The primary goal of this study is to present a novel suggestion to uncover the characteristic features of the peristaltic flow of Eyring–Powell nanofluid through divergent and nondivergent channels. Several strategies are used to enhance the heat transfer capacity. Heat transport can be improved by increasing the thermal conductivity of the materials using nanoparticles. The implementation of a low Reynolds number and large wavelength hypothesis brings to reduce the system’s complexity. The resulting nonlinear coupled differential equation system is solved numerically by utilizing Mathematica symbolical software (ND-Solve). Various configurations of the outer boundaries are considered, namely, square wave, multi-sinusoidal wave, trapezoidal wave, and triangular wave. Under the effect of pertinent flow parameters, graphical illustrations of axial velocity, thermal, and concentration profiles have been portrayed. In tabular form, numerical outcomes for the rate of heat as well as mass transfers are displayed. One of the most significant phenomena concerning peristaltic motion, known as the trapping phenomenon, has also been spotlighted using contour plots and circulating bolus. The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multi-sinusoidal wave gives periodic behaviors of dp dx : It is noteworthy that Eyring–Powell fluid characteristics display a tendency to diminish the thermal resistance and axial velocity near the walls for divergent channels while an enhancement in velocity is observed at the region y 2 ½1, 1 as Eyring–Powell fluid parameter is altered. Further, for various kinds of divergent channels, the rate of heat transmission is enhanced due to an augmentation in Eyring–Powell fluid characteristics. Also, the present study uncovers that the parameters of the magnetic field and the Eyring–Powell fluid materials have a significant influence on the trapping phenomenon for both types of channels.