Numerical Study of Buoyancy-Driven Melting of a Williamson Non-Newtonian Phase Change Material in a Porous Enclosure Under Magnetic Field Effects

This study numerically investigates buoyancy-driven melting of a Williamson non-Newtonian phase change material in a porous enclosure. The model incorporates an inclined magnetic field, thermal radiation, and viscous dissipation. The enthalpy–porosity method is employed to describe the melting process. The governing equations are solved using an implicit finite-difference scheme and successive over-relaxation. Grid and time-step refinement are performed to assess numerical sensitivity, while comparisons with limiting-case benchmarks are used to validate selected components of the numerical implementation. The effects of the governing parameters on fluid flow, heat transfer, and melting behavior are examined. Higher Grashof and Darcy numbers strengthen circulation and accelerate melting. In contrast, larger Williamson and magnetic parameters, together with greater mushy-zone resistance, suppress fluid motion and delay melting. Thermal radiation and viscous dissipation enhance heating and promote melting. Higher Stefan numbers also accelerate melting and increase the liquid fraction. Overall, the results demonstrate that buoyancy, permeability, thermal radiation, viscous heating, and Stefan number promote PCM melting, whereas magnetic damping, non-Newtonian effects, and mushy-zone resistance inhibit it, providing insight into the competing transport mechanisms governing PCM melting in porous enclosures.