Boiling Heat Transfer Analysis
Theory: the four regions of the boiling curve
Overview
I hear boiling carries heat very well — how much better? And I've heard that too much boiling is dangerous.
Bubbles carry away latent heat as they form and stir the liquid as they leave, so nucleate boiling of water reaches 10,000–60,000 W/m²K — over a thousand times natural convection in air. But raise the heat flux and at some point bubbles merge into a vapour film blanketing the surface, and heat transfer drops sharply. That's the critical heat flux (CHF); staying below it is a basic design premise for reactors and electronics cooling. Let's follow the boiling curve with numbers.
The four regions
| Region | Superheat (water, 1 atm) | Features |
|---|---|---|
| Natural convection | Below about 5 K | No bubbles |
| Nucleate boiling | About 5 to 30 K | Best heat transfer |
| Transition boiling | About 30 to 120 K | Heat flux falls as temperature rises |
| Film boiling | Above about 120 K | Heat passes through a vapour film |
Nucleate boiling and CHF correlations
Top is Rohsenow's nucleate boiling correlation, with heat flux proportional to the cube of superheat $\Delta T_e$; $C_{sf}$ depends on the liquid–surface pair (0.013 for water on copper). Below are Zuber's critical and minimum (Leidenfrost) heat fluxes, independent of surface material.
Nukiyama's boiling curve
The boiling curve was first measured by Shiro Nukiyama at Tohoku Imperial University in 1934. He heated platinum and nichrome wires in water with electric current and studied heat flux against wire temperature. As current (heat flux) rose, the wire temperature suddenly jumped at a certain value, glowing red or melting — the discovery of the critical heat flux. Nukiyama reasoned that temperature control would reveal the region in between, and transition boiling was later confirmed. Textbooks worldwide still call it the Nukiyama curve.
Worked example: water at 1 atm
Nucleate boiling heat flux
| Superheat | Heat flux | Heat transfer coefficient |
|---|---|---|
| 5 K | 0.017 MW/m² | 3,400 W/m²K |
| 10 K | 0.14 MW/m² | 13,700 W/m²K |
| 15 K | 0.46 MW/m² | 30,800 W/m²K |
| 20 K | 1.10 MW/m² | 54,800 W/m²K |
Critical and minimum heat flux
| Item | Value |
|---|---|
| Critical heat flux (Zuber) | 1.26 MW/m² |
| Superheat at CHF (Rohsenow) | 20.9 K |
| Heat transfer coefficient at CHF | 60,000 W/m²K |
| Minimum heat flux (Leidenfrost point) | 18.9 kW/m² |
Burnout under heat-flux control
Suppose a 1 mm wire is electrically heated and moves into film boiling while held at the critical 1.26 MW/m². Finding the superheat at which vapour-film conduction (Bromley) plus radiation (emissivity 0.8) carries that flux gives about 1,700 K. Film-side coefficients are roughly 360 W/m²K convective and 470 radiative — under a hundredth of nucleate boiling's 60,000.
From 21 K to 1,700 K — just from a slight increase in heat flux?
With imposed heat flux, only two points on the boiling curve carry that flux: one in nucleate and one in film boiling. Exceed CHF even slightly and there's no nucleate point left, so the system jumps to the film-boiling point at the same flux. The vapour film acts like insulation, so the temperature difference grows by orders of magnitude. Copper melts at 1,085 °C, so a copper wire would melt. That's why reactor fuel rods and high-power electronics keep margin to CHF. With imposed surface temperature (e.g. steam heating), transition boiling can be followed and no jump occurs.
Analysis and design tips
- First draw the boiling curve from correlations and locate the operating point.
- For heat-flux-driven devices (heaters, fuel rods, chips), always evaluate margin to CHF.
- Csf changes with finish and fouling; calibrate with measurements if available.
- With flow (forced-convection boiling), use flow-boiling correlations, not pool boiling ones.
- When resolving bubbles in CFD, verify interface tracking and wall nucleation models.
“The vapour film in quenching”
When hot steel is quenched in water, the surface is at first wrapped in a vapour film and cools surprisingly slowly (film boiling). As temperature falls past the Leidenfrost point, the film collapses into nucleate boiling and cooling suddenly accelerates. If this switch happens at different times across the part, cooling becomes uneven, causing distortion and quench cracks. Agitating the water or using additives that destabilise the film are ways to shorten and even out film boiling.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Constant heat transfer coefficient | Large error with superheat | Vary along the boiling curve |
| Ignoring CHF margin | Burnout | Evaluate margin |
| Unchecked Csf | Heat flux off by 2× | Calibrate |
| Pool correlation for flow boiling | Wrong CHF | Flow-boiling correlations |
| Neglecting radiation in film boiling | Wall temperature overestimated | Add radiation |
I'd like to learn related topics.
Try the boiling curve in the boiling heat transfer tool. Related pages include pool boiling CFD, condensation, two-phase heat exchangers, spray cooling and heat pipes.
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