Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2019) 41:483 https://doi.org/10.1007/s40430-019-1993-3 TECHNICAL PAPER Rheological and magnetic efects on a fuid fow in a curved channel with diferent peristaltic wave profles Khurram Javid 1  · Nasir Ali 2  · Zeeshan Asghar 3 Received: 29 March 2019 / Accepted: 1 October 2019 © The Brazilian Society of Mechanical Sciences and Engineering 2019 Abstract Peristalsis is one of the most dynamic phenomena that is signifcantly applicable to biomedical engineering. Motivated by such fact, the current article deals with the numerical simulation of magnetically induced fuid fow bounded within two curved peristaltic walls. Fluid rheology is approximated by linearly viscoelastic Jefrey fuid, while fve diferent wave profles are utilized to capture the peristaltic efects. A constant magnetic feld is also applied in the radial direction. The constitutive equations in curvilinear coordinates are reduced under the lubrication theory. The reduced boundary value problem is further solved by MATLAB built-in routine BVP6C. The axial velocity, pressure rise and stream function are numerically obtained in the wave frame. The impacts of diferent peristaltic wave profles and several embedded parameters, for example, the dimensionless radius of curvature, magnetic parameter (Hartmann number) and viscoelastic parameter, respectively, on the fow characteristics are shown through graphs and discussed in detail. Boundary layer phenomena are also highlighted for large values of the Hartmann number and the ratio of relaxation to retardation time parameter for diferent peristaltic waves. A special case of the straight channel is also retrieved from a large curvature parameter. This study provides fruitful informa- tion to understand the fow phenomena of blood, foods, nutrients and liquids that pass through non-uniform veins or arteries. Keywords Peristaltic waves · Radial magnetic feld · Boundary layer phenomena · Hartmann number 1 Introduction Most of the realistic fuids are non-Newtonian in nature, and it is difcult to describe the fow behavior of such fuids with Navier–Stokes equations. Non-Newtonian viscoelastic fuid (like Jefrey fuid) also exhibits the characteristics of viscosity as well as elasticity. It is much complicated to pre- dict the behavior of these fuids because of their complex and nonlinearity natures [1]. These fuids fow under certain stresses applied via diferent agents. One of such sources of fuid fow is peristalsis, in which fuid is pushed backward/forward by means of progressive waves. The applications of the peristaltic phenomenon in engineering and industrial domains are vital. Such fows also play an imperative role in the mining industry for handling the muds and slurries and in the applications of biomedical fows. MHD (magnetohydrodynamics) is a branch of fluid dynamics, which deals with the study of magnetic feld and behavior of electrically conducting fuids, for example, plasma, electrolytes and liquid water [2]. Alfven (frstly) discovered this feld and won a Nobel Prize in 1970 for his wonderful achievements. Over the past few decades, these magnetically driven fows gain the attention of many researchers due to their wide range of applications in numer- ous felds like medical science [3], engineering and indus- trial domains [4] and nuclear power reactor [5]. The usage of MHD in magnetic swimming devices (for surgical purposes) and MRI (Magnetic Resonance Imaging) is also worthwhile to mention. Coming toward the peristaltic phenomenon, Latham [6] was the frst one to discuss the peristaltic pumping Technical Editor: Edson José Soares, PhD. * Zeeshan Asghar zeeshanasghar@nutech.edu.pk; zee.qau5@gmail.com 1 Department of Mathematics, Northern University, Nowshera, KPK 24100, Pakistan 2 Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan 3 NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad 44000, Pakistan