1 3 J Braz. Soc. Mech. Sci. Eng. (2016) 38:703–708 DOI 10.1007/s40430-015-0404-7 TECHNICAL PAPER Effect of periodic body acceleration and pulsatile pressure gradient pressure on non-Newtonian blood flow in arteries S. Mosayebidorcheh 1 · M. Hatami 2 · T. Mosayebidorcheh 1 · D. D. Ganji 3 Received: 2 May 2014 / Accepted: 23 July 2015 / Published online: 26 August 2015 © The Brazilian Society of Mechanical Sciences and Engineering 2015 1 Introduction Non-Newtonian fluids have many applications, espe- cially in biomedical science. Blood can be assumed to be a non-Newtonian fluid. The physical properties of blood are presented by some researchers, e.g., Baieth [1]. Blood which is composed of plasma, red and white blood cells, platelets, etc., can be considered as one of the most important multi-component mixtures occurring in nature. Ogulu and Amos [2] modeled the pulsatile blood flow in the cardiovascular system employing the Navier–Stokes equation and found an increase in the wall shear stress when the porosity of the medium was increased. In an experimental study, Praveen Kumar et al. [3] investigated the effect of gold nanoparticles on blood from a biomedi- cal viewpoint which can be used in drug delivery appli- cations. Recently, Hatami et al. [4] studied third-grade non-Newtonian blood conveying gold nanoparticles in a porous and hollow vessel by two analytical methods called least squares method and Galerkin method. They considered the temperature dependency for blood by Vogel’s model and investigated the effect of Brownian motion and magneto-hydrodynamics on nanoparticles in the blood flow. Moyers-Gonzalez et al. [5] on the mod- eling of oscillatory blood flow in a tube, observed that as the frequency of the (constant amplitude) pressure gradi- ent oscillations increases, the peak values of the velocity field and shear stress decrease. The characteristics of flow and heat transfer of the sec- ond-grade viscoelastic electrically conducting blood in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated by Misra et al. [6]. Massoudi and Phuoc [7] modeled blood as a modified second-grade fluid where the viscosity and the normal stress coefficients depend on the shear rate. They Abstract In this paper, flow analysis for a non-Newto- nian third-grade fluid in coronary and femoral arteries is simulated numerically. The fluid is considered as a third- grade non-Newtonian fluid under periodic body accelera- tion motion and pulsatile pressure gradient. DuFort–Fran- kel and Crank–Nicholson methods are used to solve the PDE of the governing equation and a good agreement between them was observed in the results. The influences of some physical parameters such as amplitude, lead angle and body acceleration frequency on velocity and shear stress profiles are considered. For instance, the results show that increasing the amplitude and reducing the lead angle of body acceleration, make higher velocity profiles in the center line of both arteries. Also, the maximum wall shear stress increases when the amplitude increases. Keywords Third-grade non-Newtonian fluid · Crank– Nicholson method · DuFort–Frankel method · Femoral artery · Coronary artery Communicated by Marcos Pinotti. * S. Mosayebidorcheh sobhan_phd@yahoo.com 1 Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, Iran 2 Mechanical Engineering Department, Engineering and Technical College, Esfarayen University of Technology, Esfarayen, North Khorasan, Iran 3 Department of Mechanical Engineering, Babol University of Technology, Babol, Iran