Engineering task and calculation objective
This module calculates the heat transfer coefficient for convective flow boiling of saturated pure liquids in vertical tubes per Chapter H3.5.1.1 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). In convective flow boiling, the liquid evaporates predominantly at the surface of the near-wall liquid film without bubble nucleation at the wall being dominant; the heat transfer is carried by the two-phase flow itself and depends mainly on mass flux and vapor quality, hardly at all on the heat flux.
This calculation is needed for the tube-side design of natural and forced circulation evaporators, falling film and climbing film evaporators, and evaporator tubes in steam generators — wherever a vertical tube carries a boiling pure substance. The local heat transfer coefficient is evaluated at the axial position along the flow direction, since it changes with the local vapor quality.
The basis is normalization to the single-phase heat transfer: the two-phase heat transfer coefficient is referred to the value of the purely liquid or purely vapor tube flow via an enhancement function of vapor quality and phase density ratio.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the boundary condition and the operating point: The boundary condition, mass flux, vapor quality, and the axial coordinate in flow direction as well as the tube inside diameter are specified. The local vapor quality follows from the energy balance up to the tube position considered.
- Provide the property data of both phases: Density, specific heat capacity, thermal conductivity, and viscosity of the boiling liquid and the saturated vapor, plus surface tension and enthalpy of vaporization, are evaluated at the saturation state.
- Calculate the single-phase reference values: For the hypothetical all-liquid flow (total mass flow as liquid), the heat transfer coefficient of turbulent tube flow is determined; it serves as the reference value for the two-phase enhancement.
- Evaluate the two-phase enhancement: The enhancement function of vapor quality and density ratio ρ'/ρ'' yields the ratio of the convective two-phase heat transfer coefficient to the single-phase reference value; with increasing vapor quality, the vapor core accelerates the liquid film and α grows.
- Output the local heat transfer coefficient: The result is the local convective heat transfer coefficient at the tube position considered; for equipment design it is integrated over the tube length or combined with the nucleate boiling contribution (Chapter H3.5.2.1) to obtain the governing overall value.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube inside dameter | 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 |
| flüssig | PrL PrG | - |
| gas | PrL PrG | - |
| flüssig | ReLO ReGO | – |
| gas | ReLO ReGO | – |
| flüssig | Nu∞,L Nu∞,G | – |
| gas | Nu∞,L Nu∞,G | – |
| 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_0_L | NuL0 NuG0 | – |
| Nu_0_G | NuL0 NuG0 | – |
| Xi_L | ξL ξG | – |
| Xi_G | ξL ξG | – |
| Heat of evaporation | Δhv | J/kg |
| Heat transfer coefficient | α(z)k | W/(m²·K) |
Calculation options
Boundary condition
Constant wall temperature · Constant heat flux
Frequently asked questions
How do I recognize whether convective boiling or nucleate boiling dominates?
From the ratio of heat flux to mass flux: nucleate boiling only sets in above a minimum wall superheat and depends strongly on q̇, whereas convective boiling depends on ṁ and x. At low heat fluxes and high mass fluxes, the convective mechanism dominates. In design practice, both contributions are calculated and combined into the governing heat transfer coefficient.
Why does the heat transfer coefficient increase with vapor quality?
As the vapor quality grows, the volumetric velocity rises steeply, because the vapor occupies many times the liquid volume. The fast vapor core shears the liquid film on the wall thin and turbulent — the conduction path through the film becomes shorter and α rises. This holds until dryout of the film, beyond which the heat transfer drops drastically.
Is the calculation also valid near x = 0 and x = 1?
Caution is required at the boundaries: at very low vapor quality the value merges into the single-phase liquid flow; at high vapor quality the validity ends with dryout of the wall film — beyond that, mist flow with considerably poorer heat transfer prevails. The dryout point itself is not covered by this module and must be checked separately.