Effects of sequential velocity and variable magnetic field on the phase change during hybrid nanofluid convection through a 3D cylinder containing a phase-change material packed bed (PCM-PB) system is analyzed with the finite element method. As the heat transfer fluid, 40% ethylene glycol with hybrid TiO2-Al2O3 nanoparticles is considered. Impacts of the sequential velocity parameter (K, between 0.5 and 1.5), geometric factor of the conic-shaped PCM-PB (M, between 0.2 and 0.9), magnetic field strength (Ha number between 0 and 50) and solid volume fraction of hybrid nanoparticles (vol.% between 0.02% and 0.1%) on the phase change dynamics are explored. Effects of both constant and varying magnetic fields on the phase change process were considered. Due to the increased fluid velocity at the walls, the phase change becomes higher with higher values of the sequential velocity parameter (K). There is a 21.6% reduction in phase transition time (tF) between the smallest and highest values of K both in the absence and presence of a constant magnetic field. The value of tF is reduced with higher magnetic field strength and the amount of reduction depends upon the sequential velocity parameter. At K = 1.5, the reduction amount with the highest Ha number is 14.7%, while it is 26% at K = 0.5. When nanoparticle is loaded in the base fluid, the value of tF is further reduced. In the absence of a magnetic field, the amount of phase-transition time reduction is 6.9%, while at Ha = 50, it is 11.7%. The phase change process can be controlled with varying magnetic field parameters as well. As the wave number and amplitude of the varying magnetic field are considered, significant changes in the tF are observed.