condensation-film

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).