<p>This article offers a numerical investigation of the solidification in a cold storage unit improved by advanced materials and modeling techniques. A water-based ternary nanofluid, composed of silver (Ag), aluminum oxide, and titanium dioxide nanoparticles, is used as the phase change medium. To further improve thermal conductivity and promote faster solidification, the storage container is embedded with a porous metal foam matrix. The numerical model is developed using the Galerkin method, offering great correctness in solving transient problems. The unsteady thermal behavior is captured by discretizing time-dependent terms through an implicit scheme, ensuring stable and efficient computation. Given the negligible fluid motion during freezing, the momentum equations are omitted, and the simulation is based on two coupled energy and phase fraction equations. The results clearly demonstrate the effectiveness of the enhancement strategies: The integration of porous metal foam reduces the total freezing time by approximately 82.36%, while the inclusion of ternary nanoparticles contributes to an additional 13.2% improvement. Among the two, the presence of porous foam shows a more pronounced impact on quickening the freezing. This work not only validates the synergy between nanomaterials and porous media but also highlights the importance of using adaptive numerical frameworks for simulating phase change phenomena.</p>