pool-boiling

name	pool-boiling
description	Pool boiling heat transfer — boiling curve (Rohsenow, nucleate to film), critical heat flux (Zuber correlation, CHF), Leidenfrost point, boiling incipience (onset of nucleate boiling, ONB), surface effects (roughness, wettability, nanostructures), subcooled boiling, enhanced surfaces (fins, coatings, reentrant cavities), correlations (Rohsenow, Kutateladze, Zuber, Chen for flow boiling), heat transfer coefficient h [W/m²·K], and applications (electronics cooling, nuclear, refrigeration).
metadata	{"priority":7,"promptSignals":{"phrases":["pool boiling","nucleate boiling","boiling heat transfer","critical heat flux","Leidenfrost","boiling curve"],"minScore":3}}

Pool Boiling Heat Transfer — Complete Skill

Boiling Curve and Regimes

Nukiyama Boiling Curve

Complete boiling curve (q vs. ΔT_sat = T_wall - T_sat):

Regime	ΔT_sat range	Mechanism	q range
Natural convection	< 5°C	Single-phase free convection	Low
Partial nucleate boiling	5–10°C	Isolated bubbles at nucleation sites	Rising
Fully developed nucleate boiling	10–30°C	Dense bubble columns, strong agitation	Peak (CHF)
Transition boiling	30–120°C	Unstable film/nucleate; q decreases with ΔT	Decreasing
Film boiling	> 120°C	Stable vapor film; radiant + conductive	Rising again
Leidenfrost point	~120°C	Minimum film boiling; vapor film just stable	q_min

Critical Heat Flux (CHF): maximum of boiling curve; beyond → film boiling → burnout risk Leidenfrost temperature T_Leidenfrost: minimum film boiling temperature; stable vapor film below this → transitions to nucleate

Onset of Nucleate Boiling (ONB)

Incipience Criterion

Bergles-Rohsenow criterion: Active nucleation sites: r_crit = √(2 × σ × T_sat / (q_wall × h_fg × ρ_v)) [minimum active cavity radius]

Wall superheat for incipience: ΔT_sat,inc = (T_wall - T_sat) at which the largest available cavity begins nucleating ΔT_sat,inc = 2 × σ × T_sat × q_wall / (k_l × h_fg × ρ_v) [first approximation; substituting h = q/ΔT]

Practical ONB: For water at atmospheric pressure: ΔT_sat,inc ≈ 3–5°C for a commercial surface For refrigerants (lower σ): ΔT_sat,inc ≈ 1–3°C

Nucleate Boiling Correlations

Rohsenow Correlation

Most widely used nucleate boiling correlation: q = μ_l × h_fg × [g(ρ_l - ρ_v)/σ]^(1/2) × [c_p,l × ΔT_sat / (C_sf × h_fg × Pr_l^r)]³

Rearranged for h (or ΔT_sat from q): ΔT_sat = C_sf × h_fg × Pr_l^r / c_p,l × [q / (μ_l × h_fg × (g(ρ_l-ρ_v)/σ)^(1/2))]^(1/3)

C_sf (surface-fluid combination constant):

Surface-Fluid	C_sf	r
Water-copper (polished)	0.0130	1.0
Water-stainless (mechanically polished)	0.0080	1.0
Water-brass	0.0060	1.0
R-134a-copper	0.0065	1.7
Benzene-chromium	0.0100	1.7

Properties evaluated at T_sat; ρ_v, ρ_l, σ, h_fg, μ_l, c_p,l, Pr_l all at saturation

Example (water-copper, P = 1 atm, q = 300 kW/m²): Properties at 100°C: ρ_l = 958, ρ_v = 0.60 kg/m³, σ = 0.0589 N/m, h_fg = 2,257 kJ/kg, μ_l = 2.82×10⁻⁴ Pa·s, c_p,l = 4,215 J/kg·K, Pr_l = 1.75 [g(ρ_l-ρ_v)/σ]^(1/2) = [9.81×957.4/0.0589]^(1/2) = 399 m^(-1/2)·s^(-1/2) Numerator: 2.82×10⁻⁴ × 2.257×10⁶ × 399 = 254,000 W/m² [q/254,000]^(1/3) = [1.18]^(1/3) = 1.057 ΔT_sat = 0.0130 × 2,257,000 × 1.75^1.0 / 4,215 × 1.057 = 0.0130 × 2,257 × 1.75 / 4.215 × 1.057 ≈ 14.5°C h = q/ΔT_sat = 300,000/14.5 = 20,700 W/(m²·K)

Stephan-Abdelsalam (Alternative)

For water (1977 correlation): Nu_boiling = 0.0546 × (ρ_v/ρ_l)^(0.45) × (q×D_b/(k_l×T_sat))^0.67 × (h_fg×D_b²/(α_l²))^(0.57) × (D_b × g × ρ_l/(σ))^0.22 D_b = bubble departure diameter = 0.0208 × θ × [σ/(g(ρ_l-ρ_v))]^(1/2) [θ = contact angle in radians]

Critical Heat Flux (CHF)

Zuber Correlation

Hydrodynamic CHF model (flat horizontal surface): q_CHF = K × h_fg × ρ_v × [σ × g × (ρ_l - ρ_v) / ρ_v²]^(1/4) K = π/24 ≈ 0.131 [Zuber; theoretically derived from Helmholtz instability of vapor jets] Or K = 0.149 [Kutateladze empirical; better agreement with data]

