PCM Thermal Storage Panel: Latent-Heat Melt Front (2D Stefan-Problem Engine)

PCM Material

Melting point 54 °C · latent heat 200 kJ/kg · low thermal conductivity (0.20 W/m·K)

Heated Boundary

Wall temperature 90 °C

Panel thickness 100 mm

Simulation speed 4×

Melt-Front State

Elapsed (sim.)

0 h 00 m

Front position

0.5 mm

Melted fraction

0 %

Front velocity

0 µm/s

Energy stored (latent + sensible)

0 kJ/m²

log-log regression slope (√t check)

— (need more data)

How it works

This is the classic single-phase Stefan moving-boundary problem. The wall is held at a fixed temperature above the PCM's melting point T_m; the melted liquid layer of thickness x(t) conducts heat quasi-statically while the still-solid PCM ahead of the front sits at T_m. Every frame the engine numerically integrates the interface energy balance — heat conducted through the liquid layer must equal the latent heat absorbed as the front advances by dx:

k·(T_wall − T_m) / x(t)  =  ρ·L·dx/dt

x(t+dt) = x(t) + dt · [ k·(T_wall−T_m) / (ρ·L·x(t)) ]   (adaptive-step Euler)

Because dx/dt shrinks as 1/x, the growing liquid layer keeps adding thermal resistance and the front decelerates — integrating that ODE analytically gives the textbook result x(t) = √(x₀² + 2k(T_wall−T_m)t / (ρL)) ∝ √t. The engine never assumes that shortcut: it re-derives the front position frame-by-frame from the ODE above, then a live least-squares fit of log(x) against log(t) on the actual trajectory reports the measured slope — it should converge to ≈0.5 once enough of the transient has passed.

Material buttons — switch k, ρ, L and T_m to real PCM classes, same as the 3D capsule-array version of this panel.
Wall temperature — the driving ΔT = T_wall − T_m; larger ΔT accelerates the front but the √t shape is unchanged.
Panel thickness — how far the front has to travel before the whole panel is molten and the plateau ends.

T_m (front)T_wall