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Heat Transfer Simulator

Boiling Curve Simulator — Nukiyama Curve and Pool Boiling

Visualize heat flux versus wall superheat for pool boiling of water at 1 atm using the four-regime Nukiyama model, including CHF and the burnout phenomenon.

Parameters
Wall superheat ΔT_e
K
Nucleate boiling coefficient C
—
Critical heat flux CHF
MW/m²
Emissivity ε (film boiling)
—

Water at 1 atm (T_sat = 100°C) is fixed. Natural convection h_nc ≈ 1000 W/(m²·K) and film boiling h_fb ≈ 30 W/(m²·K) are assumed.

Results
—
Boiling regime
—
Heat flux q
—
Boiling HTC h_boil
—
Margin to CHF
Boiling curve (log q vs log ΔT_e)

x = wall superheat ΔT_e (K, log) / y = heat flux q (W/m², log) / blue = four-regime model / red dashed = CHF and Leidenfrost point / yellow dot = current state

Theory & Key Formulas

Pool boiling heat flux $q''$ exhibits four distinct regimes as a function of wall superheat $\Delta T_e = T_w - T_\text{sat}$, as first mapped by Nukiyama (1934).

Natural convection ($\Delta T_e < 5$ K). $h_{nc}$ is the natural convection coefficient:

$$q'' = h_{nc}\,\Delta T_e$$

Nucleate boiling ($5 \leq \Delta T_e < 30$ K). Simplified Rohsenow form:

$$q'' = C\,\Delta T_e^{3}$$

Critical heat flux (Zuber, ≈ 1 MW/m² for water at 1 atm):

$$q''_\text{CHF} \approx 0.131\,\rho_v^{1/2}\,h_{fg}\,[\sigma g(\rho_l-\rho_v)]^{1/4}$$

Film boiling (Bromley convection plus radiation):

$$q'' = h_{fb}\,\Delta T_e + \varepsilon\sigma_{SB}(T_w^4 - T_\text{sat}^4)/2$$

What is the Boiling Curve Simulator

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I always thought boiling was just water making bubbles, but this curve has four different regions. What makes them so different from each other?
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Great catch. Back in 1934, Professor Nukiyama in Japan showed experimentally that boiling actually has four distinct faces. Roughly: if you slowly raise the surface temperature, the liquid first moves by quiet natural convection, then begins vigorous bubbling (nucleate boiling), then a strange unstable regime where heat transfer gets worse (transition), and finally film boiling where vapor blankets the surface. The plot uses log axes because the heat flux varies by orders of magnitude.
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Wait — the nucleate region shoots up steeply, then suddenly the curve goes back down. What is actually happening there physically?
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In nucleate boiling, vapor bubbles nucleate from tiny surface cavities and vigorously stir the liquid, so heat transfer ramps up as roughly $q\propto\Delta T^3$. But once superheat exceeds about 30 K, bubbles merge into vapor patches that cling to the wall. That is transition boiling. Vapor is a thermal insulator, so even as wall temperature rises, the net heat flux falls. In the simulator, sweep ΔT_e from 20 to 50 to 100 and watch the heat flux card peak and then drop.
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There is a red line labeled CHF. What happens if I cross it?
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That is the dreaded burnout. When you control the heat flux — like an electric heater — and push above CHF, the system cannot stay in nucleate boiling. It jumps instantly to the matching point on the film-boiling branch. Read the chart vertically: at CHF ≈ 1 MW/m², the nucleate side sits near ΔT_e ≈ 30 K but the film side needs ΔT_e ≈ 600 K or more. So the surface temperature jumps by hundreds of degrees in a flash, which melts boiler tubes or fuel cladding. That is why we design with CHF margins of 1.5 to 2.
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Is the Leidenfrost effect — droplets dancing on a hot pan — related to this curve as well?
🎓
Exactly. The Leidenfrost point on the right of the curve is the gateway into stable film boiling. The droplet bottom vaporizes instantly and a thin vapor cushion lifts the droplet off the surface. That vapor film is an insulator, so heat transfer plummets. Sliding to ΔT_e ≈ 200 K in the simulator shows the heat flux dropping orders of magnitude compared with the same superheat on the nucleate branch. The reason a splash of liquid nitrogen on your hand does not give you frostbite is exactly the same Leidenfrost behavior.

