Engineering task and calculation objective
The module calculates heat pipes according to chapter N5 of the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). A heat pipe is a closed tube partially filled with a working fluid, in which heat is transported by evaporation in the heating zone, vapor flow to the cooling zone, condensation, and return of the condensate — in classic heat pipes via the capillary action of a porous wick structure. The module checks the pressure balance of the circuit and calculates the performance limits: capillary limit, viscous limit, sonic limit and entrainment limit with the associated heat flux densities.
Heat pipes transfer large heat flows at very small temperature differences and without moving parts. They are used in electronics and power electronics cooling, in heat pipe heat exchangers for waste heat recovery, in aerospace, and for temperature homogenization in apparatus. To design a heat pipe, it must be demonstrated that the maximum capillary pressure difference of the wick exceeds the sum of all pressure losses of the circuit — the frictional pressure drop of vapor and liquid, the hydrostatic pressure difference, and the pressure differences in the evaporation, adiabatic and condensation zones.
The module evaluates this balance using the axial and radial Reynolds numbers of the vapor flow and delivers, for each operating limit, the corresponding limiting power, whose minimum determines the transferable power of the heat pipe.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define geometry, working fluid and wick: Inputs are the lengths of the evaporation, adiabatic and condensation zones, tube and vapor space diameters, inclination, the wick structure (pore radius, permeability) and the working fluid with its physical properties in the operating temperature range.
- Characterize the flow regime of the vapor: From the axial vapor mass flow, the axial and radial Reynolds numbers are formed; they determine which approaches apply for the frictional pressure drop of the vapor in the individual zones and whether compressibility effects must be considered.
- Set up the pressure balance of the circuit: The maximum capillary pressure difference of the wick is compared against the sum of the frictional pressure drop of vapor and liquid (divided into evaporation zone, adiabatic zone and condensation zone), the hydrostatic pressure difference in inclined operation, and the pressure differences from evaporation and condensation. Only if the capillary pressure difference covers all losses does the condensate return work.
- Calculate the performance limits: For each operating limit, the heat flux density and limiting power are determined: the viscous limit at low vapor pressure (e.g. during start-up), the sonic limit when the vapor flow reaches the speed of sound in the narrowest cross-section, the entrainment limit above which the vapor tears condensate droplets out of the wick, and the capillary limit from the pressure balance. In addition, the boiling limit constrains the radial heat flux density in the evaporator.
- Evaluate the operating envelope: The transferable power is the minimum of all limiting powers at the respective operating temperature. Since the limits vary differently with temperature, an operating envelope results, from which the working range and safety margin of the heat pipe are read.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Sintered structure | = 2 ⇒ | - |
| Grid structure | = 3 ⇒ | - |
| Density of thermal liquid | ρl | kg/m³ |
| Density of thermal gas | ρg | kg/m³ |
| Thermal conductivity (liquid) | λl | W/(m·K) |
| Kinematic viscosity (liquid) | νl | m²/s |
| Kinematic viscosity (gas) | νg | m²/s |
| Surface tension | σ | N/m |
| Heat of evaporation | Δhv | kJ/kg |
| Operating temperature | ϑB | °C |
| Inclination heat pipe | α | ° |
| Contact angle | ϑ | ° |
| Minimum effective radius of curvature | Reff,min | mm |
| Heat pipe length | l | mm |
| Effective length | leff | mm |
| Length of adiabatic zone | lad | mm |
| Length of evaporation zone | lverd | mm |
| Length of condenser zone | lkond | mm |
| Difference in altitude, heat pipe | h | mm |
| Groove depth | h | mm |
| Groove-/mesh width/artery radius w or R | Rillenweite | mm |
| Spacing between grooves | b | mm |
| Area of all grooves | Al | mm² |
| Area of single groove | ARille | mm² |
Frequently asked questions
Which performance limit is usually governing in normal operation?
For capillary-driven heat pipes in the medium temperature range, almost always the capillary limit: the wick structure can build up only a limited pressure difference to return the condensate against all flow losses. The viscous and sonic limits become relevant mainly during start-up from a cold state or at low operating temperatures with low vapor pressure; the entrainment limit at high axial heat flux densities.
What distinguishes a heat pipe from a two-phase thermosiphon?
In a thermosiphon, gravity alone returns the condensate; it works only if the cooling zone lies above the heating zone. The classic heat pipe uses the capillary action of a wick and operates independently of orientation — against gravity, however, with reduced power, because the hydrostatic pressure difference appears as an additional loss in the pressure balance.
How is the working fluid selected?
The fluid must have a suitable vapor pressure in the operating temperature range and is rated via a figure of merit (Merit number) formed from surface tension, enthalpy of vaporization and viscosity. Typical choices are ammonia and acetone for low temperatures, water for medium temperatures (approx. 30–250 °C) and liquid metals such as sodium for very high temperatures. In addition, the fluid must be compatible with the tube and wick materials, since corrosion generates non-condensable gases that block the condensation zone.
Why does the power collapse when the capillary limit is exceeded?
If the sum of the pressure losses exceeds the maximum capillary pressure difference, less condensate arrives in the evaporator than evaporates there. The wick dries out locally (dry-out), the wall temperature in the heating zone rises abruptly, and the heat transport breaks down. A heat pipe should therefore be operated with a clear margin below the calculated capillary limit.