<p>In this investigation, the significance of Hall and ion-slip impacts on the transient hydromagnetic convective flow of Titanium oxide-engine oil (TiO₂-EO) second-grade nanofluid over a permeable vertically oriented surface has been explored. The considered convective flow originated due to the buoyancy action, rotatory fluid action, and oscillatory free-stream motion. The tractable mathematical model of the fluid flow problem is derived using the constitutive and magnetic field equations under the boundary layer approximation. An analytical convergent solution of the derived model has been analyzed with a perturbation solution scheme. Two physical cases of interest are considered, namely, the case of non-resonance and the case of resonance. The upshots of impacting flow parameters to the flow are measured graphically via computational findings for the non-resonance case. An essential property of the flow explored from the study is that both the ion slip and Hall current tend to stabilize the principal flow due to the revolution of ions and elections about a robust exerted magnetic field. The Hall effect destabilizes the secondary flow. The consequence of the ion-slip current in the secondary velocity direction is opposite to that of the Hall current because of the heavier mass of ions compared to the electrons.</p>