Frequently Asked Questions

When heat flux exceeds the critical heat flux (CHF), the heating surface becomes blanketed by a vapor film, heat transfer collapses, and surface temperature jumps by hundreds of degrees, often destroying the wall. It is the dominant failure mode for heat-flux-controlled systems like electric heaters, boiler tubes, and electronic chip cooling. Designers typically maintain a safety margin of 1.5 to 2 against CHF.
In BWRs and in PWR accident cooling (ECCS), avoiding the Departure from Nucleate Boiling (DNB) on fuel rod surfaces is the central safety concern. Once film boiling sets in, the heat transfer coefficient drops by orders of magnitude and cladding temperature soars, risking fuel damage. Safety analysis requires the DNB Ratio (DNBR) to stay above about 1.3 under all transients.
When a droplet contacts a very hot surface, the bottom vaporizes instantly and the droplet rides on its own vapor layer. This corresponds to the Leidenfrost point (q_min) on the boiling curve; beyond it lies the stable film boiling regime. The familiar dancing of water on a hot skillet is the same phenomenon. The insulating vapor film causes a dramatic drop in heat transfer.
Pool boiling occurs in stagnant liquid heated only by the surface; it is described by the simple Nukiyama curve. Forced convection boiling occurs in flowing liquid and depends additionally on flow velocity, subcooling and channel geometry, making it far more complex. Industrial steam generators and reactor fuel bundles operate in forced convection boiling, but understanding the four pool boiling regimes is the essential starting point.

Real-world Applications

Thermal and nuclear power boilers: Power stations boil water at high pressure to produce steam, and a tube that crosses CHF will rupture instantly. Designers evaluate CHF with correlations such as the Groeneveld look-up tables and maintain safety margins of at least 1.3 to 2.0. Understanding the boiling curve is the foundation for safe power-plant operation.

High-density electronics cooling: CPUs, GPUs and power semiconductors already dissipate over 100 W/cm², beyond what air cooling can handle. Immersion cooling and jet-impingement cooling exploit the high heat transfer coefficients of nucleate boiling (CHF reaches the MW/m² range). Data centers and EV inverters are early adopters of this technology.

Steel quenching and heat treatment: When hot steel is quenched into water or oil, the surface initially enters film boiling and cools slowly. As temperature drops past the Leidenfrost point, the regime shifts back to nucleate boiling and rapid cooling begins. The dramatic change in cooling rate controls phase transformations, so quench-oil selection and agitation are essentially design choices about which boiling regime to traverse.

Cryogenics and aerospace: Superconducting magnets and rocket engines using liquid helium or liquid nitrogen face boiling at the cold-fluid side of warm walls. Such systems often start in film boiling, which is inefficient. Designers use porous or treated surfaces to promote an early transition to nucleate boiling and improve cool-down rates.

Common Misconceptions and Pitfalls

The most common misconception is to assume that hotter surface always means better heat transfer. In reality, beyond the CHF peak of nucleate boiling, raising wall temperature actually reduces the heat flux in the transition regime. Try sweeping ΔT_e from 30 to 60 to 90 K in the simulator: the heat flux card decreases instead of increasing. This counter-intuitive behavior is the defining feature of boiling heat transfer — and the root cause of many design accidents.

The second common error is treating CHF as an absolute physical limit. CHF is the maximum heat flux at which nucleate boiling can be maintained; crossing it does not always destroy the surface. In heat-flux-controlled systems (electric heaters) you jump immediately to film boiling and burnout occurs. In wall-temperature-controlled systems (reheaters, solar receivers) you traverse the transition regime smoothly and may avoid catastrophic failure. Always confirm whether your real system is flux-controlled or temperature-controlled before applying the simulator results.

Finally, remember that this simulator uses a simplified model for water at 1 atm. The coefficients C, CHF and h_fb are representative textbook values. Accurate engineering predictions require evaluating Rohsenow's surface coefficient $C_{sf}$, Zuber's CHF correlation, forced-convection corrections, and channel-geometry effects individually. CHF varies sharply with pressure (rising at high pressure, falling at vacuum). Real plant designs always rely on validated correlations such as the Groeneveld look-up table or subchannel codes (VIPRE, COBRA).

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