Stokes flow in a two-dimensional spatially periodic boundary driven by a combination of line singularities
Authors:
K. Ma and D. W. Pravica
Journal:
Quart. Appl. Math. 50 (1992), 743-757
MSC:
Primary 76D07
DOI:
https://doi.org/10.1090/qam/1193664
MathSciNet review:
MR1193664
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Abstract: The analytical solution is obtained for two-dimensional creeping flow generated by a source-sink combination located on a spatially periodic boundary. Separation is found to occur when the source and sink are located on concave regions of the boundary. The velocity profile of the two-dimensional Poiseuille flow for a channel is compared to that of the circle problem and the rough channel obtained from the analytical solution. It is found that the mid-channel velocity (or pressure gradient) of the rough case is greater (less) than that of the circle problem.
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N. Phan-Thien, C. J. Goh, and M. B. Bush, Viscous flow through a corrugated tube by boundary element method, Z. Angew. Math. Phys. 36, 475–480 (1985)
H. Tennekes and J. L. Lumley, A First Course in Turbulence, M.I.T. Press, Cambridge, MA, 1972
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M. Lessen and P. S. Huang, Poiseuille flow in a pipe with axially symmetric wavey walls, Physics Fluids 19, 945–950 (1976)
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E. G. Philips, Functions of a Complex Variable with Applications, Oliver and Boyd, Interscience Publishers Inc., 1958, p. 31
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A. C. Payatakes, Chi Tien, and R. M. Turian, A new model for granular porous media, A. I. Ch. E. J. 11, 58–76 (1973)
N. Phan-Thien, C. J. Goh, and M. B. Bush, Viscous flow through a corrugated tube by boundary element method, Z. Angew. Math. Phys. 36, 475–480 (1985)
H. Tennekes and J. L. Lumley, A First Course in Turbulence, M.I.T. Press, Cambridge, MA, 1972
N. Phan-Thien, On the Stokes flow of viscous fluids through corrugated pipes, A. S. M. E. J. Appl. Mech. 47, 961–963 (1980)
M. Lessen and P. S. Huang, Poiseuille flow in a pipe with axially symmetric wavey walls, Physics Fluids 19, 945–950 (1976)
A. M. J. Davis and K. B. Ranger, A model for Stokes flow through a stenotic channel, Phys. Fluids A 1, 193–198
D. E. R. Godfrey, Theoretical Elasticity and Plastics for Engineers, Thames and Hudson, London, 1959, pp. 58–59
E. G. Philips, Functions of a Complex Variable with Applications, Oliver and Boyd, Interscience Publishers Inc., 1958, p. 31
Lord Rayleigh, Scientific Papers, Vol. IV, Cambridge, 1900
K. B. Ranger and H. Brenner, A model for Stokes flow in a two-dimensional bifurcating channel, J. Fluid Mech. 152, 1–13 (1985)
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Article copyright:
© Copyright 1992
American Mathematical Society
