Display omitted •A computational framework applied to consider the natural convection problem in a cavity with micropolar fluid.•The material parameter decreases with Rayleigh number and particle volume fraction.•The values of Ψmax and Nuave decrease 17.1% and 10.8%, respectively while Nmax increases 19.8% when K increases from 1 to 2. Micropolar fluids are the media in which their behavior is affected by the microrotation of the substructure particles. In the present work, the natural-convection flow of a micropolar-nanofluid (Al2O3/water) in the presence of an inclined magnetic field in a semi-annulus enclosure is investigated. The influence of active parameters on magneto-natural convection is investigated. The governing equations (mass, momentum, microrotation, and energy) are numerically solved by CVFEM. Moreover, for some conservative comparisons, the equations are solved by Ansys Fluent CFD code which is conjugated by an innovative nondimensionlization scheme. The effects of important parameters are investigated on the streamlines, isotherms, microrotation contours, the maximum absolute value of stream function (Ψmax), the average Nusselt number (Nuave) and the maximum absolute value of microrotation Nmax∗. The results discovered that the values of Nuave descend with ascending the Hartmann number (Ha) and material parameter (K) while it ascends with ascending Rayleigh number (Ra) and particle volume fraction (ϕ). The value of Nuave descends 10.8% while Nmax∗ increases 19.8% when K increases from 1 to 2. The value of Nuave descends 44.83% when Ha increases from 25 to 75 at λ=45°. The minimum value of Nuave occurs at λ=45° for Ha=25 and at λ=30° for Ha=50 and Ha=75.