Latent heat storage is among the most effective thermal energy storage techniques. The heat can be stored or released in a phase change substance undergoing melting or solidification. The present research addresses the melting process of paraffin, a phase change material, enhanced with metallic alumina nanoparticles, inside a hexagonal heat storage unit in the presence of a uniform magnetic field is investigated. The melting process occurs during the thermal charge of the latent heat storage unit. The enthalpy-porosity method was employed to model the melting process. The influence of the Lorentz force strength and magnetic field inclination angle as well as the nanoparticle concentration on charging level was scrutinized. It was found that the Lorentz force can suppress the charging level of the thermal energy storage system, while the magnetic field inclination angle can be suitable to control the energy transport performance and melting motion within the thermal energy storage unit. Moreover, raising the nanoadditives concentration diminishes the melting process. Overall, the obtained results confirmed that altering the intensity or direction of the external magnetic field presents indeed a mean for controlling the flow and thermal behavior of nano-enhanced phase change materials. Imposing the Ha up to 500 increases 266% the dimensionless melting time compared to ignoring magnetic field (Ha = 0).