The dynamics of Jeffrey nanofluids over an elongated surface heated by convection are addressed adequately under the nonlinear Boussinesq’s sense. Novel attributes of exponential heat source and thermal radiation are included. Buongiorno’s revised nanoliquid model is implemented to study the uneven dispersion and thermophoresis of nanoparticles subjected to passive control of nanoparticles on the surface. Wall suction or injection effects are also considered. Mathematical modeling is developed and treated numerically using the similarity approach. The results are presented considering numerous values of the physical parameters. Stimulus variables that regulate the resulting dimensionless physical quantities are examined graphically. Nonlinear convection has occurred to reinforce the nanofluid motion and reduce the thermal boundary layer thickness. The results of this study are useful in polymer industries.