Developing blood flow in the entrance region of an artery

Presented herein are the studies of the flow behaviour of blood in the entrance region of a segment of an artery. The artery has an axisymmetric mild stenosis developed right from the entry cross section. The blood has been represented by a Bhingham fluid model which also takes the core region, formed due to axial migration of the red blood cells, into account. The flow in the artery has been divided into two regions developing boundary layer and a central core region. A fourth degree velocity profile satisfying the boundary conditions at the wall and the matching conditions at the core and the boundary layer interface is introduced in the governing momentum integral equation. The indicated integration provides a relation for the boundary layer thickness for each axial position. The results for the pressure distribution, entrance length and the wall shear stresses are discussed for the various values of the parameters involved in the analysis. The analysis predicts that the entrance length increases as the stenosis grows and therefore the heart has to put in more energy into transporting blood. It seems that there is some inbuilt mechanism which keeps the entry region of every segment to a minimum in normal arteries at each junction. This length increases in pathological states leading to various types of hypertensive diseases due to the formation and growth of the stenosis.