Engineering task and calculation objective
The module calculates heat transfer on vertical falling films according to chapter M3 of the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). A falling film is a thin, gravity-driven liquid film flowing down a vertical wall or the inside or outside of vertical tubes. The module determines the film thickness, flow regime and the heat transfer coefficient between wall and film — both for pure heating or cooling and for evaporation at the film surface, up to the onset of nucleate boiling in the film.
Falling film apparatus is widespread in process engineering wherever temperature-sensitive or viscous media must be treated gently with short residence times: falling film evaporators in the food, pulp and chemical industries, concentration of solutions, falling film coolers and absorbers. To calculate heat transfer in a falling film evaporator, one must distinguish between laminar, wavy and turbulent films, because the governing relationships change with the film Reynolds number.
The calculation is based on Nusselt's film theory with the extensions of the VDI Wärmeatlas for wavy and turbulent films and for evaporation at the phase interface.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Determine wetting rate and film Reynolds number: From the liquid mass flow rate and the wetted perimeter, the wetting rate (mass flow per unit width) is formed. With the dynamic viscosity, the film Reynolds number follows, which defines the flow regime of the film.
- Classify the flow regime of the film: Based on the Reynolds number, a distinction is made between smooth laminar, wavy laminar and turbulent films. Waves on the film surface already appear at small Reynolds numbers and improve heat transfer compared with the smooth Nusselt solution.
- Calculate the film thickness: For the laminar film, Nusselt's falling film theory gives the film thickness from the balance of gravity and wall shear stress; in the turbulent regime, empirical extensions apply. The film thickness is also the characteristic length of the problem.
- Determine the heat transfer coefficient: Depending on the selected option, heat transfer is calculated for heating/cooling without phase change or for evaporation at the film surface. The dimensionless relationship links the Nusselt number of the film with the Reynolds and Prandtl numbers; at high heat flux densities, the onset of nucleate boiling in the film is additionally checked.
- Check wetting and operating limits: Finally, it is checked whether the wetting rate lies above the minimum wetting rate so that the film does not break up, and whether film overheating or local dry-out is imminent — both limit the permissible operating range of a falling film apparatus.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Wetted perimeter | l | m |
| Tube length | L | m |
| Mass flow | Ṁ | kg/s |
| Density | ρ | kg/m³ |
| Kinematic viscosity | ν | m²/s |
| Dynamic viscosity | η | mPa·s |
| Dynamic viscosity (wall) | ηw | mPa·s |
| Prandtl number | Pr | – |
| Thermal conductivity | λ | W/(m·K) |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Area | A | m² |
| Wall temperature (in) | ϑW,e | °C |
| Factor | (Nu5) C∞ | – |
| Factor | (Nu6) C0 | – |
| Boiling point | ϑS | °C |
| Factor | (Nu6) C0 | – |
| Wall temperature (out) | ϑW,a | °C |
| Specific heat capacity | cp | J/(kg·K) |
| Mean wall temperature | ϑW | °C |
| Boundary condition | Wärmestromdichte | – |
| Geometry | Wand | – |
| Tube diameter | d | m |
| Number of vertical tubes | n | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Film thickness (laminar falling film) (for Re < 400) | slam | m |
| Film thickness (turbulent falling film) (for Re ≥ 400) | sturb | m |
| Nusselt number (acc. to equation 5) | Nu5 | – |
| Nusselt number (acc. to equation 6) * only for Re < 10 | Nu6* | – |
| Nusselt number (acc. to equation 7) | Nu7 | – |
| Nusselt number (acc. to equation 8) | Nu8 | – |
| Nusselt number (max. from Nu and Nu6) | Numax | – |
| Heat transfer coefficient | α | W/(m²·K) |
| Reynolds number | Re | - |
| Heat duty | Q̇ | W |
| Heat flux | q̇ | W/m² |
| Heat transfer coefficient (for a water film) | αB | W/(m²·K) |
| Nusselt number | Nu | – |
| Nusselt number (acc. to equation 6) | Nu6 | – |
Calculation options
Boundary condition
Constant wall temperature · Constant heat flux
Geometry
Tube · Plane wall
Options
Non-boiling falling films · Convective boiling · Nucleate boiling of water films
Frequently asked questions
Why are falling film evaporators particularly suitable for temperature-sensitive products?
In the thin film, heat transfer is good and the liquid holdup is small, so small driving temperature differences suffice and the residence time in the heated zone is only seconds. Evaporation takes place predominantly at the free film surface without nucleate boiling at the wall, which largely avoids local overheating and product degradation.
What happens if the wetting rate becomes too small?
Below the minimum wetting rate, the film breaks up and dry patches form. There, heat transfer collapses, dissolved substances crystallize out or burn on, and the wall can overheat locally. In practice, the minimum wetting limits the evaporation rate per pass; at high concentration ratios, recirculation or several stages in series are therefore used.
When does a falling film become turbulent, and what does that mean for heat transfer?
With increasing film Reynolds number, the film passes from the smooth via the wavy laminar to the turbulent state; the transition to the turbulent film occurs at Reynolds numbers on the order of about 400 (based on the definition used in the VDI Wärmeatlas). In the laminar regime, the heat transfer coefficient decreases with increasing wetting rate (thicker film); in the turbulent regime it increases again — in between lies a minimum that must be considered in the design.
Which sources of error are typical in the design?
Common errors are non-uniform liquid distribution at the top of the tubes (individual tubes are starved and dry out), neglecting the viscosity increase during concentration along the tube, and applying the correlations outside their Reynolds-Prandtl validity range. The shear stress influence of the vapor flowing in counter-current or co-current on the film is also often overlooked.