© 2021 Elsevier LtdThe primary objective of the present paper is to examine the combined effect of a uniform magnetic field and nanoparticle volume fraction on the melting process of copper-water (ice) as Nano-enhanced Phase Change Material (NePCM). The NePCM is enclosed in a rectangular cavity subjected to a fluctuating temperature at the hot wall. The phase change process is formulated and solved using the Lattice Boltzmann Method. The numerical outcomes of the developed code are validated by comparing them with available experimental and numerical results in the literature. For the melting process of NePCM, the considered parameters include Hartmann number (Ha=0, 30, 60 and 90), nanoparticle volume fraction (ϕ=0, 2, 4 and 6 vol%), and Rayleigh number (Ra=103, 104 and 105). The results showed that the melting time is considerably extended at high Ra as the Ha is increased. Furthermore, addition of nanoparticles notably contributes to the shortening of melting time at low Ra, while they have an adverse effect and extends the melting time up to 7% at high Ra in the existence of magnetic field (MF). However, they decrease melting time up to 10% at Ra=105 when the MF is not applied (Ha=0). It is also noted that the influences of examined parameters become prominent for Fo>0.5. These results may help understanding the control of melting process of electrically-conducting materials, specifically the nano-enhanced energy storage materials.