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Purpose: This study aims to examine the flow of unsteady mixed convective hybrid nanofluid over a rotating sphere with heat generation/absorption. The hybrid nanofluid contains different shapes of nanoparticles (copper [Cu] and aluminium oxide [Al2O3]) in the base fluid (water [H2O]). The influence of different shapes (sphere, brick, cylinder, platelets and blades) of nanoparticle in water-based hybrid nanofluid is also investigated. Design/methodology/approach: To analyse the nanomaterial, the flow model is established, and in doing so, the Prandtl's boundary layer theory is incorporated into the present model. The bvp4c approach, i.e. finite difference method, is used to find the numerical solution of differential equations that is controlling the fluid flow. The effect of relevant flow parameters on nanofluid temperature and velocity profile is demonstrated in detailed explanations using graphs and bar charts, whereas numerical results for Nusselt number and the skin's coefficient for various form parameters are presented in tabular form. Findings: The rate of heat transfer is least for spherical-shaped nanoparticle because of its smoothness, symmetricity and isotropic behaviour. The rate of heat transfer is highest for blade-shaped nanoparticles as compared to other shapes (brick, cylindrical and platelet) of nanoparticles because the blade-shaped nanoparticles causes comparatively more turbulence flow in the nanofluid than other shapes of nanoparticle. Heat generation affects the temperature distribution and, hence, the particle deposition rate. The absorption of heat extracts heat and reduce the temperature across the rotating sphere. The heat generation/absorption parameter plays an important role in establishing and maintaining the temperature around the rotating sphere. Research limitations/implications: The numerical study is valid with the exception of the fluctuation in density that results in the buoyancy force and the functional axisymmetric nanofluid transport has constant thermophysical characteristics. In addition, this investigation is also constrained by the assumptions that there is no viscosity dissipation, no surface slippage and no chemically activated species. The hybrid nanofluid Al2O3–Cu/H2O is an incompressible and diluted suspension. The single-phase hybrid nanofluid model is considered in which the relative velocity of water (H2O) and hybrid nanoparticles (Al2O3–Cu) is the same and they are in a state of thermal equilibrium. Practical implications: Study on convective flow across a revolving sphere has its applications found in electrolysis management, polymer deposition, medication transfer, cooling of spinning machinery segments, spin-stabilized missiles and other industrial and technical applications. Originality/value: The originality of the study is to investigate the effect of shape factor on the flow of electrically conducting hybrid nanofluid past a rotating sphere with heat generation/absorption and magnetic field. The results are validated and provide extremely positive balance with the recognised articles. The results of the study provide many appealing applications that merit further study of the problem. [ABSTRACT FROM AUTHOR]