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Heat Transfer

Film Condensation on a Vertical Plate Simulator

Solve "film condensation" — saturated vapour condensing on a cooler vertical wall, forming a thin liquid film that drains down under gravity — with Nusselt theory. Change the fluid, saturation temperature, wall temperature and plate height to see the average heat transfer coefficient, film thickness, heat flux and condensation rate update in real time.

Parameters
Condensing fluid
Sets liquid density, conductivity, viscosity and latent heat
Saturation temperature T_sat
°C
Saturation temperature of the condensing vapour
Wall temperature T_w
°C
Surface temperature of the cooled plate
Plate height L
m
Vertical length of the plate on which vapour condenses
Results
—
Avg. h̄ (W/m²K)
—
Film thickness δ (mm)
—
Heat flux q (kW/m²)
—
Condensation rate (kg/m²·h)
—
Film Reynolds number Re
—
Subcooling ΔT (K)
—
Condensate film animation

Vapour condenses onto the cool wall and drains down as a liquid film. The film thickness δ(x) grows as x^(1/4) from top to bottom, and that film is the controlling resistance for vapour-to-wall heat transfer.

Film thickness δ vs height x
Average h̄ vs subcooling ΔT
Theory & Key Formulas

$$\bar h=0.943\left[\frac{\rho_l(\rho_l-\rho_v)g\,h_{fg}\,k_l^3}{\mu_l\,L\,\Delta T}\right]^{1/4}$$

Average heat transfer coefficient h̄ for laminar film condensation on a vertical plate (Nusselt theory). ρl, ρv: liquid and vapour density, g: gravity, hfg: latent heat, kl: liquid thermal conductivity, μl: liquid viscosity, L: plate height, ΔT = Tsat − Tw: subcooling. h̄ scales as ΔT and L each to the power −1/4.

$$\delta(L)=\left[\frac{4\mu_l k_l L\,\Delta T}{\rho_l(\rho_l-\rho_v)g\,h_{fg}}\right]^{1/4}$$

Condensate film thickness δ at the bottom edge (x = L). The film thickness grows as the 1/4 power of the height x from top to bottom.

$$q=\bar h\,\Delta T,\qquad Re=\frac{4\,\dot m\,L}{\mu_l}$$

Heat flux q and film Reynolds number Re (ṁ: condensation mass flux per area, q/hfg). The gravity-drained liquid film is the controlling resistance, and Nusselt theory assumes a laminar, gravity-drained film. When Re exceeds about 1800 the film becomes turbulent.

What is the Film Condensation on a Vertical Plate Simulator?

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Is "film condensation" the same thing as when the cold bathroom mirror fogs up with steam and streams of water trickle down it?
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Exactly that. When saturated vapour touches a wall colder than its saturation temperature, it condenses into liquid. That liquid covers the whole wall like a "film" and drains downward under gravity — that is film condensation. It happens in every heat exchanger that turns vapour back into liquid, from a power-plant condenser to an air-conditioner condenser. The vertical plate is the most basic model of it.
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I see. But if vapour just touches the wall and hands over its heat, that should transfer heat very well. Why do we need to calculate anything?
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Good question. The point is that what actually touches the wall is not the vapour but the liquid film. For heat to reach the wall from the vapour, it has to conduct through that film. The film is thin, but its thermal conductivity is not very high, so the film itself becomes the main thermal resistance. Roughly, h̄ ≈ kl/δ — a thinner film transfers heat better. On the left, bring the wall temperature T_w close to the saturation temperature to make the subcooling small, and you will see the film thin out and h̄ rise.
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Wait — so if I increase the subcooling and "cool it harder", the heat transfer coefficient actually drops?
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Yes, and that is the interesting part. A larger subcooling ΔT does increase the "heat flux q", but it also condenses more liquid and thickens the film. So the heat transfer per unit temperature difference — h̄ itself — falls as ΔT to the power −1/4. Look at the "h̄ vs subcooling" chart on the right: it is a gently downward-sloping curve. The plate height L behaves the same way; h̄ drops as L to the power −1/4, because on a tall wall the liquid piles up toward the bottom and thickens the film.
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So the film thickness really matters. Is the film the same thickness from top to bottom?
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No. At the very top the condensation has just started and the film is almost zero. Going downward, liquid arriving from above keeps merging in, so the film gets thicker. In Nusselt theory this film thickness δ(x) is proportional to the 1/4 power of the height x. That is why the upper part has a thin film and transfers heat well, while the lower part has a thick film and transfers heat poorly. In the animation you can see the wall thin at the top and bulging thick at the bottom edge.
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There is also a "film Reynolds number" in the results. What does that one tell us?
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It tells you whether the liquid film flow is laminar or turbulent. The draining film is a "flow" too, so you can characterise it with a Reynolds number. When Re exceeds about 1800 the film transitions to turbulent. A turbulent film mixes internally and transfers heat better, so the laminar Nusselt theory underpredicts the heat transfer coefficient. Tall condensers and high-subcooling operation tend to give turbulent films, and then you have to switch to a correlation that includes a turbulent correction.

