Engineering task and calculation objective
This module calculates the heat transfer coefficient for nucleate boiling of mixtures per Chapter H2.4 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). When a mixture boils, the more volatile component evaporates preferentially; the less volatile component accumulates at the bubble surface, the local boiling temperature rises, and part of the wall superheat is lost to mass transfer. The heat transfer coefficient of a mixture is therefore systematically lower than the ideal value interpolated from the pure-component values.
Quantifying this degradation is crucial for the design of evaporators and reboilers in distillation and absorption plants, where mixtures boil in practically every case. The calculation follows the Schlünder approach: from the heat transfer coefficients of the pure components, the mole fractions in liquid and vapor, the boiling temperature difference, and the mass transfer coefficient, enthalpy of vaporization, and density, the real heat transfer coefficient of the mixture is determined.
The results are the mixture heat transfer coefficient, the driving temperature difference, and the required wall temperature — the basis for not systematically undersizing heating surfaces for mixture evaporation.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Capture the equilibrium data of the mixture: For both components, the mole fractions in liquid (x) and vapor (y) and the boiling temperatures at system pressure are specified. The difference y − x and the slope of the bubble-point line determine how strongly the mixture effect degrades the heat transfer.
- Form the ideal heat transfer coefficient: The ideal reference value of the mixture is interpolated from the nucleate boiling heat transfer coefficients of the pure substances 1 and 2 (each calculated with the pure-substance method).
- Calculate the mass transfer degradation: Using the mass transfer coefficient, the liquid density, the enthalpy of vaporization, and the parameter B₀ (approximately 1, adjustable to measured data), the resistance caused by the accumulation of the less volatile component at the phase interface is captured; the auxiliary quantity (∂T_s/∂x₁)·(y₁ − x₁) enters the correction directly.
- Evaluate the mixture heat transfer coefficient: The real heat transfer coefficient is obtained by dividing the ideal value by the degradation term, which grows with the heat flux q̇. The module offers two evaluation variants.
- Determine the wall temperature: From q̇ and the mixture value, the driving temperature difference ΔT and the required wall temperature ϑ_m + ΔT follow for sizing the heating surface.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure | pm | Pa |
| Temperature | ϑm | °C |
| Mol fraction liquid | xm,1 | – |
| Mol fraction vapour | ym,1 | – |
| Mol fraction liquid | xm,2 | – |
| Mol fraction vapour | ym,2 | – |
| Boiling temperature | ϑs,1 | °C |
| Boiling temperature | ϑs,2 | °C |
| Heat of evaporation | Δhv | J/kg |
| Density mixture | ρl | kg/m³ |
| Coefficient of diffusion | βl | m²/s |
| Heat flux | q̇Z | W/m² |
| Heat transfer coefficient substance 1 for nucleate boiling | αB,1 | W/(m²·K) |
| Heat transfer coefficient substance 2 | αB,2 | W/(m²·K) |
| Factor in equation (23) | A0 | – |
| Factor in equation (26) B0 is a parameter that has approximately equated to unity but can be adapted to accommodate experimental measurements. | B0 | – |
| Parameter | K12 (23) | - |
| Ratio | x1/α1 | m²·K/W |
| Ratio | x2/α2 | m²·K/W |
| Ratio | α/αid (24) | - |
| Heat transfer coefficient | αid (21a) | W/(m²·K) |
| Auxiliary value (∂Ts/∂x1)∙(y1-x1) | H1 (26a) | °C |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Option (1) or (2) | alphaZ | – |
| Heat transfer coefficient (1) | αZ(24) | W/(m²·K) |
| Heat transfer coefficient (2) | αZ(26) | W/(m²·K) |
| Heat transfer coefficient (2) | αZ | W/(m²·K) |
| Temperature difference | ΔT | K (diff) |
| Required wall temperature (ϑm + ΔT) | ϑw | °C |
Frequently asked questions
Why does a mixture boil less effectively than its pure components?
At the growing bubble, the more volatile component evaporates preferentially. The boundary layer becomes depleted in it, the local boiling temperature rises above that of the bulk mixture, and part of the wall superheat drives only mass transfer instead of evaporation. The larger the gap between the dew-point and bubble-point lines (y − x, i.e. the boiling range) and the poorer the mass transfer, the further the heat transfer coefficient falls below the ideally interpolated value.
What does the parameter B0 mean and how do I choose it?
B0 is an empirical fitting parameter in the degradation term of the Schlünder equation. Without measured data, it is approximated as 1; if boiling experiments with the real mixture are available, B0 can be fitted to them. For design calculations without measurements, B0 = 1 is the documented, conservatively usable choice.
Is it sufficient to simply average the heat transfer coefficient with the mole fractions?
No. The molar interpolation only yields the ideal reference value. Actually measured mixture values — especially for mixtures far from an azeotrope with a large boiling range and at high heat fluxes — are often 30 to 50 % lower. Ignoring the mass transfer degradation systematically overestimates the evaporator duty.
Does the method also apply to multicomponent mixtures?
The approach implemented in the module is formulated for binary mixtures. Multicomponent mixtures can be treated approximately as a pseudo-binary system of light and heavy boiler; the uncertainty increases, and the boiling range of the real mixture should come from an equilibrium calculation.