Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction

Numerical solution of the unsteady viscous flow in the neighborhood of an overlapping constriction is obtained under laminar flow conditions with the motivation for modeling blood flow through a local occlusion of artery formed due to arterial disease. The flowing blood is considered to be incompressible, Newtonian with variable blood viscosity. The functional dependence of blood viscosity on haematocrit (percentage volume of red cells) has been duly accounted for in order to improve resemblance to the real situation. The finite-difference technique with staggered grid distribution is employed to solve the governing equations. The recirculation regions are formed in the downstream of the overlapping constriction. It is noticed that the arterial wall shear stress, pressure distribution and flow rate in particular, in the constricted site, are significantly altered. The peak value of wall shear stress decrease with increasing haematocrit parameter. The flow separation region increases with increasing haematocrit parameter. The results are presented graphically and analyzed in detail to study the effects of variable blood viscosity on the flow field. The motion of the arterial wall and its effects on local flow dynamics are considered. The contribution of deformability of the arterial wall is to reduce the wall shear stress in comparison to the consideration of rigid wall. Arterial wall motion causes to diminish the wall shear stress significantly.