| 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
- Natural convection (ΔT_e < 5°C): q = h_conv × ΔT_e
- Nucleate boiling (5 < ΔT_e < ~30°C): q increases steeply, bubbles depart
- Critical heat flux (CHF) at ΔT_e ≈ 30°C: q_max (burnout)
- Film boiling (ΔT_e > ~120°C): vapor film insulates surface; q increases again (radiation dominates)
- 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].
