Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

Abstract

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method (Hybrid-MsDTM) and the Crank-Nicholson method (CNM) are used to solve the partial differential equation (PDE), and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when Ag increases.