The 3D sim treats the whole cell as one lumped point — a single temperature, one heat-capacity, one Arrhenius rate. This 2D companion never does that: it solves real radial heat conduction (Fourier's law in cylindrical coordinates) across 18 concentric shells, and evaluates the same three-stage Arrhenius kinetics locally in every shell using that shell's own temperature:
ρc·∂T/∂t = (1/r)·∂/∂r( r·k·∂T/∂r ) + q'''(r,t)
q'''ᵢ = Σⱼ mᵢⱼ·ΔHⱼ·kⱼ(Tᵢ)·zᵢⱼ dzᵢⱼ/dt = −kⱼ(Tᵢ)·zᵢⱼ
shell i↔i+1 conduction: Q = k_cond·2πr_face/Δr·(Tᵢ−Tᵢ₊₁)
surface shell only: Q_loss = h·2πR·(T_surf − T_amb)
Only the outermost shell exchanges heat with the chamber by convection; every other shell only receives or loses heat by conducting to its neighbours. That single structural change is what lets this model show something the lumped 3D sim structurally cannot: a genuine spatial hot spot. Total shell heat capacity is built to sum to exactly the 3D sim's 48 J/K, so both models describe the same physical 18650-format cell.
Verified numerically (standalone Node script, not shown in-browser): heat-capacity sums to 48.0 J/K exactly by construction; a locked-in energy pulse's radial temperature integral (ΣTᵢCᵢ) is conserved to machine precision as it diffuses outward with no convective loss; and the diffusive spreading rate matches the analytic time scale R²/(4α) for this cell's effective radial diffusivity. One genuinely new, real result the spatial model exposes that the lumped model cannot: because Arrhenius rate is a convex (exponential) function of temperature, whichever shell happens to run slightly hotter reacts disproportionately faster than the ensemble average would — Jensen's inequality — so under identical settings this spatially resolved model can reach its T1/T2 landmarks measurably earlier than the 3D sim's single-point average, not later. That is expected physics, not a bug: it's the same reason real cells fail from local hot spots (nail penetration, a bad weld, an internal short) well before their bulk average temperature looks dangerous.
- Core vs. surface readout — the spread between them is this model's whole point: a large spread means the cell's real worst-case (core) temperature is running well ahead of what a single external thermocouple (near the surface) would report.
- Biot number h·R/k — when it's well above 1 (typical here), internal conduction resistance dominates over surface convection resistance, so the lumped-capacitance assumption the 3D sim makes is not strictly valid — exactly the regime where a spatial model matters.
- Trigger Internal Short (local) — unlike the 3D sim's uniform +25 °C bump, this deposits the same total pulse energy concentrated in the innermost few shells, the way a real nail-penetration or crush short actually nucleates a point-like hot spot rather than heating the whole cell at once — then lets conduction physically carry that heat outward, shell by shell, exactly as the radial PDE above predicts.