Pulsatile flow of a viscous fluid through a porous elastic vessel of variable cross-section—A mathematical model for haemodynamic flows

An oscillatory flow of a viscous incompressible fluid in a porous elastic vessel of variable cross-section has been investigated. The study pertains to a case where the motion is oscillatory, the shear rate is high, and the Reynolds number as well as the horizontal velocity gradient is small. Because of this, the method of linear approximation of the equations governing the flow has been employed in the analysis. The vessel wall is taken to be tethered, porous, thin, and elastic. The dissipation due to filtrate permeation through the membrane wall has been taken into account. The computational work presented at the last part of the paper has been performed for two different geometries of the wall, by considering the blood as a viscous fluid. On the basis of the theoretical investigation, it has been predicted that the geometry as well as the elasticity of the vessel wall contributes significantly to the velocity distribution in the small vessels and also that the magnitude of the radial velocity at any radial station is more than that in a uniform vessel.