Engineering task and calculation objective
This module calculates film condensation of pure vapors on vertical surfaces and tubes according to Section J1 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019), the standard German reference work for heat transfer. The basis is Nusselt's classical film condensation theory: the vapor condenses on the cold wall, the condensate runs off as a closed, gravity-driven film, and the thermal resistance of that film determines the heat transfer coefficient. The module evaluates local quantities along the run length — condensate loading per unit width, film Reynolds number, laminar and turbulent Nusselt numbers — and from these the local heat transfer coefficient.
This calculation is needed for the design of condensers with vertical tubes or plates, of falling-film condensers, and for re-rating vessel walls on which vapor condenses. Anyone who wants to calculate film condensation must in particular capture the transition from the laminar, wavy film to the turbulent film, because there the trend reverses: for the laminar film the heat transfer decreases with growing film thickness, whereas for the turbulent film it rises again with the film Reynolds number.
The VDI Heat Atlas covers both regimes with a continuous interpolation and additionally accounts for the waviness of the film surface as well as property corrections via the temperature drop across the film.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Determine the condensate loading and film Reynolds number: The local film Reynolds number is formed from the condensate mass flow per unit width arriving at the surface (local condensate loading) and the dynamic viscosity of the condensate — it characterizes the flow state of the draining film.
- Calculate the laminar Nusselt number: Using the characteristic length of the film (formed from viscosity and gravity), the local laminar Nusselt number is calculated according to Nusselt's film condensation theory; the waviness correction increases the value compared with the smooth film.
- Calculate the turbulent Nusselt number: In parallel, the local turbulent Nusselt number is determined from the film Reynolds number and the Prandtl number of the condensate; it grows with increasing condensate loading.
- Superimpose the regimes and apply corrections: The laminar and turbulent contributions are combined according to the interpolation rule of the VDI Heat Atlas into the local Nusselt number without shear stress influence; correction factors capture the temperature-dependent fluid properties in the film and, where applicable, the surface condition.
- Evaluate the heat transfer coefficient: The local heat transfer coefficient follows from the Nusselt number; integration over the run length yields the mean value for sizing the condenser surface.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Local trickle density | Γx,e | kg/(m·s) |
| Local mass flow of condensate | MF,x | kg/s |
| Condensate mass flow | MF,L | kg/s |
| Tube inside diameter | di | m |
| Dyn. viscosity | ηF | mPa·s |
| Dyn. viscosity | ηW | mPa·s |
| Density | ρF | kg/m³ |
| Thermal conductivity | λF | W/(m·K) |
| Specific heat capacity | cpF | J/(kg·K) |
| Kinematic viscosity | νF | m²/s |
| Prandtl number | PrF | - |
| Density | ρD | kg/m³ |
| Characteristic length | L | m |
| Local Reynolds number of film | ReF,x | - |
| Correction for rippling | fwell | - |
| Correction factor | fη | - |
| Local Nu number, laminar | NuF,x,l | - |
| Local Nu number, turbulent | NuF,x,t | - |
| Local Nu number (without shear) | NuF,x | - |
| Local heat transfer coefficient | αF,x | W/(m²·K) |
| Velocity of vapour | uD | m/s |
| Velocity of liquid phase | uF | m/s |
| Dyn. viscosity | ηD | mPa·s |
| Hydraulic diameter | dh | m |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Local trickle density | Γx,e | kg/(m·s) |
| Trickle density | ΓL | kg/(m·s) |
| Characteristic length | L | m |
| Local Reynolds number of film | ReF,x | - |
| Reynolds number | ReF,L | - |
| Correction for rippling | fwell | - |
| Correction factor | fη | - |
| Local Nu number, laminar | NuF,x,l | - |
| Local Nu number, turbulent | NuF,x,t | - |
| Local Nu number (without shear) | NuF,x | - |
| Nu number, laminar | NuF,l | - |
| Nu number, turbulent | NuF,t | - |
| Nu number | NuF | - |
| Local heat transfer coefficient | αF,x | W/(m²·K) |
| Heat transfer coefficient | αF | W/(m²·K) |
| Local Nu number | Nu+F,x | - |
| Heat transfer coefficient | α+F,x | W/(m²·K) |
| Tube length | l | m |
| Mean overall heat transfer coefficient | k | W/(m²·K) |
| Pressure drop | Δp | Pa |
| Local Nu number | Nu+F,x | - |
| Heat transfer coefficient | α+F,x | W/(m²·K) |
| Overall heat transfer coefficient | kx | W/(m²·K) |
| Overall heat transfer coefficient | kx | W/(m²·K) |
Calculation options
Flow direction of vapour:
Vertical downward (cocurrent flow from vapour and condensate) · Vertical upwards (countercurrent flow from vapour and condensate)
Condensation
in the tubes · around the tubes
Condensation
Local heat transfer coefficient · Mean heat transfer coefficient, stationary vapour · Film condensation in vertical tubes, flowing vapour
Worked example
Saturated steam (water) at 1.013 bar (ϑs = 100 °C) condenses on a vertical wall of height L = 1.5 m. The wall temperature is 90 °C. Find the mean heat transfer coefficient of the laminar condensate film according to Nusselt's film condensation theory, and check the film Reynolds number.
