Engineering task and calculation objective
This module calculates the heat transfer in subcooled flow boiling per Chapter H3.4 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). Subcooled boiling occurs when the wall temperature already exceeds the boiling temperature but the core flow is still below saturation: vapor bubbles form at the wall and condense again in the subcooled core. The heat transfer is therefore considerably higher than in single-phase forced convection.
This regime is of practical relevance at the inlet of evaporator tubes, in high-performance cooling systems (e.g. cooled walls of furnaces and reactors), and wherever locally high heat fluxes occur while the fluid is still subcooled. Engineers who want to calculate the heat transfer coefficient in subcooled flow boiling need, besides the pressure, fluid temperature, and boiling temperature, the dimensionless numbers of the flow: Reynolds number, Prandtl number (also at the wall temperature), and Péclet number.
The module evaluates the boundary condition of the case, determines the degree of subcooling via the phase number, and superimposes the convective contribution of the single-phase flow with the nucleate boiling contribution at the superheated wall.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the boundary condition and the operating point: Pressure, fluid temperature, and the boiling temperature corresponding to the pressure are specified. The difference between boiling and fluid temperature describes the subcooling of the core flow; the boundary condition defines which quantity (e.g. heat flux or wall temperature) is imposed.
- Form the flow parameters: From mass flux, tube geometry, and property data, the Reynolds number and the Prandtl number of the liquid as well as the Péclet number are formed; the Prandtl number at wall temperature captures the property-variation effect of the near-wall superheat.
- Calculate the single-phase convective contribution: The heat transfer coefficient of single-phase turbulent tube flow is determined with the Gnielinski correlation from Re and Pr; it forms the base on which the subcooled boiling builds.
- Superimpose the boiling contribution: As soon as the wall superheat activates bubble formation, the nucleate boiling contribution is superimposed on the convective contribution. The phase number describes the ratio of subcooling to driving temperature difference and controls the transition from the single-phase regime to fully developed subcooled boiling.
- Evaluate the wall temperature or heat flux: Depending on the boundary condition, the module delivers the resulting wall temperature for a specified heat flux or vice versa — the basis for checking the onset of boiling and the wall temperature level along the tube.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Rho | ρ | kg/m³ |
| Eta | η | mPa·s |
| Cp | cp | J/(kg·K) |
| Lam | λ | W/(m·K) |
| Sigma | σ | mN/m |
| Prandtl number at wall temperature | Prw | - |
| dHv | Δhv | J/kg |
| Rho | ρ | kg/m³ |
| Prandtl number at wall temperature | Prw | - |
| ps1 | ps ps ps | Pa |
| ps2 | ps ps ps | Pa |
| ps3 | ps ps ps | Pa |
| ts1 | ϑs ϑs ϑs | °C |
| ts2 | ϑs ϑs ϑs | °C |
| ts3 | ϑs ϑs ϑs | °C |
| Mass velocity | mPkt | kg/(m²·s) |
| Heat flux | q | W/m² |
| Wall temperature | ϑw | °C |
| Tube diameter | Db | m |
| Angle of inclination of the tube | γ | ° |
| Wall shear stress | τ0 | N/m² |
| Maximum bubble radius | rmax | m |
| Heat flux | q0 | W/m² |
| Heat flow exponent | n(p*) | - |
Calculation options
Condition
Subcooled boiling at constant heat flux · Subcooled boiling at constant wall temperature
Frequently asked questions
What distinguishes subcooled boiling from saturated boiling?
In subcooled boiling, the bulk mean temperature of the fluid is still below the boiling temperature; vapor forms only in the superheated wall boundary layer and condenses again in the core. The flow quality remains practically zero, even though bubbles form vigorously at the wall. Only once the fluid reaches saturation does saturated flow boiling with increasing vapor quality begin (Chapter H3.5).
Why does the heat transfer increase so strongly compared with single-phase flow?
The bubbles that grow at the wall and condense in the core act like an intense micro-agitation of the boundary layer and additionally transport latent heat. As a result, the wall temperature becomes largely decoupled from the flow velocity: in fully developed subcooled boiling, the wall superheat depends almost exclusively on the heat flux.
Which limit must also be observed in subcooled boiling?
The critical heat flux. Even in subcooled flow, a vapor film can blanket the wall at very high loads (departure from nucleate boiling); subcooling and mass flux raise the limit but do not eliminate it. For thermally highly loaded cooling channels, the margin to the boiling crisis must be verified separately.