A study on two-layered model (Casson–Newtonian) for blood flow through an arterial stenosis: Axially variable slip velocity at the wall

Abstract The present paper sheds some light on a mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall. The model consists of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma as a Newtonian fluid. For such models, in literature, the peripheral layer thickness and slip velocity are assumed a priori based on experimental observations. In the present analysis, new analytic expressions for the thickness of the peripheral layer, slip velocity and core viscosity have been obtained in terms of measurable quantities (flow rate ( Q ), centerline velocity ( U ), pressure gradient (− dp / dz ), plasma viscosity ( μ p ) and yield stress ( θ )). Using the experimental values of Q , U , (− dp / dz ), μ p and θ , the values of the peripheral layer thickness, core viscosity, and slip velocity at the wall have been computed. The theoretically obtained peripheral layer thickness has been compared with its experimental value. It is found that the agreement between the two is very good (error