Engineering task and calculation objective
This module calculates the heat transfer coefficient for nucleate pool boiling of pure substances on finned tubes and other structured high-performance tubes per Chapter H2.3.5.2 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). The starting point is the reference heat transfer coefficient of the plain tube at the reduced pressure p* = 0.1 and the standard heat flux; from this, the heat transfer on the finned tube is derived via the fin geometry, the area enhancement factor, and adjusted heat flux exponents.
This calculation is needed when designing flooded evaporators in refrigeration, kettle reboilers, and heat exchangers in which low-viscosity fluids such as refrigerants boil on the outside of finned tube bundles. Low fins and structured surfaces increase the nucleation site density and the effective area, so that at the same wall superheat considerably higher heat fluxes are transferred than on a plain tube.
Besides the heat transfer coefficient for the individual finned tube, the module also delivers the driving temperature difference and the required wall temperature — the basic quantities needed to compare finned tube against plain tube economically and to size the heating surface of an evaporator.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the operating point and the fluid: The reduced pressure p* = p/p_c is formed from the boiling pressure, boiling temperature, and critical pressure. In addition, it is specified whether the fluid is water and whether the tube is used in a horizontal bundle.
- Describe the fin geometry: The outside diameter of the core tube, the fin height, the clear fin spacing, and the area enhancement factor φ characterize the high-performance tube. The area enhancement factor relates the actual finned surface area to the envelope area of the plain tube.
- Apply the plain-tube reference values: For the plain tube, the heat transfer coefficient at p* = 0.1 and q̇ = 100 kW/m² together with the corresponding heat flux exponent serve as reference values; the finned tube has its own, usually smaller, heat flux exponent.
- Evaluate the pressure and heat flux functions: The pressure functions convert the reference state p* = 0.1 to the actual reduced pressure; the ratio of the heat flux to the reference value is raised to the power of the finned tube's heat flux exponent.
- Evaluate the result: The module delivers the nucleate boiling heat transfer coefficient on the individual finned tube, the driving temperature difference ΔT, and the required wall temperature ϑ_s + ΔT as the basis for sizing the heating surface.
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 for the plain tube) | α0 | W/(m²·K) |
| Heat flux (Reference value) | q̇0 | W/m² |
| Tube outside diameter (plain tube) | da | m |
| Fin height | hr | m |
| Distance between adjacent fins | tl | m |
| Area enlargement factor | φ | – |
| Wall temperature | ϑw | °C |
| Acceleration due to gravity | g | m/s² |
| Heat flux | q̇B | W/m² |
| Convective boiling without bubble formation | αe,K | W/(m²·K) |
| Reduced pressure (p* = p / pc) | p* | - |
| Heat transfer coefficient for the plain tube at p* = 0.1 and q̇ = 100 kW/m² | α100,g | W/(m²·K) |
| Heat transfer coefficient (Reference value for the finned tube) | α0,r | W/(m²·K) |
| Heat flux exponent | nr(p*) | - |
| Nucleate boiling on the outer surface of a single finned tube | αr,e,B | W/(m²·K) |
Calculation options
Is it water?
No · Yes
Frequently asked questions
For a finned tube, does the heat transfer coefficient refer to the actual surface or to the envelope surface?
This must be clearly defined in every comparison. The usual convention is to refer to the total finned outside surface; via the area enhancement factor φ, the result can be converted to the envelope surface of a plain tube of the same outside diameter. Mixing up the reference surface is one of the most common sources of error when comparing manufacturer data with calculated values.
Why is the heat flux exponent different for a finned tube than for a plain tube?
In the narrow fin channels, the vapor is removed differently and the nucleation site density is higher than on the plain surface. As a result, the heat transfer coefficient increases with heat flux more weakly, or differently, than on the plain tube; the advantage of the finned tube is greatest at low and moderate heat fluxes and diminishes towards high loads.
Is the method valid for arbitrary high-performance tubes?
The correlation is validated for low-finned tubes and commercially available structured boiling tubes. For tubes with strongly undercut structures (re-entrant cavities), manufacturer data scatter considerably; in that case, the reference value of the heat transfer coefficient should be taken from the manufacturer's measurements, with the module used only to scale the pressure and load dependence.