Analysis of melting behavior of PCMs in a cavity subject to a non-uniform magnetic field using a moving grid technique

•The melting heat transfer of an electrically conductive fluid addressed.•The melting fluid is subject to a line source magnetic field.•A moving grid method is utilized to track the phase change interface.•The FEM with ALE moving mesh technique is employed.•The magnetic-source location induces a notable effect in a convection-dominant regime. Melting flow and heat transfer of electrically conductive phase change materials subjecting to a non-uniform magnetic field are addressed in a square enclosure. The top and bottom walls of the cavity are adiabatic, and the sidewalls are isothermal at different temperatures. The temperature of the hot wall is higher than the fusion temperature of PCM (Tf), and the cold wall is at the fusion temperature or lower. At the initial time, the cavity is filled with a solid saturated PCM. In the vicinity to the hot wall, there is an external line-source magnet, inducing a magnetic field. The location of the magnetic source (Y0) can be changed along the hot wall. The cavity domain is divided into two parts of the liquid domain and the solid domain. The moving grid method is utilized to track the phase change interface at the exact fusion temperature of Tf. The governing equations for continuity, flow and heat transfer associated with the Arbitrary Lagrangian–Eulerian (ALE) moving mesh technique are solved using the finite element method. The results are investigated for the melting behavior of PCM by the study of Hartmann number (0 ≤ Ha ≤ 50) and the location of the magnetic source (0 ≤ Y0 ≤ 1). Outcomes show that the effect of the magnetic field on the melting behavior of PCM is negligible at the initial stages of the melting (Fo < 1.15). However, after the initial stages of the melting, the effect of the presence of a magnetic field becomes significant. Moreover, the location of the magnetic source induces a feeble effect on the melting front at the initial melting stages, but its effect on the shape of the melting front increases by the increase of the non-dimensional time. The location of the magnetic source also significantly affects the streamlines patterns. Changing the position of the magnetic source from the bottom of the cavity (Y0 = 0.2) to the almost middle of the cavity (Y0 = 0.6) would decrease the required non-dimensional time of full melting from Fo = 10.4 to Fo = 9.0.