Plot the Nukiyama boiling curve in real time. Automatically identify free convection, nucleate boiling, transition, and film boiling regimes. Compute CHF and Leidenfrost point with the Rohsenow & Zuber correlations.
Parameters
Fluid
Surface–Fluid Pair (Csf)
Smaller Csf = more active nucleation sites = higher h at the same ΔTe
Surface Excess Temp. ΔTe
K
T_s − T_sat. Higher superheat raises site density & departure frequency, so h soars
Heat transfer coefficient: $h=q''/\Delta T_e$ (since $q''\propto\Delta T_e^{3}$ in nucleate boiling, $h\propto\Delta T_e^{2}$ — it rises steeply)
Bubble departure diameter (Fritz): $D_b=0.0208\,\beta\sqrt{\dfrac{\sigma}{g(\rho_l-\rho_v)}}$; departure frequency from $f\,D_b\approx0.59\left[\dfrac{\sigma g(\rho_l-\rho_v)}{\rho_l^2}\right]^{1/4}$
Jakob number (superheat measure): $\mathrm{Ja}=\dfrac{\rho_l c_{pl}\Delta T_e}{\rho_v h_{fg}}$. Critical heat flux (Zuber): $q''_{max}=0.131\,h_{fg}\rho_v\left[\dfrac{\sigma g(\rho_l-\rho_v)}{\rho_v^2}\right]^{1/4}$
Site density N is inferred from the departure-flux / latent-transport balance $q''\sim N\,f\,(\tfrac{\pi}{6}D_b^3\rho_v h_{fg})$ (a representative value combining latent transport and microlayer evaporation).
What is Boiling Heat Transfer?
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The animation shows little bubbles popping off the heated surface. Is that nucleate boiling? What's actually going on?
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Exactly — that's the mechanism of nucleate boiling itself. Bubbles are born at tiny pits and scratches (nucleation sites) on the surface, they grow, and once they reach a departure diameter (Db) buoyancy pulls them off and they rise. We call that cycle ① nucleation → ② growth → ③ departure. Each departing bubble carries vapor (latent heat) away, and the churning sweeps cool liquid back onto the surface. That's why nucleate boiling has an enormous heat transfer coefficient h. Watch the live h and q'' numbers in the top-right of the canvas.
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When I raise the superheat ΔT slider, both the number of bubbles and the h value jump up fast! Why is it so sensitive?
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Good catch. Higher superheat activates more nucleation sites (site density rises) AND each site departs bubbles more often (higher departure frequency). Site density × frequency × latent heat per bubble sets the transported heat, so the effects multiply. Rohsenow gives $q''\propto\Delta T_e^3$ in nucleate boiling, hence $h=q''/\Delta T_e\propto\Delta T_e^2$ — it climbs steeply. Push it too far, though, and bubbles merge into a vapor film: once you exceed the CHF, heat transfer collapses. When the badge turns red, that's the burnout warning.
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That makes sense. So what's the deal with the "Surface–Fluid Pair" parameter? It just says "C_sf"...
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Great question! $C_{sf}$ is an empirical constant capturing how easily bubbles nucleate on a given material–fluid pair. A smaller $C_{sf}$ means more active sites, so at the same ΔTe you get more bubbles and a higher h. Switch the dropdown from "Copper–Water (0.013)" to "Nickel–Water (0.020)" and you'll see the site density and h numbers drop in the animation. Under the hood the tool applies the Rohsenow correlation to get q'' and then $h=q''/\Delta T_e$; the red operating point on the "h vs ΔTe" chart moves along too, so you can compare the effect at a glance.
Physical Model & Key Equations
The Rohsenow correlation models the heat flux during the nucleate boiling regime, where bubble dynamics dominate heat transfer. It relates the heat flux to the excess temperature ($\Delta T_e = T_{surface}- T_{sat}$).
Where:
$q''$ = Heat flux (W/m²)
$\mu_l$ = Liquid dynamic viscosity (Pa·s)
$h_{fg}$ = Latent heat of vaporization (J/kg)
$g$ = Gravitational acceleration (m/s²)
$\rho_l, \rho_v$ = Liquid and vapor densities (kg/m³)
$\sigma$ = Surface tension (N/m)
$c_{pl}$ = Liquid specific heat (J/kg·K)
$\Delta T_e$ = Excess temperature (K)
$C_{sf}$ = Surface-fluid coefficient (from experiments)
$\mathrm{Pr}$ = Liquid Prandtl number
$n$ = Experimental exponent (often 1 for water, 1.7 for other fluids)
The Critical Heat Flux (CHF) marks the peak of the boiling curve and the transition to dangerous film boiling. A widely used correlation is the Zuber relation, which models the hydrodynamic instability limiting bubble departure.
$$q''_{max}= 0.149 h_{fg}\rho_v \left[\frac{\sigma g (\rho_l-\rho_v)}{\rho_v^2}\right]^{1/4}$$
This equation shows that CHF depends heavily on fluid properties like latent heat ($h_{fg}$), density difference ($\rho_l-\rho_v$), and surface tension ($\sigma$). The physical meaning is that at a certain vapor generation rate, bubbles coalesce into a continuous insulating vapor film, causing the heat flux to drop sharply even as temperature rises—a condition known as "burnout."