Given values
| Wall height L | 1.5 m |
| Saturation temperature ϑs | 100 °C |
| Wall temperature ϑW | 90 °C (Δϑ = 10 K) |
| Condensate density ρl (100 °C) | 958.4 kg/m³ |
| Vapor density ρg | 0.598 kg/m³ |
| Thermal conductivity λl | 0.677 W/(m·K) |
| Dynamic viscosity ηl | 282 · 10⁻⁶ Pa·s |
| Enthalpy of vaporization Δhv | 2,257 kJ/kg |
Solution
Mean heat transfer coefficient according to Nusselt
For the laminar film on the vertical wall:
αm = 0.943 · [ρl · (ρl − ρg) · g · Δhv · λl³ / (ηl · Δϑ · L)]1/4
Numerator: 958.4 · 957.8 · 9.81 · 2,257,000 · 0.677³ = 6.307 · 10¹² W³/(m⁵·K³)·kg/s³ (numerical value)
Denominator: 282 · 10⁻⁶ · 10 · 1.5 = 4.23 · 10⁻³
αm = 0.943 · (1.491 · 10¹⁵)1/4 = 0.943 · 6,214 ≈ 5,860 W/(m²·K)
Heat flux and condensate rate
q̇ = αm · Δϑ = 5,860 · 10 ≈ 58.6 kW/m²
Condensate loading at the lower edge: Γ = q̇ · L / Δhv = 58,600 · 1.5 / 2,257,000 ≈ 0.039 kg/(m·s)
Check of the film Reynolds number
Re = Γ / ηl = 0.039 / 282 · 10⁻⁶ ≈ 138
The film is wavy-laminar (Re < 400); the laminar calculation is admissible. The waviness correction of the VDI Heat Atlas would raise the heat transfer coefficient by a few percent more — the hand calculation is therefore on the safe side.
Result
| Mean heat transfer coefficient αm | ≈ 5,860 W/(m²·K) |
| Heat flux q̇ | ≈ 58.6 kW/m² |
| Film Reynolds number | ≈ 138 (wavy-laminar) |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
At what point does the condensate film become turbulent?
The governing quantity is the film Reynolds number formed from condensate loading and viscosity. Up to about Re ≈ 30 the film is smooth-laminar, above that wavy-laminar; the transition to turbulence lies at about Re ≈ 400. The VDI Heat Atlas does not assume an abrupt switch but superimposes the laminar and turbulent contributions, so the transition region is represented continuously.
Why does a long run length degrade the heat transfer — and when does it not?
In the laminar regime the film thickness grows with run length, the conductive resistance of the film increases, and the local heat transfer coefficient falls. If the film becomes turbulent, however, cross-mixing improves the heat transport and the coefficient rises again with further increasing condensate loading. At high Prandtl numbers a tall vertical surface can therefore even perform better than expected.
What assumptions underlie Nusselt's film condensation theory?
Pure, stagnant saturated vapor, a closed laminar condensate film, complete wetting, constant wall temperature, and negligible shear stress of the vapor on the film surface. If the vapor flows at appreciable velocity, the shear stress influence must additionally be accounted for; inert gas fractions reduce the heat transfer drastically and require the mixture calculation per Section J2.
Can I also use the correlation for vertical tubes?
Yes — as long as the tube diameter is large compared with the film thickness, the flat-plate treatment also applies to the inside or outside of vertical tubes. For condensation inside the tube it must additionally be checked whether the vapor flow shears the film (shear stress influence) and whether the condensate can drain freely.