Viscoplastic flow and thermal transport during melting of phase change materials (PCMs) in a Rotary Kiln

We numerically investigate the thermo-rheological melting dynamics of a phase change material (PCM) representative of clinker pyroprocessing utilizing a two-dimensional rotary kiln model. Moving beyond conventional Newtonian approximations, the molten phase is modelled as a viscoplastic Papanastasiou fluid to capture the macroscopic yield stress inherent to dense, partially molten granular ensembles. The governing equations are solved using a stabilized finite element framework integrating a phase-field method for interface capturing with an enthalpy-viscosity formulation for the phase transition (melting). Introducing viscoplasticity fundamentally alters the system’s governing physics, creating yielded and unyielded regions that dictate flow organization, wall adhesion and heat transfer. Parametric analysis reveals that higher angular velocities enhance mixing and reduce melting time by forming a thin fluid film on the wall. Furthermore, the macroscopic yield stress mechanically stabilizes the flow, making the distribution of yielded and unyielded zones insensitive to Prandtl number variations. While low Stefan numbers impose a thermal bottleneck that sustains solid cores, higher Stefan numbers accelerate thermal equilibration. Most notably, isolating the Bingham number reveals a counterintuitive heat transfer trend: although extreme yield stress suppresses bulk advective mixing, it compensates by physically pinning the solid core against the heated rotating boundary. This activates an efficient contact-melting conduction regime that outperforms convective transport, yielding higher Nusselt numbers and a 27% reduction in total melting time.