<p>This work examines unsteady tangent hyperbolic nanofluid (THNF) flow on an irregular inclined cylinder with the effects of periodic magnetohydrodynamics. The surface roughness of a cylinder is illustrated by a high-frequency sinusoidal wave having a small amplitude. In the current analysis, the flow effect at different angles between 15 and 60° has been examined. The leading equations have been solved in dimension-free form using the bvp4c technique. As outcomes of this work, it has highlighted that the chord-wise velocity distribution retards with augmentation in magnetic field parameter, Weissenberg number, nanoparticles (NPs) volume friction, and cylinder roughness parameter, while it augments with a surge in inclination angle and Richardson number. The skin friction increases up to 39.502% and 31.3129%&#xa0;by varying the NPs volume friction and angle of inclination from 0.02 to 0.04 and 15 to 60 degrees, whereas it drops up to 19.3104% and 74.2302% with the variation in magnetic factor and Richardson number from 1.0 to 3.0, respectively. The energy transfer enhances up to 2.82748203, 68.1719%, and 18.5142% by varying the Al₂O₃ NPs volume friction from 0.02 to 0.04, cylinder surface roughness from 1.5 to 2.5, and heat source parameter from 0.5 to 1.5, respectively. To validate the current work, its results have matched with the established dataset available in the literature by establishing a fine promise among all the results.</p>