Frequently Asked Questions

For laminar film condensation on a vertical plate, Nusselt theory gives the average heat transfer coefficient h̄ = 0.943·[ρl(ρl−ρv)g·hfg·kl³ /(μl·L·ΔT)]^(1/4). ρl and ρv are the liquid and vapour densities, g is gravity, hfg is the latent heat of vaporisation, kl is the liquid thermal conductivity, μl is the liquid viscosity, L is the plate height and ΔT = Tsat − Tw is the subcooling. This tool computes h̄ together with the film thickness δ, the heat flux q and the condensation rate.
Liquid that condenses on the wall drains down under gravity and forms a thin liquid film over the plate. For heat to reach the wall from the vapour, it must conduct through this film. Although the film is thin, its thermal conductivity is modest, so the film itself is the dominant thermal resistance. As a rule of thumb h̄ ≈ kl/δ, so a thinner film gives a higher heat transfer coefficient. That is why a small subcooling and a short plate, which keep the film thin, are favourable.
In Nusselt theory h̄ scales as ΔT to the power −1/4 and as plate height L to the power −1/4. A larger subcooling ΔT condenses more liquid and thickens the film, and a longer plate L lets liquid drained from above pile up so the film at the bottom is thicker. A thicker film means more thermal resistance, so h̄ falls. The film thickness δ(x) grows as the 1/4 power of the height x from top to bottom.
The condensate film Reynolds number Re = 4·ṁ·L/μl describes the state of the liquid film flow. When Re exceeds about 1800 the film transitions to turbulent flow. A turbulent film transfers heat better because of internal mixing, so the laminar Nusselt theory underpredicts the heat transfer coefficient. Tall condensers and large subcooling tend to produce turbulent films, and a correlation with a turbulent correction is then required.

Real-World Applications

Power-plant condensers: Steam leaving the turbine of a thermal or nuclear plant gives up its heat to the cooling water in the condenser, condenses, and returns as water to circulate back to the boiler. Film condensation occurs precisely on the condenser tube surfaces, and the thickness of the liquid film clinging to the tubes governs the heat exchange performance. Because it ties directly into the overall plant thermal efficiency, estimating the film-condensation heat transfer coefficient correctly is central to power-plant design.

HVAC and refrigeration condensers: In the condenser of an air conditioner or heat pump, compressed refrigerant vapour (such as R134a) condenses on air-cooled or water-cooled tube surfaces. Refrigerants have a smaller latent heat than steam and different liquid properties, so for the same subcooling the heat transfer coefficient and condensation rate change considerably. Switching the fluid in this tool lets you see that difference intuitively.

Distillation and evaporation equipment in chemical plants: In distillation-column reboilers and condensers, and in multiple-effect evaporators, solvent vapour or ammonia vapour condenses on heat transfer surfaces. Ammonia has a large latent heat and a high heat transfer coefficient, but its subcooling settings and material selection need care. Process design starts from the film-condensation theoretical value and then adds the effects of fouling factors and vapour velocity.

