Engineering task and calculation objective
This module calculates the heat transfer coefficient for convective flow boiling of saturated pure liquids in horizontal tubes per Chapter H3.5.1.2 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). Compared with the vertical tube, gravity acts transversely to the flow direction in a horizontal tube: the phases can stratify, the liquid collects at the bottom, and depending on the flow pattern the upper tube surface is only partially wetted or not wetted at all.
This calculation is the basis for designing horizontal evaporator tubes, as found in refrigerant evaporators, forced circulation evaporators, and shell-and-tube units with tube-side evaporation. The local heat transfer coefficient depends on mass flux, vapor quality, and the flow pattern, which is determined beforehand with the flow pattern map (Chapter H3.2): in annular flow the circumference is fully wetted and the heat transfer is high; in stratified and wavy flow the dry upper part of the circumference transfers only little heat.
The module captures this asymmetry via the wetted fraction of the circumference and delivers the circumferentially averaged heat transfer coefficient at the tube position considered — more conservative and more realistic than the unchecked application of the vertical-tube correlation.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Determine the flow pattern: For the mass flux and the local vapor quality, the flow pattern in the horizontal tube is determined first (stratified, wavy, plug/slug, annular, or mist flow) — it decides how much of the tube circumference is wetted.
- Calculate the single-phase reference values: As for the vertical tube, the heat transfer coefficients of the hypothetical single-phase liquid and vapor flows in the tube are determined as reference values for the two-phase enhancement.
- Evaluate the two-phase enhancement: The enhancement function of vapor quality and phase density ratio yields the convective two-phase heat transfer coefficient of the wetted wall region.
- Account for the wetting of the circumference: For stratified flow patterns, the tube circumference is divided into a wetted part and a vapor-exposed part; the circumferentially averaged heat transfer coefficient results from weighting both contributions.
- Evaluate the local value along the tube: Since the vapor quality grows along the evaporator tube and the flow pattern changes, the calculation is repeated at several positions and integrated over the tube length for the equipment design.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube inside diameter | di | m |
| Vapour mass fraction | ẋ | -- |
| Mass flux | ṁ | kg/(m²·s) |
| Surface tension | σ | mN/m |
| Density | ρL | kg/m³ |
| Density | ρG | kg/m³ |
| Dynamic viscosity | ηL | mPa·s |
| Dynamic viscosity | ηG | mPa·s |
| Flow pattern | Strömungsform | -- |
| flüssig | PrL PrG | - |
| gas | PrL PrG | - |
| flüssig | ReLO ReGO RehG | – |
| gas | ReLO ReGO RehG | – |
| flüssig | Nu∞,L Nu∞,G Nu∞,hG | – |
| gas | Nu∞,L Nu∞,G Nu∞,hG | – |
| Thermal conductivity | λL | W/(m·K) |
| Thermal conductivity | λG | W/(m·K) |
| Specific heat capacity | cpL | J/(kg·K) |
| Specific heat capacity | cpG | J/(kg·K) |
| Nu_L0 | NuL0 NuG0 NuhG | – |
| Nu_G0 | NuL0 NuG0 NuhG | – |
| Xi_L | ξL ξG ξhG | – |
| Xi_G | ξL ξG ξhG | – |
| Heat of evaporation | Δhv | J/kg |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Heat transfer coefficient | α(z)k | W/(m²·K) |
| alpha_z/Ó_L0 | α(z)k / αLO | - |
Calculation options
Flow pattern
Stratified flow · Wave flow · Bubble flow · Slug or plug flow · Turbulent gas and laminar liquid flow · Mist flow · Annular flow
Boundary condition
Constant wall temperature · Constant heat flux
Frequently asked questions
Why can't I simply calculate horizontal evaporator tubes with the vertical-tube correlation?
In a horizontal tube, gravity can separate the phases. At low mass fluxes, stratified or wavy flow prevails: the upper tube surface is dry, transfers hardly any heat, and can locally overheat in heated tubes. The vertical-tube correlation, by contrast, assumes a fully wetted circumference and considerably overestimates the heat transfer in these cases.
From what point does a horizontal tube behave like a vertical one?
At sufficiently high mass flux, inertial and shear forces dominate over gravity, and annular or mist flow with a largely symmetric phase distribution establishes itself. The results of both geometries then converge. As a design rule, the mass flux should be chosen so that stratified flow patterns are avoided in the heated section.
What does partial dryout mean for operation?
At the dry upper part of the circumference, the wall temperature rises, which can lead to fouling with temperature-sensitive products and to material problems at high heating medium temperatures. In addition, the circumferentially averaged heat transfer deteriorates, so the evaporator duty falls short of the design value if the stratification was not taken into account.