Engineering task and calculation objective
This module calculates the nucleate boiling contribution in flow boiling of saturated pure liquids in horizontal tubes per Chapter H3.5.2.2 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). As in the vertical tube, the heat transfer coefficient is scaled via the reduced pressure p* = p/pc and the ratio of the heat flux to the standard heat flux; in the horizontal tube, however, the flow pattern and the resulting non-uniform wetting of the tube circumference must additionally be taken into account.
This calculation is central to refrigerant evaporators, horizontal forced circulation evaporators, and heated coils in which the pure substance evaporates in a horizontal tube at a significant heat flux. The module also captures the tube wall itself: the tube wall thickness and the thermal conductivity of the tube material enter as the thermal conductance of the wall, since circumferential heat conduction evens out the temperature differences between the wetted and dry parts of the circumference; the number of tubes accounts for the distribution of the mass flow over parallel tubes.
The result is the local nucleate boiling heat transfer coefficient at the position considered, which is combined with the convective contribution to give the governing design value for the horizontal evaporator tube.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the boundary condition, substance class, and flow pattern: In addition to the boundary condition and the substance class, the flow pattern is required (from Chapter H3.2), since it determines which part of the tube circumference is wetted and how strongly nucleate boiling can act around the circumference.
- Capture the tube geometry and mass flow: Inside diameter, tube wall thickness, thermal conductivity of the tube material, roughness, and the number of parallel tubes define the geometry and the wall behavior; the mass flux in the individual tube follows from the mass flow and the number of tubes.
- Normalize the operating point: From the boiling pressure and the critical pressure, the reduced pressure p* is formed and the heat flux is referred to the standard heat flux; the property data of both phases are evaluated both at the operating pressure and at the normalized boiling pressure p₀ = 0.1·p_c.
- Account for the wall effect: The thermal conductance of the tube wall (from wall thickness and thermal conductivity) influences how strongly the uneven heating of the circumference manifests in the local wall superheat and thus where nucleate boiling is active.
- Evaluate the local heat transfer coefficient: From the standard value, the pressure function, the heat flux function, and the geometry, roughness, and wetting corrections, the local nucleate boiling contribution at the axial coordinate is obtained; along the tube, the evaluation is repeated with the local vapor quality.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Inside tube diameter | 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 |
| Flow pattern | Strömungsform | -- |
| Prandtl number | Pr | - |
| 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) |
| Reference tube diameter | d0 | m |
| Arithmetic mean roughness height | Ra | m |
| Arithmetic mean roughness height | Ra0 | m |
| Boiling pressure | pS | Pa |
| Critical pressure | pc | Pa |
| Heat flux | q̇ | W/m² |
| Reference heat flux | q̇0 | W/m² |
| Type of substance | Stoffart | – |
| Reduced pressure (p* = p / pc) | p* | - |
| n | n(p*) = | - |
Calculation options
Flow pattern
Stratified flow · Wave flow · Bubble flow · Slug or plug flow · Turbulent gas and laminar liquid flow · Mist flow · Annular flow
Type of substance
Non-cryogen · Cryogen
Boundary condition
Constant wall temperature · Constant heat flux
Frequently asked questions
Why does the tube material enter the boiling calculation for a horizontal tube?
Because the heating of the circumference acts non-uniformly: at the dry upper part of the circumference the wall temperature rises, while at the wetted lower part heat is removed intensively. A well-conducting, thicker wall (high thermal conductance) evens out these differences through circumferential heat conduction and improves the effective boiling behavior; with thin-walled tubes of poorly conducting material, hot zones persist.
What role does the number of tubes play?
In tube bundles with parallel flow, the total mass flow is divided; the governing quantity for flow pattern and heat transfer is the mass flux in the individual tube. Too many parallel tubes reduce the mass flux, promote stratified flow and maldistribution — a frequent cause of underperformance in horizontal evaporators.
Why are property data additionally required at the normalized boiling pressure p0 = 0.1·pc?
The correlation normalizes the heat transfer coefficient to a reference state at the reduced pressure p* = 0.1. To scale from the reference to the operating state, density, surface tension, enthalpy of vaporization, and further property data must be available consistently at both states; inconsistent property data sources are a typical source of error here.