**1. Introduction**

The peristaltic motion induced by channel or tube boundaries has a main role of fluid transport in living organisms and industrial pumping. Additionally, it has attracted attention in the fields of engineering and physiology. This transport is a means of fluid flow in an elastic path by the processes of contraction and expansion. In particular, such flows of viscous and non-Newtonian fluids are widely familiar in several biological systems including the human body in the transport of urine from the kidney to the bladder; chyme movement in the gastrointestinal tract, bile ducts, ureter, esophagus; spermatozoa in ducts efferent of the male reproductive tract; blood circulation in blood vessels; and movement of ovum in female fallopian tubes. Technical roller and finger pumps also function under this type of mechanism. In addition, with the existing of heat transfer, peristalsis is imperative in many processes such as oxygenation and hemodialysis. Further, heat transfer is also noteworthy in the treatment of diseased tissues in cancer. The cram of magnetohy drodynamic (MHD) peristaltic flow is useful as it is used in the reduction of bleeding during surgeries, targeted transfer of drugs via magnetic particles as drug carries, and MRI (magnetic resonance imaging) to diagnose diseases. It also has a pivotal role in the motion of physiological fluids including blood and blood pump machines. Furthermore, mass transfer in peristaltic flow occurs during the chemical breakdown of food, amalgamation of gastric juices with food, diffusive and ionic flows by means of membrane channels, diffusive oxygen transmission in tissue, drug delivery inside the body, and in other digestion processes.

There area lot of models for non-Newtonian fluids due to the complexity of fluids behaviour, like Carreau [1–3], Herschel [4,5], Oldroyd [6,7], Williamson [8], Johnson [9–11], Casson [12], Couette [13] and further as in [14–21]. Amongst these, the Jeffrey fluid model is considered as the simplest linear model that presents non-Newtonian fluid properties in a way which may enable the researchers to attain exact and analytical solutions. See, for example [22–25]. Kothandapani and Srinivas [26] have investigated peristaltic transport for Jeffrey fluid under consequences of a magnetic field in an asymmetric channel under the premise of a low Reynolds number and a long wavelength. Tripathi et al. [27] studied MHD peristaltic flow of Jeffrey fluid by means of a finite length cylindrical tube. Further, Nadeem et al. [28] examined the peristaltic flow of MHD Jeffrey fluid in eccentric cylinders. Khan et al. [29] investigated peristaltic transport for Jeffrey fluid with variable viscosity via a porous medium in an asymmetric channel. Srinivas and Pushparaj [30] have presented non-linear peristaltic flow in an inclined asymmetric channel.

In 1827, Navier [31] stated that shear stress at surface is linearly proportional to slip at surface. Fluids revealing slip effects are vital in polishing internal cavities and artificial heart valves. In particular, the application of this condition in peristaltic flows has perfect relevance in the field of polymers and physiology. Studies towards this point of research have been recently taken into account and a wide range of analytical and numerical studies have been reported in [32,33] and [34]. In a porous channel, effects of wall slip conditions and heat transfer on peristaltic transport of MHD Newtonian fluid with elastic wall properties have been discussed by Sirinivas et al. [35]. Hayat et al. [36] introduced a mathematical model in order to study the slip effects of heat and mass transfer on peristaltic transport of MHD power-law fluid and second grade fluid in the channel by flexible walls. Further, Hayat et al. [37] and [38] examined the influence of slip conditions and wall properties in the planar channel on MHD peristaltic flow of Maxwell fluid, and Williamson fluid in the non-uniform channel by heat and mass transfer, respectively. Nadeem and Akram [39] presented effects of partial slip on peristaltic flow of MHD Newtonian fluid in an asymmetric channel. They obtained the solutions using the method of Adomian decomposition and showed that trapping reduces with an increase of the velocity slip parameter, while pressure rise increases with an increase in the slip parameter. Hayat et al. [40,41] have analyzed effects of the slip condition on peristaltic flow of Phan-Thien-Tanner and of an Oldroyd 6-constant fluid, respectively. Mishra and Rao [42] investigated the effects of peristaltic flow of Newtonian fluid in an asymmetric channel. Akram and Nadeem [43] studied consequences with different waveforms of partial slip and nanofluid on peristaltic transport of non-Newtonian fluid. Recently, Hina et al. [44] investigated the peristaltic flow of pseudoplastic fluid with wall properties in a curved channel by heat or mass transfer.

In their important study, Ro¸sca and Pop [45] showed that the second order slip flow model is essential to predict flow characteristics precisely. Very recently, Aly [46,47] and Aly and Vajravelu [48] have studied the effect of second velocity slip on fluid flow. In these studies, it was reported that these type of boundary conditions is compulsory and should be taken into consideration, otherwise, false results will be gained. As mentioned above, there are a considerable number of published papers regarding the effect of the first slip parameter, however, very less consideration has been given to peristaltic flows in the presence of the velocity second slip condition. Recently, Aly and Ebaid [49] presented an exact solution for the outcome of second slip on peristaltic flow of nanofluid in an asymmetric channel.

The intent of the current study is, therefore, to examine the effect of velocity second slip in non-Newtonian fluids by heat and mass transfer in the presence of an inclined magnetic field over an inclined tapered asymmetric channel, as many researchers have recently givenconsiderable attention to this geometry, for example [50–52]. As per our knowledge, no effort has been reported yet to discuss this multidimensional analysis, even in the absence of heat and mass transfer; hence, this study may be helpful in this direction of research. The present governing equations for motion, concentration and energy are simplified by assumptions of long wavelength approximation. Then, exact solutions

of reduced equations are outlines. Therefore, with help of Mathematica software, many graphical outcomes are plotted and reported for various involved physical parameters of interest.
