The present analysis intends predominantly to explore the multiple behaviors of radiating ethylene glycol‐based titanium dioxide nanofluids during their steady boundary layer flows near a vertical permeable surface under the prominent impacts of uniform blowing and nonuniform internal heating processes. By incorporating the dynamical contribution of Lorentz and buoyancy forces in the momentum equation and adopting the single‐phase nanofluid approach along with the constitutive equations of the second‐grade rheological model and Corcione's correlations, the governing partial differential equations and their appropriate boundary conditions are derived mathematically based on the boundary layer theory and other admissible physical approximations. After several simplifications, the aforesaid differential formulation is converted into a set of ordinary differential equations and realistic boundary conditions, which are solved thereafter numerically using GDQ's‐NT method. Moreover, it is demonstrated that the strengthening in the blowing and internal heating processes has a boosting effect on the velocity and temperature profiles. However, the other influencing parameters show dissimilar dynamical and thermal trends. Furthermore, it is witnessed that the mixed convective heat transfer, the viscoelasticity trend of the nanofluidic medium, and the nanoparticles’ loading exhibit an enhancing impression on the surface heat transfer rate.