<p>The present study scrutinises the impact of the nanoparticle shape on the heat transfer performance of hybrid nanofluid flowing over a permeable stretching sheet. The shapes of nanoparticles considered here are lamina, brick, platelets, and blade, with working fluid composed of Al₂O₃ and TiO2 as nanoparticles and C2H6O2-H2O (50:50) as the base fluid. Here, the problem is modelled considering the flow to be unsteady, with the momentum equation modelled using external forces such as magnetic field, porous media, and the energy equation using Fourier’s law with heating assisted by thermal radiation and Ohmic-viscous dissipation. In addition, velocity-thermal slip conditions along with suction effects are also considered. The bvp4c method is implemented to solve nonlinear ODEs. Additionally, the flow model is reduced to three different special cases, and their behaviours are discussed in detail. The findings of the study show that by escalating the values of the radiation factor and the magnetic field, the heat transfer performance of the lamina-shaped nanoparticle is better than that of bricks, platelets, and blades. The rate of heat transfer declined for all shapes of nanoparticles with an increase in the unsteadiness parameter and Eckert number. Additionally, the maximum decline in the local Nusselt number, specifically 5.64%, is observed for a brick-shaped nanoparticle when the inclination angle increases by 6 degrees.</p>