nucleate-boiling

name	nucleate-boiling
description	Nucleate boiling — pool boiling curve (Nukiyama), incipience superheat, heat transfer correlations (Rohsenow, Chen, Forster-Zuber), critical heat flux (CHF, Lienhard-Dhir correlation), flow boiling (Bergles-Rohsenow), two-phase flow regimes (bubbly/slug/annular), departure from nucleate boiling (DNB), void fraction, boiling number, and applications in nuclear/heat exchanger/electronics cooling.
metadata	{"priority":7,"promptSignals":{"phrases":["nucleate boiling","boiling heat transfer","critical heat flux","pool boiling","CHF boiling","departure from nucleate boiling"],"minScore":3}}

Nucleate Boiling Heat Transfer — Complete Skill

Boiling Modes and Pool Boiling Curve

Nukiyama Boiling Curve

Regimes (q vs. ΔT_sat = T_wall - T_sat):

Natural convection (ΔT_sat < 5°C): Single-phase; no boiling; h = h_natural_convection q = h_NC × (T_wall - T_sat)

Nucleate boiling (5 < ΔT_sat < ΔT_CHF): Bubble nucleation from surface cavities; vigorous mixing; high h q increases steeply with ΔT_sat; most efficient heat transfer regime Bubble dynamics: formation, growth, detachment, condensation (subcooled) or rise (saturated)

Critical Heat Flux (CHF/DNB): Maximum q achievable in nucleate boiling: q_max (Lienhard-Dhir or Zuber correlation) Beyond q_max: vapor film forms → transition boiling → q drops catastrophically Corresponds to ΔT_sat ≈ 25–30°C for water at 1 atm

Transition boiling (unstable; negative slope): Partial vapor film; unstable; hysteresis between nucleate and film boiling

Film boiling (Leidenfrost regime; ΔT_sat > ~200°C for water): Stable vapor film; q = h_FB × ΔT_sat + radiation contribution q_min at Leidenfrost point (ΔT_Leidenfrost ≈ 200°C for water; q_min ≈ 0.05 × q_max) Beyond Leidenfrost: radiation dominates at very high T_wall

Nucleation Incipience

Onset of Nucleate Boiling (ONB) — Bergles-Rohsenow: q_ONB = (k_f × T_sat × ΔT_sat) / (h_fg × ρ_v × r_crit × C_sf) More practically: ΔT_ONB = 8σ × T_sat × q / (k_f × h_fg × ρ_v) [wall superheat at incipience] r_crit = critical bubble radius = 2σ T_sat / (ρ_v × h_fg × ΔT) [from Clausius-Clapeyron]

Nucleation site density N_a [sites/m²]: N_a = C × (ΔT_sat)^m [C, m = surface-dependent; typically m = 3–8] Rough surface: higher N_a → earlier nucleation; polished: lower N_a; requires higher ΔT

Active cavity radius: r_min ≤ r_cavity ≤ r_max for nucleation r_min = 2σ/(p_l_sat × (T_wall - T_sat)/(T_sat))

Nucleate Boiling Correlations

Rohsenow Correlation (Pool Boiling)

Most widely used for pool boiling: q = μ_f × h_fg × [g(ρ_f - ρ_g)/σ]^0.5 × [c_pf × ΔT_sat / (C_sf × h_fg × Pr_f^n)]^3

Or equivalently (heat transfer coefficient form): h = q / ΔT_sat [from inverting Rohsenow]

Parameters: C_sf = surface-fluid constant (from Rohsenow table):

• Water/copper: C_sf = 0.0130, n = 1.0
• Water/stainless: C_sf = 0.0060, n = 1.0
• Water/nickel: C_sf = 0.0060, n = 1.0
• Water/Teflon: C_sf = 0.0058, n = 1.0
• Ethanol/copper: C_sf = 0.0027, n = 1.7

Variables: μ_f = dynamic viscosity [kg/m·s]; h_fg = latent heat [J/kg]; g = 9.81 m/s²; ρ_f, ρ_g = liquid/vapor density [kg/m³]; σ = surface tension [N/m]; c_pf = liquid specific heat [J/kg·K]; Pr_f = liquid Prandtl number

Water at 1 atm (T_sat = 100°C): h_fg = 2.257×10⁶ J/kg; ρ_f = 958 kg/m³; ρ_g = 0.60 kg/m³; σ = 0.0589 N/m c_pf = 4216 J/(kg·K); μ_f = 2.82×10⁻⁴ kg/(m·s); Pr_f = 1.76

Rohsenow accuracy: ±±25–50% (order-of-magnitude estimate); surface condition dominates

Jakob-Stephan Correlation (Modern)

