Condensation Heat Transfer: Nusselt Film Theory, Dropwise & Condenser Design

Introduction to Condensation

Condensation — the phase change from vapour to liquid at a cooled surface — achieves extraordinarily high heat-transfer coefficients (h = 5 000–100 000 W/m²·K). Unlike boiling, where vapour generation resists heat removal, condensation deposits latent heat directly at the cooled wall through a thin liquid film. This makes condensers among the most compact process heat exchangers possible.

The two primary condensation modes are filmwise condensation (the norm for clean engineering surfaces) and dropwise condensation (the exception, requiring specially treated non-wetting surfaces). Filmwise condensation produces a continuous liquid film; dropwise condensation forms discrete droplets that roll off, exposing fresh surface. Dropwise condensation achieves h values up to 10× higher than filmwise but is difficult to maintain reliably in industrial service.

Nusselt Film Condensation Theory

Nusselt (1916) derived an analytical solution for laminar filmwise condensation on a vertical isothermal plate. The liquid film grows in thickness δ as it flows downward under gravity, increasing its conductive resistance. The key result for the local heat-transfer coefficient at position x from the top:

where h_fg* = h_fg + 0.375 c_p,l ΔT is the modified latent heat accounting for subcooling of the condensate film, and ΔT = T_sat − T_s.

Integrating over a vertical surface of height L gives the average heat-transfer coefficient:

This is the Nusselt equation — the foundation of all condenser design in process engineering. Despite its derivation assuming a laminar film, it remains accurate for many practical applications with appropriate corrections.

Condensation on Horizontal Tubes

Nusselt also derived the average coefficient for filmwise condensation on the outside of a single horizontal cylinder of outer diameter d_o:

The 0.725 vs 0.943 coefficient reflects the difference in film flow path — the film runs around the tube circumference rather than straight down a plate.

Tube Bundle Effect

In a shell-and-tube condenser with N_t horizontal tubes in a vertical row, condensate from upper tubes inundates lower tubes, thickening the film and reducing h. The Kern correction for N_t tubes in a vertical tier:

For example, with N_t = 16 rows:

The bundle h is only 64.5% of the single-tube value — a significant penalty in multi-row bundles. Design solutions include: using smaller tubes (higher h), using tubes with horizontal grooves to drain condensate sideways, or selecting vertical orientation where inundation is avoided.

Worked Example: Steam Condenser

Given: Steam condenses at 60°C (P_sat = 19.9 kPa) on the outside of horizontal 19.05 mm OD (d_o = 0.01905 m) carbon steel tubes cooled by cooling water. T_s = 45°C (wall temperature). Single row of tubes. Find h_condensation.

Fluid properties at film temperature T_film = (60 + 45)/2 = 52.5°C:

• ρ_l = 986 kg/m³, ρ_v = 0.130 kg/m³
• k_l = 0.644 W/m·K
• μ_l = 5.06 × 10⁻⁴ Pa·s
• h_fg = 2 357 kJ/kg (at 60°C)
• c_p,l = 4 183 J/kg·K

Modified latent heat (ΔT = 60 − 45 = 15°C):

Nusselt horizontal tube equation:

This high coefficient (nearly 60 000 W/m²·K) confirms why the condensing side is rarely the controlling resistance in steam condensers — the tube-side cooling water h (typically 5 000–12 000 W/m²·K) controls the overall U.

Turbulent Film Condensation

The Nusselt theory assumes a laminar condensate film. As the film thickens (long vertical surfaces, high flow rates), turbulence develops. The transition Reynolds number for the condensate film:

where Γ = condensate mass flow rate per unit width of tube [kg/m·s]. Turbulence onset at Re_film ≈ 1 800 (some sources use 1 600). Above this, h actually increases with film thickness because turbulent mixing enhances heat transport through the film:

For tall vertical condensers (L > 1 m for steam at moderate pressures), the Grober/Labuntsov turbulent correction applies to the lower portion of the tube, increasing average h by 20–40% over the laminar Nusselt prediction.

Filmwise vs Dropwise Condensation

Standard engineering practice: size condensers for filmwise condensation regardless of intended promoter use, because dropwise performance cannot be guaranteed over equipment lifetime.

Non-Condensable Gases (NCG): The Silent Condenser Killer

Even small amounts of non-condensable gas (air, nitrogen, CO₂) in a condenser can severely degrade performance. NCGs accumulate in the vapour space because they do not condense; the condensable vapour must diffuse through the NCG boundary layer to reach the cold surface. This introduces a mass-transfer resistance in addition to the thermal resistance:

• 1% air by mass in steam reduces h by 50–60%
• 5% air reduces h by >90%

Design mitigations:

1. Vent connection: Locate NCG vent at the coolest point in the vapour space where NCGs accumulate (usually the outlet end of the condenser).
2. Vacuum systems: Steam jets or liquid ring vacuum pumps continuously withdraw NCG-rich vapour. Size based on expected air in-leakage (HEI Standards).
3. Condenser orientation: Horizontal shell condensers with vapour flowing across tube bundles allow better NCG sweeping than vertical units.
4. Operating margin: Add 30–50% extra area when NCG concentration is uncertain or variable (e.g., atmospheric condensers on columns with vent connections).

Subcooling of Condensate

In many designs, liquid condensate must be subcooled before leaving the condenser (e.g., to prevent flashing in the condensate return line). Subcooling can be achieved by:

• Extended condensing section: Allow condensate to pool in the shell below the tube bundle and be subcooled by the tube-side cooling fluid.
• Separate subcooler: A second small heat exchanger downstream of the condenser dedicated to subcooling.
• Integral subcooler: TEMA configuration with an internal weir in the shell (KET type) creating a pool of liquid condensate over part of the tube bundle.

Subcooler heat duty: Q_sub = ṁ_cond c_p,l ΔT_sub. Use single-phase convection h on the condensate side, typically 500–2 000 W/m²·K depending on liquid viscosity and velocity.

Horizontal vs Vertical Condenser Orientation

Condenser Design Checklist

1. Identify condensing duty Q, vapour inlet flow, composition, and pressure.
2. Determine condensing temperature range (for mixtures: dew point to bubble point).
3. Calculate condensing-side h using Nusselt horizontal or vertical equation.
4. Apply tube bundle inundation correction (Kern, N_t^-0.167).
5. Compute tube-side cooling water h (Dittus-Boelter) and add TEMA fouling resistances.
6. Calculate overall U and required area A = Q / (U × LMTD).
7. Check NCG: if present, increase area by 30–50% or specify vacuum venting system.
8. Design condensate drain to prevent flooding (condensate level should not cover tubes).
9. Specify NCG vent nozzle location and size vacuum system if below atmospheric pressure.

Try the Calculator

Use the Heat Transfer Coefficient Calculator panel to compute your condenser's overall U — enter the condensing h (from Nusselt equation), cooling-water h, wall conductance, and fouling resistances to get the complete thermal picture.