## NUMERICAL SOLUTION OF UNSTEADY MHD PULSATING FLOW OF COUPLE STRESS FLUID THROUGH POROUS MEDIUM BETWEEN PERMEABLE BEDS USING DIFFERENTIAL QUADRATURE METHOD (DQM)

Published: 2015-10-31

Page: 8-28

I. M. ELDESOKY *

Department of Basic Engineering Sciences, Faculty of Engineering, Menofia University, Shebin El-Kom, Egypt.

M. H. KAMEL

Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Egypt.

E. R. EL-ZAHAR

Department of Basic Engineering Sciences, Faculty of Engineering, Menofia University, Shebin El-Kom, egypt and Department of Mathematics, Faculty of Science and Humanities, Prince Sattam University, KSA

R. M. ABUMANDOUR

Department of Basic Engineering Sciences, Faculty of Engineering, Menofia University, Shebin El-Kom, Egypt.

*Author to whom correspondence should be addressed.

### Abstract

Study of unsteady MHD pulsating flow of an incompressible Newtonian electrically conducting couple stress fluid through a porous medium between permeable beds under the influence of periodic body acceleration and slip condition has been made. The couple stress fluid is injected into the channel at the lower permeable bed with a certain velocity and is sucked from the upper permeable bed with the same velocity. The slip condition is taken into account and it plays an important role in shear skin, spurt, and hysteresis effects. The fluids that exhibit boundary slip have important technological applications such as in polishing valves of artificial heart and internal cavities. Numerical solutions of the governing equation of the motion are obtained using modified generalized differential quadrature method (MGDQM) by applying a generalized differential quadrature method (GDQM) to derivatives with respect to space variables and for the time derivative applying 4th order Runge-Kutta Method (RKM). This combination of DQM and 4th order RKM gives very good numerical technique for solving time dependent problems. The numerical results and the effects of the material parameters are presented and discussed through graphs.

Keywords: Pulsatile blood flow, couple stress fluid, MHD;, permeable beds, body acceleration, porous medium, generalized differential quadrature method, Runge-Kutta method

#### How to Cite

ELDESOKY, I. M., KAMEL, M. H., EL-ZAHAR, E. R., & ABUMANDOUR, R. M. (2015). NUMERICAL SOLUTION OF UNSTEADY MHD PULSATING FLOW OF COUPLE STRESS FLUID THROUGH POROUS MEDIUM BETWEEN PERMEABLE BEDS USING DIFFERENTIAL QUADRATURE METHOD (DQM). Asian Journal of Mathematics and Computer Research, 9(1), 8–28. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/124