Exploring the movement of blood in a blood vessel has been fascinated by clinicians and biomedical researchers because it is predominant in cell tissue engineering, drug targeting and various treatments like hypothermia, hyperthermia, and cancer. It is noticed that numerous non-Newtonian rheological fluids like Carreau fluid, tangent hyperbolic fluid, Eyring–Powell fluid and viscoelastic fluid manifest the characteristics of blood flow. Further, the investigation of entropy generation can be used to raise the performance of medical equipments. Consequently, the present mathematical model scrutinizes the transport characteristics and entropy generation of the peristaltic Eyring–Powell nanofluid in a permeable vertical divergent channel in the presence of dissipation and linear radiation. The non-similar variables are employed to convert the dimensional partial differential equations into dimensionless form which are tackled by the Homotopy perturbation method. The impacts of emerging parameters like Eyring–Powell parameters, left and right wall amplitudes, thermophoresis, mean flow rate, radiation, permeability parameter, Brownian motion, Eckert number, Hartman number on Eyring–Powell nanofluid axial velocity, temperature, and concentration are manifested. Present results disclose that the thermal Grashof number highly inflates the pressure rise. Eyring–Powell nanofluid temperature reduces for uplifting the linear radiation parameter. Growing values of the non-uniform parameter lead to move the trapping bolus towards the left and right wall. The total entropy generation diminishes for magnifying the temperature difference parameter. © IMechE 2021.