The primary focus behind this research work is to unfold the characteristics of peristaltic transport of Eyring–Powell fluid through uniform/non-uniform channel. Consideration of wall flexibility as well as Joule heating is one of the key factors of this investigation. Implementation of small Reynolds number and large wavelength concepts leads to a reduction in the complexity of the system. The governing two-dimensional coupled differential equations are simplified after incorporating dimen- sionless variables. Graphical demonstrations for velocity, temperature, concentration profiles have been sketched out under the influence of pertinent flow parameters. Numerical values for the rate of mass as well as heat transfers are presented in tabular form. One of the most important occurrence regarding peristaltic movement namely trapping phenomenon has also been highlighted by means of circulating bolus through contour plots. Noteworthy findings are that for both uniform and non-uniform channels, Eyring–Powell fluid parameters exhibit a tendency to reduce the fluid velocity as well as the temperature of the fluid. Apart from this, another significant observation is that higher values of both velocity and temperature fields are observed in non-uniform channel as compared to uniform channel. Rate of heat transfer is enhanced due to an increment in Eyring–Powell fluid parameters for different types of non-uniform channels. Also for both the kind of channels, the cur- rent study explores that magnetic parameter and Eyring–Powell fluid parameter show a prominent impact on the trapping phenomenon. • Peristaltic transport of Eyring–Powell fluid through uniform/non-uniform channel. • Behaviours of wall flexibility as well as Joule heating are taken into consideration. • Rate of heat transfer is enhanced due to an increment in Eyring–Powell fluid parameters for different types of non-uniform channels. • The results are well described by graphically and tables.
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