In this research, a theoretical investigation into the heat transport characteristics of an Eyring–Powell nanomaterial boundary layer flow on a wedge surface with passively controlled nanoparticles is carried out. In this model, thermal convective boundary conditions, thermal radiation, heat production, and absorption are also studied. The non-Newtonian Eyring–Powell fluid’s features are predicted using the model under consideration. The Buongiorno model is used to study how a temperature gradient affects thermophoresis and how nanoparticles affect the Brownian motion. The prevailing nonlinear boundary layer equations are derived and then renewed in an ordinary differential boundary value problem (ODBVP) by substituting apt similarity transformations. The acquired nonlinear ODBVP is then resolved using the bvp4c method to explore the fields of nanofluid velocity, nanofluid temperature, and nanoparticle concentration. A mathematical examination of the surface drag force coefficients and Nusselt number is carried out using various physical parameters. The Eyring–Powell fluid parameter (K1) reduces the thickness of the momentum boundary layer thickness. The thermophoresis aspect (Nt) enhances the thermal field and solutal field. The Nusselt number (NuRex−0.5) reduces the need for a stronger internal heat source mechanism.