Simplified form: q_CHF = 0.131 × h_fg × ρ_v × [σ × g × (ρ_l - ρ_v) / ρ_v²]^(1/4)

Example (water at 1 atm): q_CHF = 0.131 × 2,257,000 × 0.60 × [0.0589 × 9.81 × 957.4 / 0.36]^(1/4) = 0.131 × 2,257,000 × 0.60 × [1,530]^(0.25) = 177,000 × 6.25 = 1.11 MW/m² [≈ 1.0 MW/m² typical for water at atmospheric; matches data]

CHF enhancement: Roughened/porous surfaces: CHF × 2–3 vs. smooth Subcooled liquid: q_CHF,sub = q_CHF,sat × (1 + A × Ja_sub) [Ja_sub = c_p(T_sat-T_bulk)/h_fg; A ≈ 0.1–0.3] Orientation: horizontal flat surface maximum; vertical surface CHF ≈ 0.9× horizontal

Kutateladze Correlation

Empirical form: q_CHF = 0.149 × h_fg × ρ_v × [σ × g × (ρ_l - ρ_v) / ρ_v²]^(1/4) Slightly higher K = 0.149; matches more datasets

Effect of pressure: q_CHF peaks at P/P_cr ≈ 0.32 (reduced pressure); decreases at very high or very low pressure For water: maximum CHF near 70 bar; q_CHF,max ≈ 4–5 MW/m²

Film Boiling

Bromley Correlation (Film Boiling, Horizontal Cylinder)

Heat transfer coefficient: h_film = 0.62 × [k_v³ × ρ_v × (ρ_l - ρ_v) × g × h_fg' / (μ_v × D × ΔT_sat)]^(1/4) h_fg' = h_fg + 0.4 × c_p,v × ΔT_sat [corrected latent heat; vapor sensible heat] D = heater diameter; evaluate vapor properties at T_film = (T_wall + T_sat)/2

Radiation contribution: At very high wall temperatures (T_wall > 300°C above T_sat): add radiation h_total = h_film + (3/4) × h_rad [not simply additive; coupling factor 3/4] h_rad = ε_w × σ_SB × (T_wall⁴ - T_sat⁴) / (T_wall - T_sat)

Enhanced Surfaces

Enhancement Techniques

Micro/nano-structured surfaces: Wettability: superhydrophilic (θ < 5°) → CHF increase to 2× baseline; delayed transition to film boiling Microporous coatings (sintered particles): h_nucleate × 3–5 vs. smooth; CHF × 1.5–2 Re-entrant cavities (Thermoexcel, High Flux): guaranteed nucleation sites; h × 3–8 × smooth

Micro-fin surfaces (Turbo-B, Turbo-E): Surface area increase + enhanced nucleation → h × 2–5 vs. plain tube Used in refrigeration evaporators, process reboilers

Nanoparticle suspensions (nanofluids): Al₂O₃, TiO₂, CNT in water: CHF increase 10–50% at low concentration (0.01–0.1 vol%) h_nucleate: mixed results; often decreases at higher concentrations (surface fouling)

Flow Boiling (Chen Correlation)

Saturated Flow Boiling in Tubes

Chen correlation: h_tp = S × h_pool + F × h_l [superposition of nucleate and forced convection contributions] h_l = Dittus-Boelter: 0.023 × Re_l^0.8 × Pr_l^0.4 × k_l/D [liquid-only forced convection] h_pool = Rohsenow correlation at local heat flux F = Reynolds number factor = f(1/X_tt) [two-phase multiplier; from Chen chart] S = suppression factor (0–1): reduces nucleate boiling contribution in forced convection X_tt = Martinelli parameter: (x/(1-x))^0.9 × (ρ_l/ρ_v)^0.5 × (μ_v/μ_l)^0.1

Applicable range: Saturated nucleate boiling regime; quality x = 0–0.7; vertical upward tubes

Standards and References

Standard	Scope
ASHRAE Fundamentals Handbook	Boiling and condensation correlations
Rohsenow (1951)	Original nucleate boiling correlation
Zuber (1958)	Hydrodynamic CHF theory
Lienhard & Dhir (1973)	Extended CHF correlations and geometry effects
Bergles & Rohsenow (1964)	Onset of nucleate boiling criterion
ASME HTD-97	Two-phase flow and heat transfer

Output

Provide: fluid and conditions (P [bar]; T_sat [°C]; subcooling ΔT_sub [°C]; geometry), heater geometry (horizontal/vertical plate, cylinder, tube; characteristic dimension D or L [m]), regime identification (natural convection/nucleate/CHF/film boiling from ΔT_sat [°C]), Rohsenow h_nucleate [W/m²·K] and ΔT_sat [°C] at given q [W/m²] (with C_sf, r values stated), CHF from Zuber/Kutateladze [MW/m²] (enhancement factor if textured surface), Leidenfrost ΔT_sat [°C] and q_min [kW/m²], film boiling h [W/m²·K] (Bromley; include radiation if T_wall >> T_sat), safety margin (q_operating / q_CHF; target ≥ 1/2 for electronics, ≥ 1/3 for nuclear), enhancement recommendation (if h insufficient: microporous coating; fin; nanostructure; expected improvement factor), flow boiling correction (if relevant: Chen F and S factors; h_tp [W/m²·K]), and applicable reference (Rohsenow 1951, Zuber 1958, Chen 1966, ASHRAE Handbook).