Fluid movement in a channel of varying gap with permeable walls covered by porous media

Abstract

Blood flow in arteries idealized into a channel of varying gap bounded by porous layer is studied. Analytical solutions are obtained using Beavers and Joseph slip condition by three approximate methods depending upon the geometrical configuration. The general solutions are applied to a particular problem of smooth constriction idealized into an artery with stenosis. The resistance of the porous layer to the flow in the channel and the shear stress at the nominal surface are discussed in detail. It is shown that for a given porous layer, depending on the value of the porous parameter α σ₀, this may lead to an increase or decrease in the resistance and the shear stress may be used in evaluating the performance of various prosthetic devices which ultimately may be implanted in the living system.