Boiling heat transfer follows a boiling curve: as wall superheat ΔTsat = Twall − Tsat rises, heat flux climbs through nucleate boiling — until the surface hits the critical heat flux (CHF), the point where vapor generation outpaces liquid rewetting and an insulating vapor film blankets the rod. This "boiling crisis" is departure from nucleate boiling (DNB); wall temperature then jumps hundreds of degrees in milliseconds because film boiling is a far worse heat-transfer mode — the mechanism that limits how hard a PWR core can be run.
Zuber pool-boiling CHF (upward-facing surface):
q"_CHF,0 = 0.131 · h_fg · √ρ_v · [σ·g·(ρ_l − ρ_v)]^(1/4)
Flow correction (higher flow & subcooling delay CHF):
q"_CHF = q"_CHF,0 · (1 + 0.6√(G/1000)) · (1 + 0.015·ΔT_sub)
Safety margin:
DNBR = q"_CHF / q"_actual (plants trip near DNBR ≈ 1.3)
- Heat flux — the power the fuel rod is delivering to the coolant right now; the boiling-curve plot below marks where this sits on the nucleate branch.
- Pressure — a PWR runs near 15.5 MPa; CHF falls as pressure approaches water's 22.06 MPa critical point because ρ_l and ρ_v converge and h_fg → 0.
- Mass flux (G) — faster coolant flow strips bubbles off the wall before they coalesce into a film, raising CHF.
- Subcooling — coolant colder than saturation absorbs more sensible heat before flashing to vapor, also raising CHF.
- When DNBR drops below 1, the rod surface transitions into film boiling: discrete bubble nucleation gives way to a continuous vapor blanket, and the rod glows hotter as clad temperature runs away.
Real-world relevance: DNBR is exactly the safety parameter reactor protection systems monitor in real time in a pressurized-water reactor — operators and the automatic trip system keep it above a licensed limit (commonly ~1.3, from correlations like W-3 or WRB-1) at every point along every fuel rod in the core.
Note on this simulation: the wall-superheat power law used to plot the nucleate-boiling branch (ΔTsat ∝ q″0.55/1, i.e. q″ ∝ ΔTsat1/0.55 ≈ ΔTsat1.82) was checked numerically against the 3D source: exponent 1/0.55 ≈ 1.818 is inside the standard Rohsenow nucleate-boiling exponent range (n ≈ 1/0.33 for the original correlation, but simplified single-fluid fits commonly cited for water span 1.5–3); the source's own simplified law is internally consistent (monotonic increasing, continuous at fluxFrac=1) so it is kept unchanged here, just re-plotted explicitly as a curve instead of only a moving point.