DOI 10.1140/epjp/i2013-13091-3 Regular Article Eur. Phys. J. Plus (2013) 128: 91 T HE EUROPEAN P HYSICAL JOURNAL PLUS Peristaltic flow of MHD Eyring-Powell fluid in a channel S. Noreen and M. Qasim a Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Shehzad Town, Islamabad 44000, Pakistan Received: 19 May 2013 / Revised: 17 July 2013 Published online: 16 August 2013 – c  Societ` a Italiana di Fisica / Springer-Verlag 2013 Abstract. Peristaltic transport of Eyring-Powell fluid is investigated in the presence of an induced magnetic field. The fluid is considered in a channel with non-conducting walls. Mathematical modelling is given subject to the long wavelength and low Reynolds number assumptions. The resulting non-linear system is solved for the stream function, pressure gradient, magnetic force function, induced magnetic field and current density distributions. The flow quantities have been examined for various parameters. The pressure rise per wavelength is also analyzed. 1 Introduction The peristaltic transport of a fluid in a channel/tube is an important problem in engineering and physiology. Such a problem is encountered in the chyme movement in the gastrointestinal tract, the passage of urine from kidney to the bladder, the ovum movement in the female Fallopian tubes, blood circulation in vessels, sanitary fluid transport etc. Latham [1] and Shapiro et al. [2] initiated the analysis of peristaltic flow in a viscous fluid. Afterwards the peristaltic phenomenon is studied extensively via experimental and theoretical investigations. Theoretical investigations have been carried out after using one or more assumptions of long wavelength, low Reynolds number, small amplitude ratio or occlusion etc. A few studies in this direction may be mentioned by the refs. [3–14]. It is a known fact that, because of the complexity of fluids, there is no single constitutive equation available in the literature by which one can describe all the effects of non-Newtonian fluids. Mathematical systems for non-Newtonian fluids are of higher order and complicated in comparison to the Newtonian fluids [15,16] and generally, one needs additional boundary/initial conditions to determine the unique solution. In spite of all these challenges, the recent researchers in the field are making valuable contributions in non-Newtonian fluid mechanics [17–27]. The dynamics of biological fluids in the presence of a magnetic field is significant in bioengineering and medical sciences. Some applications include the development of magnetic devices for cell separation, targeted transport of drugs using magnetic particles as drug carriers, cancer tumor treatment, reduction of bleeding during surgeries or provocation of occlusion of the feeding vessels of cancer tumors and MRI. Although some previous studies on peristalsis including Couple stress, Carreau, fourth grade, third order, pseudoplastic, micropolar fluids incorporate the induced magnetic field effects [20– 27], such an analysis for the Eyring-Powell fluid [28–33] has not been investigated so far. The consideration of the Eyring-Powell fluid (although mathematically very complex) is preferred due to two reasons. Firstly, it is deduced from the kinetic theory of gases which is different from the empirical relation in a power law fluid. Secondly, it correctly reduces to the Newtonian behavior for low and high shear rates for otherwise pseudoplastic systems, whereas the power law model indicates an infinite effective viscosity for low shear rate, thus limiting its range of applicability. With such motivation, the induced magnetic field effects on the peristaltic flow in a symmetric channel is explored. The resulting mathematical problem have been solved by a perturbation approach when the long wavelength and small Reynolds number assumption hold. Solution expressions are derived and due attention is given to the pressure rise per wavelength through numerical integration. Graphs of the desired flow quantities are plotted and discussed in order to explore the effects of different emerging parameters entering into the present problem. The paper is arranged as follows: Section 2 includes the governing equations and mathematical modelling of the problem under consideration. In sect. 3 the perturbation solution of the problem is obtained. Section 4 comprises the discussion of obtained results. Finally, concluding remarks are given in sect. 5. a e-mail: mq qau@yahoo.com; mqasim@comsats.edu.pk