Stephan-Abdelsalam (1980) for water: Nu_D = 0.23 × Ra_D^0.674 × (ρ_g/ρ_f)^0.297 × (h_fg × D_b²/α_f²)^0.371 × (c_pf × T_sat/h_fg)^0.35 × (a_f/ν_f)^0.273

Fritz equation (bubble departure diameter D_b): D_b = 0.0208 × θ_contact × √(σ / (g × (ρ_f - ρ_g))) [m; θ_contact = contact angle [rad]]

Critical Heat Flux (CHF)

Zuber Correlation (Pool Boiling, Horizontal Flat Plate)

Zuber (1958) for saturated pool boiling: q_max = C_cr × h_fg × ρ_g × [σ × g × (ρ_f - ρ_g) / ρ_g²]^(1/4) C_cr = π/24 = 0.131 (theoretical); C_cr = 0.149 (empirical Lienhard-Dhir)

Lienhard-Dhir correlation (flat heater, L' based): q_max / (h_fg × ρ_g × [σg(ρ_f - ρ_g)/ρ_g²]^0.25) = f(L') L' = L × √(g(ρ_f - ρ_g)/σ) [dimensionless heater size] Large flat heater (L' > 27): f(L') = 0.149 (Zuber) Short cylinder/wire (L' < 0.15): f(L') = 0.89/L'^0.5

Water at 1 atm (T_sat = 100°C): q_max ≈ 1.26 MW/m² (Zuber/Lienhard) Corresponds to ΔT_sat ≈ 25–35°C

Pressure effect (Rohsenow-Griffith): q_max/q_max,0 = (p/p_c)^0.35 × (1 - p/p_c)^0.9 [p_c = critical pressure; q_max,0 at low pressure] Peak q_max near p/p_c ≈ 0.3–0.4

DNB in Flow Boiling (Nuclear/Power Applications)

DNB (Departure from Nucleate Boiling): Local boiling crisis in subcooled or saturated flow; vapor blanket prevents liquid rewet Critical in nuclear fuel assemblies: loss of DNB → fuel damage → design limit

DNBR (Departure from Nucleate Boiling Ratio): DNBR = q_CHF / q_local_heat_flux ≥ DNBR_limit (≥ 1.30 typical; NRC approval required)

W-3 Correlation (Westinghouse, PWR fuel): q_CHF = [2.022 - 0.0004302 × p] × [0.1722 - 0.0000984 × p] × exp[(18.177 - 0.004129 × p) × x_e] × [0.8258 + 0.0003413 × (h_f - h_in)] × [1 - 0.4 × exp(-0.066 × G / 1000)] × [0.2664 + 0.8357 × exp(-124.1 × D_e)] × [0.8258 + 0.3413 × (h_f - h_in)/h_fg] × [F_f] [simplified; see original paper] p in psia; G in lb/(ft²·hr); x_e = local quality; complex formulation

Simplified CHF for flow boiling: q_CHF = C × G^a × x_crit^b [Tong correlation family; C, a, b from experimental fit; application-specific]

Flow Boiling

Two-Phase Flow Regimes

Progression along heated channel (increasing quality x):

Subcooled boiling (x < 0): Bulk subcooled; wall nucleation; bubbles condense; net steam generation near wall Onset: ΔT_ONB from Bergles-Rohsenow

Bubbly flow (0 < x < 0.05): Dispersed bubbles; continuous liquid phase; relatively uniform

Slug/plug flow (0.05 < x < 0.25): Large intermittent Taylor bubbles; slug instability; pipe flow pulsation risk

Churn flow (0.25 < x < 0.50): Irregular; transition regime; high pressure drop

Annular flow (x > 0.50): Liquid film on wall; vapor core with droplets; dominant at high quality Most efficient heat transfer regime for flow boiling (thin film evaporation) Dry-out: film thins → dry-out → increase in T_wall sharply

Mist/dispersed flow (x → 1.0): Droplets in vapor; poor heat transfer; T_wall can be very high

Chen Correlation (Flow Boiling)

Chen (1966) — most widely used for saturated flow boiling: h = h_mic + h_mac h_mic = S × h_Forster_Zuber [microconvection; nucleate boiling suppressed by flow; S = suppression factor] h_mac = F × h_Dittus_Boelter [macroconvection; enhanced single-phase forced convection; F = two-phase multiplier]

F (convection enhancement): F = 1 for 1/X_tt ≤ 0.10 [X_tt = Martinelli parameter = ((1-x)/x)^0.9 × (ρ_g/ρ_f)^0.5 × (μ_f/μ_g)^0.1] F = 2.35 × (1/X_tt + 0.213)^0.736 for 1/X_tt > 0.10

