Engineering task and calculation objective
This module calculates film condensation of pure vapors on the outside of horizontal tubes according to Section J1 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019), the standard German reference work for heat transfer. On a horizontal tube the condensate forms a thin film draining around the circumference; because the drainage length corresponds to only half the circumference, the film stays thin and the heat transfer coefficient is significantly higher than on a vertical surface of the same size. This arrangement is therefore the standard case in horizontal shell-and-tube condensers.
In practice, this calculation is needed for the design of shell-side condensers in distillation plants, refrigeration systems, and power-plant condensers. Beyond the single tube, the VDI Heat Atlas treats the tube bundle: condensate draining from upper tube rows floods the tubes below, thickens the film there, and reduces their heat transfer — an effect captured via row-effect factors.
Anyone who wants to calculate condensation on horizontal tubes obtains from this module the mean heat transfer coefficient as the basis for the overall heat transfer calculation and for sizing the condenser surface — including a worked example.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Record the operating data and geometry: The saturated vapor state (pressure or condensation temperature), the wall or coolant temperature, the tube outside diameter, and — for the bundle — the tube layout and the number of tube rows stacked above one another are defined.
- Determine the condensate properties: Density, thermal conductivity, and viscosity of the condensate as well as the enthalpy of vaporization are evaluated at the governing film temperature — they enter the Nusselt correlation with different exponents.
- Calculate the heat transfer on the single tube: According to Nusselt's film condensation theory, the mean heat transfer coefficient on the single tube is determined from the density difference, gravity, enthalpy of vaporization, film thermal conductivity, viscosity, driving temperature difference, and tube diameter.
- Account for the bundle effect: For tube bundles, the flooding of the lower tube rows by condensate from the upper rows is captured via the row-effect factor; in addition it is checked whether the vapor velocity in the bundle produces a shear-induced improvement of the heat transfer.
- Carry the result into the equipment design: The mean condensation-side heat transfer coefficient is combined with the coolant-side heat transfer, the tube wall, and the fouling resistances into the overall heat transfer coefficient, from which the required condenser surface is determined.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube arrangement in-line or staggered? | versetzt | - |
| Number of tube rows | nRR | - |
| Tube outside diameter | do | m |
| Tube length | L | m |
| Condensate mass flow per tube | MF,R | kg/s |
| Dynamic viscosity | ηF | 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 |
| Heat of evaporation | Δhv | J/kg |
| Velocity of vapour | uD | m/s |
| Dynamic viscosity | ηD | mPa·s |
| Saturation temperature | ϑS | °C |
| Wall temperature | ϑW | °C |
| Correction factor for Nu number of tube rows | i | - |
| Number of tubes | nR | - |
| Condensate mass flow | MF | kg/s |
| Condensation | Bauform | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Characteristic length | LC | m |
| Trickle density | Γ | kg/(m·s) |
| Reynolds number | ReF | - |
| Reynolds number gas flow | ReGS | - |
| Nu number single tube | NuF,L | - |
| Mean heat transfer coefficient | αF,L | W/(m²·K) |
| Nu number horizontal tube rows | NuF,L,RR | - |
| Mean heat transfer coefficient | αF,L,RR | W/(m²·K) |
| Phase transition factor | Ph | - |
| Froude number | Fr | - |
| Parameter acc. Eq. 43 | G | - |
| Parameter acc. Eq. 43 | χ | - |
| Nusselt number of tube bundles | NuF,L,B | - |
| Heat transfer coefficient of tube bundle | αF,L,B | W/(m²·K) |
Calculation options
Tube arrangement in-line or staggered?
in-line · staggered
Condensation
Condensation around single tubes or tube rows, stationary vapour · Condensation on horizontal tube bundles with vapour flow
Worked example
Saturated steam (water) at 1.013 bar (ϑs = 100 °C) condenses on the outside of a horizontal tube with da = 25 mm. The tube wall temperature is 90 °C. Find the mean heat transfer coefficient according to Nusselt's film condensation theory and the transferred heat flux.
Given values
| Tube outside diameter da | 25 mm |
| 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
Heat transfer coefficient on the single tube
For the horizontal single tube, according to Nusselt:
αm = 0.728 · [ρl · (ρl − ρg) · g · Δhv · λl³ / (ηl · Δϑ · da)]1/4
Numerator: 958.4 · 957.8 · 9.81 · 2,257,000 · 0.677³ = 6.307 · 10¹²
Denominator: 282 · 10⁻⁶ · 10 · 0.025 = 7.05 · 10⁻⁵
αm = 0.728 · (8.945 · 10¹⁶)1/4 = 0.728 · 17,294 ≈ 12,590 W/(m²·K)
Heat flux
q̇ = αm · Δϑ = 12,590 · 10 ≈ 126 kW/m²
The comparison with the vertical wall at the same temperature difference shows the advantage of the horizontal arrangement: due to the short drainage length of the film (half the tube circumference instead of the wall height), the heat transfer coefficient is roughly twice as high.
Result
| Mean heat transfer coefficient αm | ≈ 12,590 W/(m²·K) |
| Heat flux q̇ | ≈ 126 kW/m² |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why is the heat transfer on a horizontal tube better than on a vertical wall?
Because the effective drainage length of the condensate film on a horizontal tube is only about half the circumference, the film stays thin and its conductive resistance small. In the Nusselt correlation, the tube diameter d takes the place of the wall height L under the fourth root — for typical dimensions this gives the tube heat transfer coefficients about 1.5 to 3 times higher. That is why condensers are preferably built with horizontal tube bundles.
How much does the tube bundle reduce the heat transfer?
Condensate from the upper tubes drips or runs onto the lower rows and thickens the film there; according to the classical Nusselt treatment, the mean over n stacked rows falls with n^(-1/4). In reality the reduction is smaller, because the impinging condensate stirs up the film and partly splashes off sideways — the VDI Heat Atlas therefore uses milder row factors. Staggered layouts are more favorable than in-line ones.
When can the influence of the vapor velocity no longer be neglected?
The pure gravity solution applies to nearly stagnant vapor. If the vapor flows across the bundle at appreciable velocity, it shears the condensate film, thins it out, and improves the heat transfer; at very high velocities it can entrain condensate. The VDI Heat Atlas provides shear-corrected correlations for this — relevant above all for vacuum condensers with large volume flows.
What happens when inert gases are present in the vapor?
Even a few percent of non-condensable gases accumulate at the phase interface and build up a diffusion resistance that can degrade the heat transfer by factors. The pure-fluid correlations of this module then no longer apply; the mixture or inert-gas calculation per Section J2 must be used, and an inert-gas vent must be provided in the design.