ENGINEERING EXPLAINED / DECAY
The reaction stops.
The heat doesn’t.
Control rods stop the chain reaction. Radioactive decay in the fuel keeps releasing energy. That energy still needs a way out.
Explore the heat ↓Approximate decay heat at Fukushima Daiichi Unit 1, one hour after shutdown.
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01 / SHUTDOWN IS NOT HEAT-OFF
Stop the reaction.
Follow the energy.
Water takes heat from the fuel. Control blades are withdrawn.
Simplified teaching illustration. Orange shows heat generation, not the visible appearance of radiation. Cooling loss is accelerated here: this animation does not predict a plant’s water level or time to fuel exposure. Actual emergency cooling can use natural circulation or steam-driven systems as well as electric pumps.
02 / SMALL PERCENTAGES. LARGE POWERS.
Choose the reactor’s
full thermal power.
MWth is thermal power, not electrical output. The reel’s approximate guide values are 6.5% at shutdown, 1.5% at one hour, 0.4% at one day and 0.2% at one week. The connecting curve is our teaching interpolation. It is not a depletion calculation, a safety standard or an exact Unit 1 reconstruction.
Why operating history changes the answer
Fission-product inventories depend on the fuel and its prior irradiation. A real heat-source calculation needs that history and decay data. A thermal solver then uses the source term to calculate temperatures, heat transfer and fluid response. Coupled tools can calculate both; the thermal equations alone do not supply the radionuclide inventory.
The Way–Wigner approximation illustrates this dependence for constant pre-shutdown power:
P(t) / P₀ = 0.066 [t⁻⁰·² − (t + T)⁻⁰·²]
t is seconds since shutdown; T is seconds of prior operation. This separate approximation is not fitted to the reel’s guide points. It is unsuitable at t = 0 and is not the curve integrated below.
03 / THE AREA IS ENERGY
Every second
adds to the total.
E₂₄ₕ = ∫₀²⁴ʰ P(t) dt
Integrate the orange teaching curve over the first day. Power is a rate; its time integral is the energy that must leave the fuel and surrounding system.
—energy released in the first 24 hoursEQUIVALENT BOIL-OFF
—tonnes of already-boiling water at 1 atm
m = E / hfg · hfg ≈ 2.257 MJ/kg
This is an energy equivalent, not an accident prediction. It assumes all decay energy vaporizes saturated water at 100°C, with no heat loss, replenishment, pressure change or heat stored in equipment. Reactor coolant is pressurized and those assumptions do not describe its transient.
Exactly what is integrated
We hold 6.5% from 0 to 1 second, then interpolate each pair of guide points with a power law in elapsed time: f(t) = f₁(t/t₁)ᵇ, where b = ln(f₂/f₁)/ln(t₂/t₁). Each segment has an analytic integral. The first-day calculation ends at 86,400 seconds. Changing these assumed guide points or the interpolation changes the result.
04 / FUKUSHIMA DAIICHI, UNIT 1
The rods went in.
The cooling was lost.
- 14:4611 March 2011: the operating Units 1–3 scrammed after the earthquake. Units 4–6 were already offline.
- ~1 hourTsunami flooding disabled power and heat-removal equipment. Unit 1 still produced roughly 22 MW of decay heat.
- ~3 hoursThe reconstructed Unit 1 sequence places the falling water level at the top of the fuel. These are approximate accident estimates.
Unit 1’s isolation condenser could remove heat through natural circulation. Its availability depended on valves, controls and water inventory; the accident was more complex than an electric pump simply stopping. The universal lesson is the need for a sustained path from the fuel to a heat sink.
World Nuclear Association accident overview ↗ · TEPCO investigation attachments ↗
05 / THE INPUTS MATTER
A model needs
the right history.
The missing input is often more consequential than the solve button. For decay heat it is the fuel’s history and inventory. For your process model, it may be composition, operating history or a boundary condition. Reflux helps engineers work through their simulation cases and assumptions.
Sources & scope
NRC: decay heat definition · NRC: reactor concepts and cooling systems · NRC: boiling-water reactors · Guide values and Way–Wigner overview used in the reel brief · NIST: water and steam properties.
Educational illustration, October 2026. No plant design, operating instruction or reactor safety analysis is supplied.