The Navier-Stokes equations have been solved in order to obtain an analytical solution of the fully developed laminar flow in a duct having a rectangular cross section with two opposite equally porous walls. We obtained solutions both for the case of steady flow as well as for the case of oscillating pressure gradient flow. The pulsating flow is obtained by the superposition of the steady and oscillating pressure gradient solutions. The solution has applications for blood flow in fiber membranes used for the artificial kidney.
Exact Solution of the Navier-Stokes Equations for the Fully Developed, Pulsating Flow in a Rectangular Duct With a Constant Cross-Sectional Velocity1
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division Sept. 28, 2001; revised manuscript received Sept. 24, 2002. Associate Editor: I. Celik.
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Tsangaris , S., and Vlachakis , N. W. (March 27, 2003). "Exact Solution of the Navier-Stokes Equations for the Fully Developed, Pulsating Flow in a Rectangular Duct With a Constant Cross-Sectional Velocity." ASME. J. Fluids Eng. March 2003; 125(2): 382–385. https://doi.org/10.1115/1.1537250
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