| name | condensation-film |
| description | Film condensation — Nusselt film theory, Chato correlation, condensate flooding, effect of vapor velocity, non-condensable gases, enhancement methods, tube vs. flat plate, TEMA condenser. |
| metadata | {"priority":7,"promptSignals":{"phrases":["film condensation","condensation heat transfer","Nusselt condensation","condensate film","laminar film condensation","vapor condensing"],"minScore":3}} |
Film Condensation Heat Transfer — Complete Skill
Nusselt Film Condensation Theory (Laminar)
Vertical Plate (Nusselt, 1916)
Local heat transfer coefficient:
h_x = [k³_L ρ_L (ρ_L - ρ_V) g h'_fg / (4 μ_L (T_sat - T_w) x)]^(1/4)
Average coefficient (over plate height L):
h̄ = 0.943 × [k³_L ρ_L (ρ_L - ρ_V) g h'_fg / (μ_L (T_sat - T_w) L)]^(1/4)
Variable definitions:
k_L = liquid thermal conductivity [W/(m·K)]
ρ_L, ρ_V = liquid and vapor densities [kg/m³]
g = 9.81 m/s²
h'_fg = modified latent heat = h_fg + 0.68 c_p_L (T_sat - T_w) [J/kg; accounts for subcooling]
μ_L = liquid dynamic viscosity [Pa·s]
T_sat - T_w = wall subcooling (driving force) [K or °C]
Nusselt number form:
Nu_L = h̄L/k_L = 0.943 × [Ja × Re_δ × Pr_L]^(1/4) [approximate; various forms exist]
Condensate film thickness:
δ = [4 μ_L k_L x (T_sat - T_w) / (g ρ_L (ρ_L - ρ_V) h'_fg)]^(1/4) [m]
Horizontal Cylinder (Condensation Outside)
Average h (Nusselt for horizontal tube):
h = 0.725 × [k³_L ρ_L (ρ_L - ρ_V) g h'_fg / (μ_L D ΔT)]^(1/4)
D = outer tube diameter; ΔT = T_sat - T_wall
Comparison to vertical plate:
h_horizontal ≈ 1.3 × h_vertical (for same L = tube length; horizontal is better)
Reason: shorter flow path per unit tube before flooding
Inside Tube (Chato Correlation — Laminar)
For stratified flow (gravity-driven condensation in horizontal tube):
h̄ = 0.555 × [k³_L ρ_L (ρ_L - ρ_V) g h'_fg / (μ_L D ΔT)]^(1/4)
Chato (1962) — most widely used for in-tube laminar condensation:
h_Chato = 0.555 × Nusselt-form × correction for void fraction and angle
Valid for: Reg < 35,000; gravity-dominated (low vapor velocity)
Alternative (Shah correlation): valid for wider Re range including annular flow
Shah (1979) correlation (in-tube):
h = h_L × [1 + 3.8 / (Z^0.95 × (1-x)^0.04)]^0.82 [h_L = Dittus-Boelter for all-liquid; Z = (1/x - 1)^0.8 × Pr_L^0.4]
x = quality (vapor mass fraction)
Valid: turbulent + laminar; vertical and horizontal
Effect of Vapor Velocity
Low vapor velocity (stagnant): Nusselt theory applies; film thickness increases with position → h decreases
Moderate vapor velocity (downward): vapor shear reduces film thickness → enhances h
High vapor velocity (upward): vapor retards film drainage → thickens film → reduces h; flooding possible
Akers-Deans-Crosser equivalent for in-tube:
G_eq = G_L + G_V × √(ρ_L/ρ_V) [equivalent mass flux for two-phase condensing flow]
h = 0.026 × Re_eq^0.8 × Pr_L^0.33 × k_L / D [forced convection correlation]
Transition from film to drop condensation:
For surface promoting drop condensation (hydrophobic coating, fluoropolymer): h → 10× film
Dropwise condensation: h = 300,000–600,000 W/(m²·K) vs. 10,000–30,000 W/(m²·K) film
Effect of Non-Condensable Gases
Non-condensable gas (air, N₂): accumulates at vapor-liquid interface; forms diffusion resistance layer
Degradation: even 1% air by mass → h reduced by 50–80%!
Analysis: mass transfer resistance in series with heat transfer
h_effective = 1 / (1/h_cond + δ_nc/(D_vg × ρ_nc)) [simplified; D_vg = diffusion coefficient of vapor in NC gas]
Prevention:
- Vacuum vent or purge to remove NC gas
- Vent at highest point (where NC gas accumulates)
- Minimum vent flow rate: ensures NC concentration < 0.5% by mass
Multi-Tube Bank (Outside Shell-and-Tube)
N-tube vertical row correction (Kern):
h_N = h_1 × N^(-1/4) [h for N tubes in vertical row below first; increasing film thickness]
For N = 4: h₄ = h₁ × 0.71 (30% reduction)
For N = 20: h₂₀ = h₁ × 0.47 (53% reduction)
Eissenberg correction (empirical, better than Kern):
h_N = h_1 × [1 - 0.2(N-1) × (4δ₁/D_o)^(3/4)]
TEMA condenser design:
Baffle cut for condensate drainage: vertical baffles not recommended for condensers (impede flow)
Use horizontal baffles with notches; or rod-type baffles (minimum blockage)
Nozzle for NC gas vent at top; condensate outlet at bottom
Enhanced Condensation
Low-fin tubes (19 fins/in or 26 fins/in):
h_o × 3–5× vs. smooth tube; fin effectiveness η_fin + area increase
Most common enhancement for shell-side condensation
Corrugated tubes:
Grooves or helical corrugation → promotes film thinning + mixing → h enhancement 1.5–3×
Flute/corrugated vertical tubes:
For vertical tube condensers; grooves drain condensate faster → thinner film → higher h
Practical Design
Heat flux from condensation:
q = h × (T_sat - T_wall) [W/m²]
q_max (laminar film): design for ΔT = 5–20°C; h typically 5,000–25,000 W/(m²·K)
Overall U (tube condenser):
1/U = 1/h_o + R_o_fouling + t_wall/k_wall + R_i_fouling + 1/h_i
h_i = coolant side HTC (Dittus-Boelter for turbulent water)
Pressure drop (condensing side):
ΔP_vapor ≈ ρ_V V²/2 × (L/D) × f [small; vapor flow velocity usually low in condenser]
Standards
| Standard | Scope |
|---|
| TEMA | Heat exchanger design; condensers classification (N,R,C type) |
| ASME VIII | Pressure vessel code for heat exchangers |
| ASME PTC-12.2 | Steam surface condenser test standard |
| HEI | Heat Exchange Institute; steam surface condenser standards |
Output
Provide: condensation configuration (vertical plate/horizontal tube/in-tube), ΔT driving force [°C], average film condensation coefficient h̄ [W/(m²·K)], modified latent heat h'_fg [kJ/kg], film Reynolds number (laminar < 30 check), NC gas correction factor (if present), multi-tube row correction for N rows, overall U [W/(m²·K)], required heat transfer area A [m²], condensate flow rate [kg/s], and applicable standard (TEMA, ASME PTC-12.2).