A reference benchmark for CAE and heat transfer analysis: Two-phase CFD analyses and heat-exchanger simulations that include condensation need a reference to check whether the result is physically reasonable. Nusselt theory is one of the few condensation problems with an analytical solution, and for the simple vertical-plate condition you can compare the tool value directly against the analysis. If a CFD result differs from this theoretical value by an order of magnitude, it is a sanity check that points to a phase-change-model or boundary-condition mistake.

Common Misconceptions and Pitfalls

The biggest pitfall is confusing film condensation with dropwise condensation. This tool deals with film condensation, where the liquid covers the wall as a uniform film. By contrast, on a wall that repels liquid (a hydrophobic surface), the condensate does not form a film but rolls off as countless small droplets — "dropwise condensation". Because most of the wall is not covered by a liquid film, dropwise condensation can have a heat transfer coefficient five to ten times that of film condensation. Nusselt theory is exclusively for film condensation and cannot be applied to dropwise condensation. A real condensing surface becomes wetted over time and usually settles into film condensation, so a conservative design uses film condensation.

Next, assuming that a larger subcooling improves condensation performance. A larger subcooling ΔT does increase the heat flux q = h̄·ΔT. But the heat transfer coefficient h̄ itself drops as ΔT to the power −1/4. In other words, "the more you cool it, the more efficiently heat transfers" is not true. Moreover, pushing the subcooling or the plate height too far makes the film Reynolds number exceed 1800 and the film transitions to turbulent, at which point the laminar Nusselt theory no longer holds. When this tool's verdict shows "turbulent", understand that the laminar-formula value is an underestimate and switch to a turbulent correlation.

Finally, treating the Nusselt-theory value as the real machine performance. Nusselt theory rests on idealisations: laminar flow, gravity drainage, negligible film inertia, no vapour shear stress and constant properties. In a real condenser, a high vapour velocity can drag the liquid film thinner and improve heat transfer, or instead make the film ripple and change its behaviour. And if non-condensable gas (such as air) leaks into the heat transfer surface, it accumulates near the wall and severely impedes condensation. The tool value is only an idealised starting point; in machine design always add corrections for vapour velocity, non-condensable gas, fouling and surface inclination.

How to Use

  1. Enter saturation temperature (T_sat) between 40–100°C for the condensing vapor; typical values are 80°C for steam at atmospheric pressure.
  2. Set wall temperature (T_w) below saturation to drive condensation; for example, T_w = 20°C creates a 60 K subcooling difference.
  3. Input vertical plate length (L) in meters, ranging 0.5–2.0 m typical for industrial heat exchangers.
  4. Click Calculate to solve the Nusselt film condensation equation and obtain heat transfer coefficient h̄, film thickness δ, heat flux q, and condensation rate.

Worked Example

Steam at T_sat = 85°C condenses on a vertical copper plate cooled to T_w = 25°C with length L = 1.2 m and width = 0.5 m. Water properties at mean film temperature: ρ = 990 kg/m³, c_p = 4180 J/kg·K, μ = 0.65 mPa·s, k = 0.67 W/m·K, h_fg = 2257 kJ/kg. The ΔT = 60 K subcooling yields h̄ ≈ 3200 W/m²·K, film thickness δ ≈ 0.18 mm at plate base, heat flux q ≈ 192 kW/m², and condensation rate ≈ 3.1 kg/m²·h with Re_f ≈ 285 in laminar regime.

Practical Notes

  1. Film Reynolds number Re_f below 30 confirms laminar condensate flow; above 1800 indicates turbulent entrainment and higher h̄ correlations apply—simulator handles transition automatically.
  2. Increasing subcooling (T_sat − T_w) dramatically improves h̄ and reduces δ; doubling ΔT from 30 K to 60 K increases h̄ by ~26% for identical geometry.
  3. Plate inclination affects gravity-driven flow; simulator assumes perfect vertical orientation—tilts reduce condensation rate by up to 40% depending on angle.
  4. Noncondensable gases (air) trapped at the surface degrade h̄ by 50–70%; ensure vapor purge in vacuum condenser designs below 1 bar absolute.