Perturbation Analysis for Blood Flow in Stenosed Arteries under Body Acceleration

In this theoretical study, the pulsatile flow of a two-fluid model for blood in narrow arteries with mild stenosis under periodic body acceleration is analyzed. The suspension of all the erythrocytes in the core region is assumed as Herschel-Bulkley fluid and the plasma in the peripheral layer region is treated as Newtonian fluid. Perturbation method is used to solve the resulting system of nonlinear partial differential equations. The expressions for the physiologically important flow quantities such as velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of the parameters( body acceleration, depth of the stenosis, yield stress, width of the peripheral layer, pulsatility and lead angle) on these flow quantities are analyzed through appropriate graphs. It is observed that the plug core radius, wall shear stress and longitudinal impedance to flow increase with the increase of the yield stress, lead angle and stenosis depth. It is found that the velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and width of the peripheral layer thickness. It is also noted that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model than that of the single-fluid Herschel-Bulkley model. Also, it is noticed that the estimates of the mean flow rate and mean velocity increase significantly with the increase of body acceleration and peripheral layer.