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The peristaltic phenomenon has intended the researcher’s attention due to its extensive applications in bio-mechanics, industries and biological sciences. The applications of peristaltic transport problems are observed in the transportation of cilia, food mixing in digestive tract, small blood vessels vasomtion, urine transportation etc. Following to such motivating applications in minds, this theoretical analysis presents the peristaltic flow of magnetized Jeffery fluid through accounted by curved channel in presence of heat transfer. The assumed flow is confined by different wave frames. The heat transfer inspection has been performed by utilizing the non-linear thermal radiation and joule heating features. The curvilinear coordinate system is used to model the two dimensional, laminar and incompressible Jeffrey fluid with peristaltic phenomenon. The partial differential equations are transformed into ordinary differential equations in view of appropriate quantities. The implementation of wave length with long magnitude and the assumptions of smaller Reynolds assumptions, the governing system of ordinary system is solved numerically by using shooting technique. The dynamic of involved quantities and physical variables is observed carefully. A declining observation in the temperature in all forms of waves has been noticed for increasing the viscoelastic parameter. The heat transfer coefficient for all waves enhanced for the radius of curvature. Moreover, the velocity of the fluid declines in the lower half of the channel and rises near upper wall of the curved channel due to magnetic parameter.

In this paper peristaltic motion of an Oldroyd-4 constant nanofluid under the influence of Buoyancy forces is taken into account. The Buongiorno model is utilized to see the effects of Brownian motion and thermophoresis on the different features of the flow, heat transfer and concentration. In order to facilitate the solution of modeled equations first the governing equations are transformed to system of ordinary differential equations under the assumption of long wavelength and low Reynolds number. The resulting equations are solved using shooting method along with fourth order R. K. method. It is observed that the amplitude of heat flux rises and effective moment of nanoparticles from wall to the center line of the channel which enhance the thermal conductivity at the wall. This is due to the increase in the kinetic energy and Brownian motion. The effects of different parameters are illustrated through graphs and tabulated data is given to compare the effects of shear stress on walls of the channel with Newtonian fluids.