The optimal performance of industrial and manufacturing processes, cooling devices, as well as energy storage systems relies on the efficiency of a thermal systems. This study investigates the thermal performance of a ternary hybrid nanofluid consisting of Al2O3, TiO2 and Cu nanoparticles suspended in water, under the influence of a magnetic field and the phase transition like melting process. The research problem focuses on understanding how the melting parameter, Eckert number and magnetic field strength affect the fluid flow and heat transfer characteristics. The similarity transformation technique is employed to reduce the complexity of the developed governing equations. Then, the simplified governing equations are solved numerically using the Keller-Box method. The findings reveal that the magnetic field increases the temperature profile due to Joule heating, while an increase in the melting parameter inversely affects the temperature profile. The melting parameter enhances the Nusselt number by 35.05% without the magnetic field’s influence. The novelty of this study lies in its comprehensive analysis of the interplay between magnetic field, melting parameter and the thermal behavior of ternary hybrid nanofluid, providing valuable guidance for optimizing thermal systems in various industrial applications.