The moment control rods SCRAM the chain reaction, fission power drops to near zero within seconds — but the fuel keeps producing decay heat from fission-product radioactivity, roughly 6–7% of full power right after shutdown, falling off over hours and days. That heat has to go somewhere or the core temperature climbs toward cladding damage (~1200°C).
P_decay(t) ≈ 0.066·P0·t^-0.2 (Way–Wigner, t in seconds)
Q_passive ∝ vent · A(P0) · ΔT^1.3 (buoyancy-driven natural circulation)
Q_active ≫ Q_decay (motor-driven pumps, needs grid/diesel power)
dT/dt = (P_decay − Q_removed) / C_thermal(P0)
- Grid power (pumps) — forced coolant flow easily out-paces decay heat; core temperature settles close to the sink temperature within minutes.
- Blackout (passive only) — no pumps, no operator action: coolant only moves because hot fluid is buoyant. It has to work through natural circulation and a passively-opened vent to a pool or air heat exchanger.
- Reactor thermal power — surface area grows slower than volume as a core gets bigger (area ∝ power^⅔), so a smaller modular core has more heat-rejecting surface per megawatt of decay heat — the physical reason SMR designs can claim days of walk-away safety that large plants cannot.
- Vent opening — models the passive dampers/valves that must stay open (by gravity or spring-force, not motors) for the natural-circulation loop to reach its ultimate heat sink.
This is a simplified teaching model of the "walk-away safe" claim behind small modular reactor designs (e.g. NuScale-style pool cooling): it is not a licensing-grade thermal-hydraulics code.