Study of Mathematical Models for Blood Flow Through Arterial Stenosis

Abstract

Study of Mathematical Models for Blood Flow Through Arterial Stenosis In this dissertation investigations are carried out for steady two-dimensional motion of an incompressible Newtonian and second grade fluid through the channel and tube. The hemodynamic behavior of blood flow is analyzed in the presence of an arterial stenosis. In the present study Cartesian and cylindrical coordinates are considered respectively for the flow in the channel and in an axisymmetric tube with heat transfer having stenosis of cosine shape. Length of stenosis is assumed to be large as compared to the semi width of the channel or the radius of the tube. The basic governing equations are the Navier-Stokes equations which are reduced to stream function formulation by using transformation. In the last two chapters blood is assumed to behave as an isothermal Oldroyd-B fluid through the channel and tube. By eliminating pressure gradient term form momentum equations, compatibility equation is obtained. The resulting compatibility and energy equations are highly nonlinear and solved analytically with the help of two methods namely the regular perturbation method (RPM) and the Adomian decomposition method (ADM). In case of regular perturbation method δ, which is the ratio of semi width of the channel or radius of the tube to the length of the channel or tube, is considered as a small parameter. The solutions thus obtained from the present analysis are represented in terms of streamlines, wall shear stress, zero wall shear stress, pressure gradient and temperature distribution on blood flow through stenosed channel and tube. Its worthy to mention that results presented in this dissertation are compared with already published results which ensures good agreement. It is found that wall shear stress, pressure gradient and temperature increases with the development of stenosis and causing separation and reattachment points in the region. It is found that even at low xiiivelocity separation is observed, if the thickness of the stenosis is increased. Detailed discussion and graphical representations are also provided.