A Mathematical Study on Three Layered Oscillatory Blood Flow Through Stenosed Arteries

A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube (stenosed arteries).The proposed model basically consists three layers of blood (viscous fluids with different viscosities) named as core layer (red blood cells),intermediate layer (platelets/white blood cells) and peripheral layer (plasma).The analysis was restricted to propagation of small-amplitude harmonic waves,generated due to blood flow whose wave length is larger compared to the radius of the arterial segment.The impacts of viscosity of fluid in peripheral layer and intermediate layer on the interfaces,average flow rate,mechanical efficiency,trapping and reflux are discussed with the help of numerical and computational results.This model is the generalized form of the preceding models.On the basis of present discussion,it is found that the size of intermediate and peripheral layers reduces in expanded region and enhances in contracted region with the increasing viscosity of fluid in peripheral layer,whereas,opposite effect is observed for viscosity of fluid in intermediate layer.Final conclusion is that the average flow rate and mechanical efficiency increase with the increasing viscosity of fluid in both layers,however,the effects of the viscosity of fluid in both layers on trapping and reflux are opposite to each other.