Magnetohydrodynamic effects on peristaltic flow of hyperbolic tangent nanofluid with slip conditions and Joule heating in an inclined channel T. Hayat a,b , Maryam Shafique a , Anum Tanveer a,⇑ , A. Alsaedi b a Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan b Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia article info Article history: Received 7 April 2016 Received in revised form 24 May 2016 Accepted 24 May 2016 Keywords: Inclined magnetic field Thermal radiation Flexible channel walls Slip conditions Joule heating Hyperbolic tangent nanofluid abstract This investigation looks at the influence of an inclined magnetic field on peristaltic transport of hyper- bolic tangent nanofluid in inclined channel having flexible walls. Nanofluid consisting of Brownian motion and thermophoresis effects is employed in the definition of problem. Thermal radiation and Joule heating are present. Formulation is further completed by consideration of slip conditions in terms of velocity, temperature and concentration. Lubrication approach has been followed for the development of problem formulation. The key role of various involved parameters on the flow phenomenon are sketched. Slip effect causes the velocity and temperature to increase while reduces the concentration. Reduction in temperature is noticed with thermal radiation whereas temperature enhances for larger Hartman number in responce to the Joule heating effect. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction The mechanism by which contents of the food moves ahead under the influence of progressive wave of contraction and expan- sion is termed as peristalsis. In particular this activity involves mixing and pushing materials through contraction or expansion of the waves propagating along the channel walls. The phe- nomenon has key role in many physiological processes like urine transport from kidney to bladder through the ureter, transport of lymph in the vessels, swallowing food through the esophagus, the movement of chyme in the gastrointestinal tract, ovum move- ment in the fallopian tube, movement of spermatozoa in the cervi- cal canal and bile movement in a bile duct. This mechanism is also influential with reference to chemical processes and medical industry which covers heart lung machine, noxious fluid transport, roller and finger pumps, novel pharmacological delivery systems and locomotion of worms etc. An extensive information on the topic existed in literature after the work initiated by Latham [1] and Shapiro et al. [2] via theoretical and experimental approaches. Apart from their works latest studies in this area can be seen through the Refs. [3–8]. At present the mathematicians, modelers, computer scientists, engineers and physiologists seem to have interest in the research area of nanofluids related to peristaltic activity. Nanofluid is a tra- ditional liquid with nanosize particles. Utilization of nanofluids has become more important due to its involvement in surgery, vivo therapy, protein engineering, cancer diagnosis and therapy, drug delivery, neuro electronic interfaces, photodynamic therapy, non- porous materials for size exclusion chromatography, shedding new light on cells, molecular motors like kinesis and charge based filtration in the kidney basal membrane etc. Even some scientists thought of using nanofoods to trick the body into feeling fuller for longer thus stopping overeating. The word ‘‘nanofluid” was coined by Choi [9]. Thus under different assumptions the works on nanofluids have been progressed by many researchers (see Refs. [10–15] and the relevant studies therein). Also importance of nanofluids in peristalsis has not been ignored by the scientists which can be witnessed through research articles (see Refs. [16–19]). Further the idea of magnetohydrodynamics is remark- able in high temperature equipments such as power generators and in conductive physiological materials including the blood, blood pump machines, Magnetic Resonance Imaging (MRI), mag- netotherapy, hyperthermia, arterial flows and in the phenomenon of aviation used by an airplane’s compass where the influence of inclined magnetic field is found meaningful. Some useful studies in this area can be cited through Refs. [20–22]. Moreover the flex- ibility of the walls is essential for the case when gap between the channel boundaries is small. Thus Hayat et al. [23,24] explored MHD peristaltic transport of Jeffrey fluid in a symmetric and http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.05.105 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +92 51 90642172. E-mail address: anum@math.qau.edu.pk (A. Tanveer). International Journal of Heat and Mass Transfer 102 (2016) 54–63 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt