Engineering task and calculation objective
This module calculates the heat transfer coefficient for nucleate pool boiling of pure substances under free convection (vessel boiling), explicitly accounting for the shape of the heated wall: horizontal tube, flat plate, or horizontal tube bundle. It is based on Chapter H2.3.5.1 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019), which builds on the Gorenflo correlation method: the heat transfer coefficient is scaled from a substance-specific reference value via the reduced pressure p* = p/pc and the heat flux.
In practice, this calculation is needed when sizing evaporators, kettle reboilers, immersion heaters, and heated vessels in which a liquid boils on a superheated wall without a dominant forced flow. Engineers who want to calculate the pool boiling heat transfer coefficient obtain not only the coefficient itself but also the wall superheat associated with the required heat flux — and thus the required wall temperature.
The shape correction via the characteristic flow length (the diameter for a tube, the height for a plate) and, optionally, the influence of the wall material properties make the method more accurate than simple one-size-fits-all correlations and cover the heated-surface geometries common in process equipment design.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the fluid and the geometry: First, specify whether the fluid is water (water has its own pressure and exponent functions), whether a horizontal tube bundle is present, and whether the influence of the tube material properties on the heat transfer coefficient should be taken into account.
- Determine the operating point: From the boiling pressure and boiling temperature together with the critical pressure of the fluid, the reduced pressure p* = p/p_c is formed. It is the central similarity parameter of the Gorenflo method and determines both the pressure function and the heat flux exponent.
- Specify the heat flux: The heat flux q̇ is the load parameter of the boiling process. Via the pressure-dependent heat flux exponent, the ratio q̇/q̇₀ relative to the reference state is raised to a power; at high loads the heat transfer coefficient rises markedly faster than the wall superheat.
- Correct for the shape of the heated wall: The characteristic flow length (tube: outside diameter, plate: height) captures the influence of the heated-wall shape on bubble formation and vapor removal. Deviations from the reference tube are applied to the heat transfer coefficient as a correction factor.
- Evaluate the heat transfer coefficient and wall temperature: The heat transfer coefficient follows from the reference value, the pressure function, the heat flux function, and the shape correction. From it, the driving temperature difference ΔT = q̇/α and the wall temperature required for the specified duty are obtained.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Boiling pressure | ps | Pa |
| Boiling temperature | ϑs | °C |
| Density | ρ' | kg/m³ |
| Specific heat capacity | cp' | J/(kg·K) |
| Coefficient of thermal expansion | β' | 1/K |
| Thermal conductivity | λ' | W/(m·K) |
| Dynamic viscosity | η' | mPa·s |
| Kinematic viscosity | ν' | m²/s |
| Critical pressure | pc | Pa |
| Heat transfer coefficient (reference value) | α0 | W/(m²·K) |
| Heat flux (reference value) | q̇0 | W/m² |
| Roughness (ref. value) | Ra0 | m |
| Length of flow path (tube:diameter, plate: height) | L | m |
| Roughness (DIN 4762 of 01.89) | Ra | m |
| Wall temperature | ϑw | °C |
| Acceleration due to gravity | g | m/s² |
| Heat flux | q̇ | W/m² |
| Heat transfer coefficient | αe,K | W/(m²·K) |
| Reduced pressure (p* = p / pc) | p* | - |
| Heating wall factor | Fw (9c) | - |
| Pressure function | F(p*) (7a,b) | - |
| Heat flux exponent | n(p*) (6a,b) | - |
| Heat transfer coefficient | αe,B | W/(m²·K) |
| Temperature difference | dT | K (diff) |
Calculation options
Is it water?
No · Yes
Worked example
Water boils at atmospheric pressure (p = 1.013 bar, ϑs = 100 °C) on a horizontal plain tube with reference roughness. The heated surface is loaded with a heat flux of q̇ = 100 kW/m². Find the nucleate boiling heat transfer coefficient and the required wall temperature in this worked example.
Given values
| Fluid | Water |
| Boiling pressure p | 1.013 bar |
| Boiling temperature ϑs | 100 °C |
| Critical pressure pc | 220.64 bar |
| Heat flux q̇ | 100 kW/m² |
| Reference value α0 (p* = 0.1; q̇0 = 20 kW/m²; Ra0 = 0.4 µm) | 5,600 W/(m²·K) |
Solution
Form the reduced pressure
p* = p / pc = 1.013 / 220.64 = 0.00459
Heat flux exponent for water
n = 0.9 − 0.3 · p*0.15 = 0.9 − 0.3 · 0.446 = 0.766
Evaluate the heat flux function
Fq = (q̇ / q̇0)n = (100 / 20)0.766 = 50.766 = 3.43
Evaluate the pressure function for water
F(p*) = 1.73 · p*0.27 + (6.1 + 0.68/(1 − p*)) · p*²
= 1.73 · 0.234 + 6.78 · 2.1·10−5 = 0.4045 + 0.0001 = 0.405
Heat transfer coefficient and wall temperature
α = α0 · F(p*) · Fq = 5,600 · 0.405 · 3.43 ≈ 7,770 W/(m²·K)
ΔT = q̇ / α = 100,000 / 7,770 ≈ 12.9 K → required wall temperature ϑw ≈ 100 + 12.9 = 112.9 °C
Result
| Heat transfer coefficient α | ≈ 7,770 W/(m²·K) |
| Driving temperature difference ΔT | ≈ 12.9 K |
| Required wall temperature ϑw | ≈ 112.9 °C |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
How does pool boiling differ from flow boiling?
In pool boiling, the liquid is at rest in the vessel; motion arises only from the buoyancy of the vapor bubbles and free convection. In flow boiling, the fluid is pumped through the tube at a significant mass flux, so a convective contribution and a nucleate boiling contribution are superimposed. The modules of the H3.5 series cover evaporator tubes with through-flow; this module applies to liquid boiling on heated walls immersed in a vessel.
Why is the calculation based on the reduced pressure p* instead of the absolute pressure?
Nucleate boiling heat transfer depends strongly on the thermodynamic state relative to the critical point: as p* increases, the nucleation site density and heat transfer grow while the enthalpy of vaporization decreases. Normalizing with p* = p/p_c allows very different substances to be described with one common pressure function; only the reference value of the heat transfer coefficient remains substance-specific.
Up to what heat flux is the calculation valid?
The correlation is valid only in the regime of stable nucleate boiling, i.e. below the critical heat flux q̇_crit. If it is exceeded, the mechanism flips to film boiling, the heat transfer coefficient collapses, and the wall temperature jumps sharply upward (burnout risk). The critical heat flux is calculated separately per Chapter H2.5.1 and should be respected with an adequate margin in the design.
What role do surface roughness and wall material play?
Bubble formation starts at nucleation sites on the surface; rougher heated surfaces therefore yield higher heat transfer coefficients than polished ones. The reference values in the VDI Heat Atlas apply to a defined reference roughness. In addition, the thermal effusivity of the wall material influences the local wall temperature fluctuation beneath the bubbles; this material effect can optionally be included in the module.