boiling-condensation

name	boiling-condensation
description	Boiling and condensation heat transfer — pool boiling Rohsenow, nucleate boiling, critical heat flux (Zuber), film boiling, flow boiling Chen correlation, Nusselt film condensation.
metadata	{"priority":7,"promptSignals":{"phrases":["boiling","condensation","Rohsenow","nucleate boiling","critical heat flux","film boiling","Nusselt condensation"],"minScore":3}}

Boiling and Condensation — Complete Skill

Pool Boiling

Boiling Curve

1. Natural convection (ΔT_e < 5°C): q = h_conv × ΔT_e
2. Nucleate boiling (5 < ΔT_e < ~30°C): q increases steeply, bubbles depart
3. Critical heat flux (CHF) at ΔT_e ≈ 30°C: q_max (burnout)
4. Film boiling (ΔT_e > ~120°C): vapor film insulates surface; q increases again (radiation dominates)
5. Leidenfrost point at q_min ≈ 20-25°C above q_max ΔT

Rohsenow Correlation (Nucleate Pool Boiling)

q_s = μ_l h_fg [g(ρ_l - ρ_v)/σ]^0.5 × [c_p,l ΔT_e / (C_sf h_fg Pr_l^n)]^3

ΔT_e = T_s - T_sat (excess temperature) h_fg = latent heat [J/kg] σ = surface tension [N/m] C_sf, n = surface-fluid combination constants: Water/polished copper: C_sf = 0.0130, n = 1.0 Water/stainless: C_sf = 0.0060, n = 1.0 Water/brass: C_sf = 0.0060, n = 1.0 Benzene/chromium: C_sf = 0.0100, n = 1.7

Rearranged for surface temperature (given q): ΔT_e = ... (implicit, solve iteratively or by substitution)

Critical Heat Flux (Zuber, 1958)

q_max = C_cr × h_fg ρ_v [σ g (ρ_l - ρ_v) / ρ_v²]^0.25 C_cr = π/24 ≈ 0.131 (horizontal flat surface)

Water at 1 atm: q_max ≈ 1.26 MW/m² At higher pressures (closer to critical point): q_max decreases

Hydrodynamic stability: Rayleigh-Taylor instability of vapor columns determines CHF

Minimum Heat Flux (Zuber)

q_min = 0.149 h_fg ρ_v [σ g (ρ_l - ρ_v) / (ρ_l + ρ_v)²]^0.25

Film Boiling (Bromley, horizontal cylinder)

h_D = C_br [k_v³ ρ_v (ρ_l - ρ_v) g h_fg' / (μ_v D ΔT_e)]^0.25 + h_rad h_fg' = h_fg + 0.8 c_p,v ΔT_e (corrected for vapor superheat) C_br = 0.62 (horizontal cylinder), 0.67 (vertical plate) h_rad = εσ_SB (T_s⁴ - T_sat⁴)/(T_s - T_sat) ≈ 0-30% of total for typical metals

Flow Boiling

Chen Correlation (Saturated Flow Boiling, Vertical Tube)

h_tp = h_NB × S + h_conv × F

h_NB (nucleate boiling): Forster-Zuber equation modified S = suppression factor = 1/(1 + 2.53×10⁻⁶ Re_TP^1.17) [S = 0 at high Re, NB suppressed]

h_conv (forced convection): Dittus-Boelter for all liquid flowing at G_total h_L = 0.023 Re_L^0.8 Pr_L^0.4 k_L/D F = enhancement factor = f(X_tt): F = 1/(X_tt < 0.10: turbulent; step function) For X_tt < 0.1: F = 2.35(1/X_tt + 0.213)^0.736

Critical Heat Flux in Flow Boiling

Departure from nucleate boiling (DNB) or dryout (annular film) DNB: subcooled or low quality; high heat flux; sudden surface temperature rise Dryout: high quality; gradual film thinning; more gradual temperature rise

Film Condensation (Nusselt Theory)

Vertical Plate/Tube (Laminar Film)

Local: h_x = [ρ_l(ρ_l-ρ_v)g k_l³ h_fg / (4 μ_l (T_sat - T_s) x)]^0.25 Average over L: h̄ = 0.943 [ρ_l(ρ_l-ρ_v)g k_l³ h_fg / (μ_l (T_sat - T_s) L)]^0.25

h_fg' = h_fg + 0.68 c_p,l (T_sat - T_s) (Rohsenow correction for subcooling)

Turbulent condensate (Re_δ > 1800): h̄ = 0.003 Re_δ^0.4 Pr_l^0.65 (k_l/μ_l^(2/3)) × [g/ν_l²]^(1/3) (Labuntsov correlation)

Horizontal Tube (Outer Surface)

h̄ = 0.725 [ρ_l(ρ_l-ρ_v)g k_l³ h_fg' / (μ_l (T_sat - T_s) D)]^0.25 Typically 20-30% higher than vertical tube of same length

Dropwise Condensation

Occurs on non-wettable surfaces (contact angle > 90°); coatings (PTFE, promoters) h ≈ 5-10× higher than film condensation Difficult to maintain in long-term service (surface contaminates); not used for design basis

Output

Provide: q_s [W/m²] or ΔT_e [°C], h_boiling or h_condensation [W/m²K], q_max (CHF) [W/m²], flow boiling h_tp [W/m²K], boiling regime identification (nucleate/film/flow), surface temperature T_s [°C].