Thermal-Hydraulics and Heat Transfer
Energy balance and flow regimes
The first tool is the steady-flow energy balance, Q = ṁ c_p ΔT for single-phase liquid, or an enthalpy form when boiling occurs. Candidates must be comfortable with quality, void fraction, slip ratio, two-phase friction multipliers, and the transition from bubbly to annular to mist flow. Heat transfer regimes in a fuel rod move from single-phase forced convection through subcooled nucleate boiling to bulk boiling.
Safety limits
CHF is the heat flux at which a vapor blanket degrades the local heat-transfer coefficient. In PWRs the governing metric is DNBR (CHF divided by local heat flux, with limits typically around 1.3 or higher); in BWRs it is MCPR. The mechanism differs: PWR departure-from-nucleate-boiling (DNB) versus BWR dryout at high quality.
Decay heat
Decay heat is roughly 6–7% of operating power at shutdown, about 1.3% after an hour, and about 0.5% after a day. This drives the need for long-term cooling and is the energy source behind most severe-accident analyses.
Traps
- Using hot-leg to cold-leg ΔT as if it were the core ΔT (pump heat and bypass flow matter).
- Mixing DNBR with CHF, or quoting a DNBR limit without noting it is a minimum on the limiting rod.
- Ignoring natural circulation: flow reverses to a core-to-SG buoyancy loop, and the flow rate is a small fraction of forced flow.
Worked example
A core producing 3400 MWt with 16,000 kg/s of coolant at c_p = 5.5 kJ/kg·K: ΔT = 3.4×10⁶ kW / (16,000 × 5.5) ≈ 38.6 K (≈ 70 °F). Sanity-check answers like this against the expected PWR range rather than trusting arithmetic alone.