The natural convective flow and heat transfer characteristics of a ternary hybrid nanofluid inside enclosures are examined under the influence of a magnetic field. Dimensionless equations of the physical domain are transformed into a set of equations of the computational domain using coordinate transformations and solved using the finite difference method. Heat transfer in right-angled and isosceles triangular cavities exceeds that of square and trapezium cavities. Interestingly, the heat transfer in the right-angled triangular cavity is higher for Rayleigh number Ra > 1.5 × 105, Hartmann number Ha < 17, and nanoparticle volume fraction φ < 2%, compared to other cavities, while in the rest of the domains, Ra, Ha, and φ are higher for the isosceles triangular cavity. Moreover, increasing the Rayleigh number enhances heat transfer in all cavities, with the highest increase (361.63%) observed in the square enclosure. On the other hand, increasing the Hartmann number reduces heat transfer, most significantly in the square cavity. The effect of φ is geometry-dependent: the heat transfer in the trapezoidal enclosure exhibits non-monotonic behavior; however, it increases by 10.15% and 24.73% in right-angled and isosceles triangular cavities, respectively, when increasing φ from 4% to 5%.