Unsteady Analysis of Viscoelastic Blood Flow through Arterial Stenosis

A mathematical model of unsteady non-Newtonian blood flow in an artery under stenotic condition has been developed. The flowing blood is considered to be a viscoelastic fluid characterized by the Oldroyd-B model and the arterial wall is considered to be rigid, having cosine-shaped stenosis. The governing equations of motion accompanied by appropriate choice of the initial and boundary conditions are solved numerically by the MAC (marker and cell) method, and the results are checked, for numerical stability with desired degree of accuracy. The key factors like the wall shear stress, resistive impedance, and the other viscoelastic parameters are also examined for further qualitative insight into the flow through arterial stenosis. Comparison of the results reveals that dimensionless pressure drop for the viscoelastic model increases while it diminishes for the shear-thinning power law model over that of the Newtonian model. Moreover, the possibility of flow separation increases with increasing relaxation time (Deborah number), and in case of Newtonian fluid, delayed separation is observed. The grid independence study has also been performed successfully in order to validate the applicability of the methodology as well as the model used under consideration. Special emphasis has duly been made to compare the present theoretical results with the existing ones, and good agreement between them has been achieved both qualitatively and quantitatively.