This is the 2D-native counterpart to the 3D orbiting-capsule PCM slurry simulator. Rather than animating spheres at one shared axial speed through an assumed instantly-mixed pipe, it solves the actual radial-axial temperature field: a laminar Poiseuille velocity profile carries the centreline fluid fastest and the near-wall fluid slowest, wall heat flux enters only at the boundary, and radial conduction is what spreads that heat inward — the classical Graetz entry-length problem, layered with the same three-segment apparent-heat-capacity latent-heat law the 3D model uses. The field heatmap, the outlet radial temperature profile, and the material's own effective heat-capacity/enthalpy curve are drawn directly from that solved field, so the near-wall thermal boundary layer and the possibility of local melting well before the bulk-mixed average reaches the melt band are visible for the first time — phenomena the 3D model's instant-mixing assumption cannot represent.