International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2015): 6.391 Volume 6 Issue 12, December 2017 www.ijsr.net Licensed Under Creative Commons Attribution CC BY The Peristaltic Transport of MHD Powell - Eyring Fluid through Porous Medium in a Symmetric Channel with Slip Condition Hayat Ali 1 , Ahmed M. Abdulhadi 2 1 University of Bagdad, Department of Mathematic, Baghdad, Iraq 2 University of Bagdad, Department of Mathematic, Baghdad, Iraq Abstract: This paper is devoted to investigate the peristaltic flow of MHD Powell- Eyring model through porous medium during two dimensional symmetric channels. Slip conditions on the walls are taken into consideration. The basic governing equations; mass and momentum equations modeled with respect to wave frame. Solution technique to find the closed form solution for the resulted dimensionless differential equation is hold depending on long wavelength approximation and low Renold assumption. The influences of various involved parameters are illustrated via graphs in details. All the mathematical results are obtained by applying Mathematica 9 program. Keywords: Peristaltic Transport, Powell- Eyring Fluid, MHD Fluid, Porous Medium 1. Introduction The phenomenon in which the fluid transport as a contraction or expansion progressive waves along the length of a distensible tube is called peristalses. It can be recognized in physiological processes like chime movement in intestinal tract, blood flow in lymphatic, urine passage from kidney to the bladder, blood flow in small vessels. Also it is a key role in biomedical engineering, chemical processes, medical industry and locomotion of worm. The essential studies in this topic are done by Latham [1], and Shapiro et al.[2] through theoretical and experimental approaches. An important observation can be made from the aforementioned application that is the fluid used in these applications is non Newtonian fluids. Moreover non- Newtonian fluids as polymer melts, blood, fruit juices, ceramics, multigrade oil, and a lot others [3] can be characterize according to its own “constitutive equation” the relationship between the shear stress and the rate of deformation. Eyring –Powell model is considered as an advantageous model than the other non- Newtonian fluid model since it is deduced from kinetic theory of liquids not the empirical relation, also it correctly reduces to Newtonian behavior for low and high shear rates. For this purpose many researchers adopted the connection of peristaltic transport and Non-Newtonian fluid as a title for their works (see [4], [5], [6]). A magnetic field when applied to a moving conducting fluid it will induce electromagnetic field which produces a force named by Lorentz force opposite the fluid motion. In connection with peristaltic flow is based of applications and process like blood pumping machines, cancer therapy, biomedical engineering, industry, power generators, electrostatic precipitation, magnetic resonance imaging (MRI) for brain diagnosis, geophysics and many others. Attempted related the peristaltic flow under the effect of magnetic fluid in different situations consulted by the studies [4], [6]-[9]. On the other hand transport through porous medium is also helpful and applicable in different aspect such as geomechanics, biomechanics, industry filtration of fluids, seepage of water in river beds, functioning of human lung and others. These applications inspired numerous researchers to investigate the combine effect of porous medium and magnetic field on the fluid flows in various geometries and situations.(see [10],[11]). Slip conditions has a vital role in many applications rather than the no- slip condition like modern material industry (polymer industry) which given as a microscopic wall slip, engineering, medical application (polishing artificial heart), and technological process. Aforementioned application reported through studies discussed the influences of slip conditions on peristaltic flow of non- Newtonian fluids. Hina. [12] discussed the effect of heat and mass transfer on the peristaltic flow for MHD Eyring- Powell fluid taken into consideration slip condition. Hayat et al.[13] analyzed the effect of slip condition on peristaltic flow of Eyring- Powell fluid. Veerakrishna. et al. [9] detected the heat transfer on peristaltic flow of Williamson fluid model in an inclined symmetric channel with slip condition. Abbas et al.[7] investigate the simultaneous effect of slip and MHD on peristaltic blood flow of Jeffery fluid model in a non- uniform porous channel. Tanveer et al.[8] studies the influence of an inclined magnetic field on peristaltic transport of hyperbolic tangent nanofluid in inclined channel having flexible walls. The aim of this study is to investigate the combination effects of magnetic field and porous medium on peristaltic transient of Non-Newtonian fluid in a symmetric channel with slip condition depending on shear stress. The non- Newtonian fluid is obeying Powell- Eyring fluid model. The investigation is done by implementing the assumption of long wavelength and low Renold number. The flow's governing equation formulated by employing the wave frame. Closed expression for stream function, velocity axial and pressure gradient have been determined also numerical integration of pressure rise per unit wave obtained with help of series approximation. Finally graphical analysis has been done to figure out the effect of some interesting parameters involving in the above functions in details. Paper ID: 19121701 DOI: 10.21275/19121701 1509