Engineering task and calculation objective
This module calculates the mean heat transfer coefficient for nucleate pool boiling of pure substances on a horizontal tube bundle per Chapter H2.3.5.3 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). In a bundle, two mechanisms are superimposed: nucleate boiling on the individual tube surface and the convective enhancement from the rising two-phase flow generated by the lower tube rows, which additionally sweeps the upper tubes.
This calculation is at the heart of the thermal design of flooded evaporators and kettle reboilers in plant engineering and refrigeration: depending on the load, the heat transfer coefficient of the bundle is significantly higher than that of a single tube, because the bubble-driven flow intensifies convection. Engineers who want to calculate the boiling heat transfer of a horizontal tube bundle obtain here the bundle mean value from the convective and nucleate boiling contributions.
Via the area enhancement factor φ, finned tubes can be covered in addition to plain tubes (φ = 1); the results are the mean heat transfer coefficient, the driving temperature difference, and the required wall temperature.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the operating point: Boiling pressure and boiling temperature define the state of the boiling fluid on the shell side of the bundle; the heat flux q̇ specifies the thermal load on the heating surface.
- Determine the single-tube contributions: For the single tube, the convective heat transfer coefficient and the nucleate boiling heat transfer coefficient are applied — the latter per the single-tube method (Chapter H2.3.5.1, or H2.3.5.2 for finned tubes, where it is accounted for via the area enhancement factor φ).
- Superimpose the bundle effect: The bundle effect is captured from the ratio of the two contributions and the factor f: the vapor-liquid flow generated by the lower tube rows increases the convective contribution at the upper tubes, so the bundle mean value lies above the single-tube value.
- Form the mean heat transfer coefficient: The superposition of the convective contribution and the nucleate boiling contribution yields the mean heat transfer coefficient of the bundle for the specified heat flux.
- Evaluate the wall temperature: From q̇ and the bundle mean value, the driving temperature difference and the required wall temperature follow, against which the heating side (e.g. heating steam or thermal oil side) is balanced.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Boiling pressure | ps | Pa |
| Boiling temperature | ϑs | °C |
| Area enlargement factor (for plain tubes φ = 1) | φ | – |
| Factor f | (0.5 < f < 1) f (13) | – |
| Heat flux | q̇Bu | W/m² |
| Heat transfer coefficient convective | αK | W/(m²·K) |
| Heat transfer coefficient nucleate boiling | αB | W/(m²·K) |
| Heat transfer coefficient | αu (13) | W/(m²·K) |
| Ratio | α/αu (14) | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Heat transfer coefficient | αBu (12) | W/(m²·K) |
| Temperature difference | ΔT | K (diff) |
| Required wall temperature | (ϑs + ΔT) | °C |
Frequently asked questions
Why is the heat transfer in a bundle higher than on a single tube?
The vapor bubbles generated at the lower tube rows rise through the bundle and create a two-phase upward flow that sweeps the upper tubes at increased velocity. This additional convective contribution matters most at low heat fluxes, where pure nucleate boiling is still weak; at very high loads, nucleate boiling dominates and the bundle effect recedes.
Is there an upper load limit in the bundle?
Yes. At high heat fluxes and tight pitch, the rising vapor can partially dry out the upper tube rows (vapor blanketing), causing the heat transfer to collapse. The critical heat flux of the bundle is well below that of the single tube and must be checked separately when designing kettle reboilers, for example using the load limits per Chapter H2.5.
How do finned tubes enter the bundle calculation?
Via the area enhancement factor φ: for plain tubes φ = 1; for low-finned tubes, the nucleate boiling contribution of the single tube is determined with the finned-tube method and converted to the reference surface with φ. The superposition with the convective bundle contribution then follows formally the same procedure as for a plain-tube bundle.