Mag. 46, 40-46 (1955)
W. Vinen, Detection of single quanta of circulation in rotating Helium II, Nature 181, 1524-5 (1958)
W. W. Wood, The asymptotic expansions at large Reynolds numbers for steady motion between non-coaxial rotating cylinders, J. Fluid Mechanics 3, 159-75 (1957)
E. Whittaker and G. Watson, Modern analysis, The University Press, Cambridge, 1952
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Article copyright:
© Copyright 1961
American Mathematical Society
