Approximation of the oscillatory blood flow using the Carreau viscosity model

Abstract

The analysis of non-Newtonian flows in tubes is very important when studying the blood flow in different types of arteries. Usually the blood viscosity is defined by shear-dependent models, for example by the Carreau model, which represents the viscosity as a non-linear function of the shear-rate. In this paper the unsteady (oscillatory) 2D model of the blood flow in a straight tube is discussed theoretically and numerically. The solution of the quasilinear parabolic equation for the velocity is constructed using appropriate analytical functions. Further the corresponding numerical solution is approximated by similar analytical functions.