Frequently Asked Questions
The number of active sites reflects the nucleation site density (inferred from superheat and Csf), the maximum bubble size reflects the Fritz departure diameter Db, and the popping cadence reflects the departure frequency f. Their product corresponds to the latent-heat transport, i.e. the heat flux q''. Raising the superheat ΔTe increases both site density and frequency, so the heat transfer coefficient h soars — visibly. When the badge turns red (near CHF), bubbles crowd together, signalling an imminent transition toward film boiling.
C_sf and n are experimental constants that depend on the combination of heating surface material and fluid. Default values (e.g., C_sf=0.013, n=1.0 for water-copper) are set, but they can be manually changed by referring to literature values. For improved accuracy, fitting with actual measurement data is recommended.
CHF is calculated using Zuber's equation (q''_CHF=0.131ρ_g^{1/2}h_fg[gσ(ρ_l-ρ_g)]^{1/4}), and the Leidenfrost point is calculated using an empirical formula based on the saturation temperature. The results are displayed as markers on the graph and can be referenced as superheat thresholds.
This tool uses representative values at the saturation temperature. For systems with strong temperature dependence (e.g., high superheat), errors may occur, so please input values near the saturation temperature as needed. For higher-precision analysis, consider incorporating a temperature-dependent model separately.
Real-World Applications
Nuclear Reactor Safety (Burnout Analysis): The most critical application is preventing the "departure from nucleate boiling" (DNB) in reactor fuel rods. Engineers use CHF calculations to set absolute power limits, ensuring the cladding temperature never enters the film boiling regime, which could lead to meltdown.
High-Power Electronics Immersion Cooling: Servers for AI and cryptocurrency mining are submerged in dielectric fluids. Designers use boiling curves to select fluids and surface finishes that maximize heat flux in the nucleate regime, allowing compact, silent cooling of chips exceeding 1000 W/cm².
Industrial Boiler & Evaporator Design: In steam generation systems, the boiling curve dictates the required heating surface area and tube material. Operating near the CHF maximizes efficiency but requires precise control of pressure and temperature to avoid scaling or tube failure.
Metal Quenching (Heat Treatment): When hot steel is plunged into oil or water, it passes through all boiling regimes rapidly. Controlling the cooling rate by manipulating the boiling process (e.g., via agitation) is essential to achieve the desired material hardness and prevent cracking.
Common Misconceptions and Points to Note
When starting to use this tool, there are several common misconceptions, especially among those learning CAE on the job. First and foremost, the Rohsenow correlation is not a universal solution. This equation provides a guideline for the nucleate boiling regime, and relying solely on it for actual equipment design is risky. For instance, if the flow passage is narrow or the heating surface is inclined, significant discrepancies can arise between calculated and measured values. Second, choose the experimental constant Csf with care. While the tool allows you to select typical combinations, actual surface roughness and fouling (scaling) vary immensely. It's not uncommon for a heat exchanger designed using a value for polished copper (Csf~0.013) to underperform predictions due to slight changes in surface condition during manufacturing. The third pitfall is avoiding setting the CHF as a target value without a safety margin. Operating right at the peak of the boiling curve can lead to a transition to film boiling with just minor condition fluctuations (e.g., system pressure changes), causing a rapid temperature rise (burnout). In practice, it's standard to incorporate a safety factor of at least 1.5 to 2.0 for the CHF (actual heat flux ≤ CHF / safety factor).
Move the wall superheat ΔTe (K) slider or use the Low/Medium/High presets; the animation's site count, bubble size and departure cadence update instantly (nucleate range ≈ 4–30 K)
Change the fluid and the "Surface–Fluid Pair (Csf)" dropdown to compare how site density, departure diameter Db and heat transfer coefficient h shift at the same superheat
Read the live numbers q'', h, ΔTe, Db, site density, departure frequency, Jakob number Ja and CHF, and watch the red operating point on the "h vs ΔTe" chart. Use Play/Pause/Reset to control the view
Worked Example
For saturated water at 100°C and 1 atm boiling on a copper surface with ΔTe = 15 K, the Rohsenow correlation (Csf = 0.013, n = 1.0) gives q'' ≈ 466.8 kW/m² and h ≈ 31.1 kW/m²K (CHF ≈ 1.111 MW/m²). The Fritz departure diameter is Db ≈ 2.34 mm, departure frequency f ≈ 39 Hz, and Jakob number Ja ≈ 45; the latent-transport balance then implies a nucleation site density of about 130 sites/cm² (≈ 1.3×10⁶/m²). Drop ΔTe to 8 K and q'' falls to ≈ 71 kW/m² with h ≈ 8.9 kW/m²K, the site density thins to ≈ 20 sites/cm², and the animation's bubbles become sparse.
Practical Notes
Nucleate boiling efficiency peaks 10–50 K superheat; exceeding CHF causes burnout in thermal management systems (reactor fuel pins, cooling jackets)
Pressure significantly shifts CHF and Leidenfrost point: R134a at 5 bar has CHF ≈ 0.8 MW/m², at 10 bar ≈ 1.5 MW/m²
Surface roughness and material wettability alter nucleate onset (ONB); polished stainless ≈ 2–3 K, oxidized copper ≈ 0.5 K
Film boiling instability in transition (hysteresis) requires careful pressure control in cryogenic systems and high-power electronics cooling
🎬 Watch it in motion
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