S (suppression factor): S = 1 / (1 + 2.53×10⁻⁶ × Re_tp^1.17) Re_tp = Re_l × F^1.25 [two-phase Reynolds number]

h_Forster-Zuber (pool boiling component): h_FZ = 0.00122 × (k_f^0.79 × c_pf^0.45 × ρ_f^0.49) / (σ^0.5 × μ_f^0.29 × h_fg^0.24 × ρ_g^0.24) × ΔT_sat^0.24 × Δp_sat^0.75

h_Dittus-Boelter (liquid phase convection): h_DB = 0.023 × Re_l^0.8 × Pr_l^0.4 × k_f / D

Chen accuracy: ±25% for most data; widely used in industry

Bergles-Rohsenow Onset of Significant Void (OSV)

Transition from single-phase to subcooled boiling: q_ONB = 0.00135 × (p/p_crit)^0.0234 × (ΔT_sub + ΔT_ONB)^2.16 / (p^0.156) [Bergles-Rohsenow modified; imperial units]

Engineering criterion for OSV (net vapor generation): q_OSV = G × c_pf × ΔT_sub / [Bo^0.75 × (G/G_ref)^0.25] [approximate; flow-dependent]

Void Fraction

Homogeneous Model

Homogeneous void fraction: α = x / (x + (1-x) × ρ_g / ρ_f) [drift-flux model with slip ratio S = 1; homogeneous]

Slip ratio S = u_g/u_f: S > 1 for bubbly/slug flow (vapor moves faster than liquid) Zivi model: S = (ρ_f/ρ_g)^(1/3) [good for annular flow]

Drift-flux void fraction (Zuber-Findlay): α = j_g / (C₀ × j + u_gj) [j_g = superficial gas velocity; j = mixture velocity; C₀ = 1.0–1.2; u_gj = drift velocity]

Boiling Number

Boiling number Bo (dimensionless): Bo = q / (G × h_fg) [q = heat flux; G = mass flux; h_fg = latent heat] High Bo → dominant boiling contribution; low Bo → convection dominant Transition from forced convection to nucleate boiling dominated: Bo ≈ 10⁻⁴

Applications

Nuclear Reactor (PWR)

PWR fuel assembly: Fuel rod OD: 9.5 mm; pitch: 12.6 mm (square array); D_e = 4 × flow area / wetted perimeter G = 3,000–5,000 kg/(m²·s) (mass flux); q = 200–600 kW/m² (heat flux) DNBR design limit: ≥ 1.30 (Westinghouse VANTAGE 5 fuel) Departure from nucleate boiling ratio (DNBR) calculated with W-3 or COBRA/TRAC codes

Boiling water reactor (BWR): Operates in saturated nucleate boiling; x_exit ≈ 0.10–0.15; void fraction 0.4–0.75 Dryout (instead of DNB) is safety limit; MFLPD (maximum fraction of linear power density) criterion

Electronics Cooling

Immersion cooling (mineral oil or fluorocarbon, e.g., 3M Novec 649): T_sat (Novec 649) = 49°C at 1 atm; q_max ≈ 60–120 kW/m² Nucleate boiling provides very high h = 2,000–10,000 W/(m²·K) at 10–30°C superheat IBM Summit: direct liquid immersion with nucleate boiling

CHF enhancement: Nanostructured surfaces: micropillar arrays → increased nucleation site density → higher q_max q_max enhancement of 2–3× over smooth surface with structured surfaces (Chu et al., MIT)

Standards and References

Source	Scope
Rohsenow (1951) Trans. ASME	Pool boiling correlation
Chen (1966) I&EC Process Des. Dev.	Flow boiling correlation
Zuber (1958) Trans. ASME	CHF prediction
Lienhard & Dhir (1973) ASME	CHF correlation for various geometries
Incropera et al. "Fundamentals of Heat and Mass Transfer"	Standard textbook reference
ASHRAE Handbook — Refrigeration	Boiling in refrigeration systems
Nuclear Regulatory Guide 1.76	Design limits for DNB in nuclear reactors

Output

Provide: fluid and operating conditions (fluid name; T_sat [°C]; P [kPa]; T_wall or q [kW/m²]), boiling mode (pool boiling saturated/subcooled; flow boiling), correlation used (Rohsenow/Chen/W-3) with C_sf or F/S factors, heat flux q [kW/m²] or T_wall [°C] (whichever specified), CHF from Zuber/Lienhard: q_max [kW/m²] at given conditions, margin to CHF = q/q_max [%], for flow boiling: G [kg/m²·s], x_quality, void fraction α, flow regime (bubbly/slug/annular), Chen correlation: h_mic [W/m²K], h_mac [W/m²K], h_total [W/m²K], ΔT_sat at given q [°C], DNB check (DNBR if applicable), ONB onset superheat [°C], surface enhancement if required, and applicable reference (Rohsenow 1951, Chen 1966, Zuber 1958, Lienhard 1973).