Abstract—The unsteady pulsatile flow of blood through porous medium has been studied under the influence of periodic body acceleration by considering blood as incompressible Newtonian electrically conducting fluid in the presence of magnetic field. A numerical solution of the equation of motion is obtained by applying a generalized differential quadrature method (GDQM), to derivatives with respect to space variables of differential equations and for the time derivative applying 4th order Runge Kutta Method. This combination of DQM and 4th order RK method gives very good numerical technique for solving time dependent problems. The algorithm is coded in Matlab 184.108.40.2069 and the simulations are run on a Pentium 4 CPU 900 MHz with 1 GB memory capacity. The numerical results show and discussed with the help graphs. The study show that the axial velocity of the blood increases with increasing the permeability parameter of porous medium and the Womersley parameter, and decreases with increasing the Hartmann number. The study is useful for evaluating the role of porosity when the body is subjected to magnetic resonance imaging (MRI).
Index Terms—Pulsatile blood flow magnetic field, body acceleration, porous medium, differential quadrature method, runge-kutta method.
I. M. Eldesoky and Ramzy M. Abumandour are with the Basic Engineering Science Department, Faculty of Engineering, Menofia University, Shebin El-Kom, Egypt. (e-mail: email@example.com)
M. H. Kamel is with the Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Egypt.
Reda M. Hussien is with the Information system department, faculty of Computers and Information, Menofia University, Shebin El-Kom, Egypt.
Cite:I. M. Eldesoky, M. H. Kamel, Reda M. Hussien, and Ramzy M. Abumandour, "Numerical Study of Unsteady MHD Pulsatile Flow through Porous Medium in an Artery Using Generalized Differential Quadrature Method (GDQM)," International Journal of Materials, Mechanics and Manufacturing vol. 1, no. 2, pp. 200-206, 2013.