چکیده (انگلیسی):

The paper deals with a problem related to the flow of blood in vessels. It is known that physiological pumps produce flow by alternate contraction and expansion of the vessel. When muscles start squeezing the vessel wall, the valve at the upstream end gets closed and that at the downstream end becomes open. As a result of this, blood is pumped out in the downstream direction. During systole, when the blood in the left ventricle is forced into the aorta, the mitral valve becomes closed, while the atrioventricular valve becomes open. In a situation such as this, the left ventricle takes the form of a vessel with one end closed. In order to study such a situation, a model has been developed here that consists of a fluid-filled long cylindrical pipe with one end closed by a compliant membrane (that prevents the axial motion of the fluid, leaving radial motion completely unrestricted). An approximate solution of the Navier–Stokes equation for the flow of a second-order
fluid is presented. The derived analytical expressions are computed numerically. The computed values indicate that if the Reynolds number of the flow is low, the effect of fluid viscoelasticity appears in higher-order terms.