A parametric investigation of blood flow in a wedge with non‐uniform viscosity and wall friction

Abstract

The radial planar wedge pattern flow with friction and normalized non-uniform viscosity function will be discussed here. Solving this problem will be done using the flow theory equations for Newtonian and Non-Newtonian cases with non-uniform viscosity assumption. General differential equation that connects between the normalized velocity profile and the normalized viscosity has been derived analytically from the flow equations. It was found that for specific wedge semi angle, the radial assumption is no longer valid for the flow velocity. Moreover, it was found that for inlet/outlet conditions the normalized mean hydrostatic pressure for Newtonian fluid is dependent on the geometry, the normalized velocity and the viscosity functions. In addition, it was found that inertia phenomenon can be neglected for small wedge semi angle. A comparison between the axial and the hydrostatic pressure distributions for inlet/outlet conditions was performed for Newtonian and non-Newtonian flows. Finally, it was found that the axial pressure distribution profile was converged to the hydrostatic profile for critical wedge semi angle. K E Y W O R D Sblood flow, hydrostatic pressure difference, non-linear viscosity, non-Newtonian fluid, viscosity, wedge