Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

Abstract

Stenosis, the abnormal narrowing of artery, significantly affects dynamics of blood flow due to increasing resistance to flow of blood. Velocity of blood flow, arterial pressure distribution, wall shear stress and resistance impedance factors are altered at different degree of stenosis. Prior knowledge of flow parameters such as velocity, flow rate, pressure drop in diseased artery is acknowledged to be crucial for preventive and curative medical intervention. The present paper develops the solution of Navier–Stokes equations for conservation of mass and momentum for axis-symmetric steady state case considering constitutive relation for Reiner–Rivlin fluid. Reiner–Rivlin constitutive relation renders the conservation equations non-linear partial differential equations. Few semi-analytical and numerical solutions are found to be reported in literature but no analytical solution. This has motivated the present research to obtain a closed-form solution considering Reiner–Rivlin constitutive relation. Solution yields an expression for axial velocity, which is utilized to obtain pressure gradient, resistance impedance and wall shear stress by considering volumetric flow rate as initial condition. The effect of viscosity, cross viscosity, flow rate, taper angle of artery and degree of stenosis on axial velocity, resistance impedance and wall shear stress are studied.