Exact Solution of the Navier-Stokes Equations for the Fully Developed, Pulsating Flow in a Rectangular Duct With a Constant Cross-Sectional Velocity1

Abstract

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.