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TECHNICAL BRIEFS

Exact Solution of the Navier-Stokes Equations for the Fully Developed, Pulsating Flow in a Rectangular Duct With a Constant Cross-Sectional Velocity

[+] Author and Article Information
S. Tsangaris, N. W. Vlachakis

Department of Mechanical Engineering, National Technical University of Athens, Fluids Section, 15710 Zografou, Athens, Greece

J. Fluids Eng 125(2), 382-385 (Mar 27, 2003) (4 pages) doi:10.1115/1.1537250 History: Received September 28, 2001; Revised September 24, 2002; Online March 27, 2003
Copyright © 2003 by ASME
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References

Dryden, H. L., and Murnaghan, F. D., and Bateman, H., 1956, Hydrodynamics, Dover, New York.
Berker, R., 1963, “Integration des Equations du Mouvement d’un Fluide Visqueux Incompressible,” Handbuch der Physik, VIII/2 , Springer-Verlag, Berlin, p. 70.
Drake,  D. G., 1965, “On the Flow in a Channel Due to a Periodic Pressure Gradient,” Q. J. Mech. Appl. Math., 18(1), pp. 1–10.
Fan,  C., and Chao,  B. T., 1965, “Unsteady, Laminar, Incompressible Flow Through Rectangular Ducts,” Z. Angew. Math. Phys., 16, pp. 351–360.
O’Brien,  V., 1975, “Pulsatile Fully Developed Flow in Rectangular Channels,” J. Franklin Inst., 300(3), pp. 225–230.
Bearman,  A. S., 1958, “Laminar Flow in an Annulus With Porous Walls,” J. Appl. Phys., 29(1), pp. 71–75.
Wang,  C. Y., 1971, “Pulsatile Flow in a Porous Channel,” ASME J. Appl. Mech., 38, pp. 553–555.

Figures

Grahic Jump Location
Iso-amplitude w̃a (left) and iso-phase angle φ (right) plots of the velocity in the cross section of a square duct (λ=1), for oscillating flow with a reduced frequency β=5 and for three different Reynolds numbers of the cross flow (Re=0,10,50)
Grahic Jump Location
Mean over the rectangular cross section amplitude w̄a (left) and phase angle θ (right) of the velocity as function of the cross flow Reynolds number R, for four different values of the aspect ratio (λ→0., λ=1, λ=2, λ→∞) and for the value of the reduced frequency M=10

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