Thermosiphon Analysis
Theory: moving heat by evaporation, condensation and gravity
Overview
I need to move heat from a hot device to a heat sink some distance away, and was told a copper rod won't do.
That's where a thermosiphon comes in. Put a little water in a sealed tube, heat the bottom and cool the top. Water evaporates below, the vapour releases heat as it condenses above, and liquid returns by gravity. Because it carries heat as latent heat, it moves orders of magnitude more than a copper rod at a small temperature difference. But gravity alone returns the liquid, so the heated end must be at the bottom. Analysis focuses on two things: how much heat it can carry (limits) and what temperature difference results (thermal resistance).
Flooding limit
As upward vapour speeds up, it pushes back the liquid film flowing down the wall, and liquid can no longer reach the evaporator. This flooding (counter-current flow) limit is the thermosiphon's typical limit. In this Wallis-type expression, $A$ is the bore area and $D$ the inner diameter. Higher vapour density $\rho_v$ means slower vapour for the same heat, raising the limit.
Condenser heat transfer
On the condenser wall, conduction through the liquid film is the resistance. Nusselt's film condensation formula gives the heat transfer coefficient, which combined with the evaporator coefficient gives the overall temperature difference.
Tubes that guard permafrost
A famous large-scale use of thermosiphons is the Trans-Alaska Pipeline built in the 1970s. To keep supports on permafrost from sinking as warm oil and summer heat thawed the ground, tens of thousands of thermosiphons were installed in the supports. They work only in winter, when the air is colder than the ground, releasing ground heat to the air and keeping the permafrost frozen. In summer the top is warmer, so they stop automatically. With no power or controls, the design exploits gravity and the thermosiphon's one-way nature.
Worked example: a water thermosiphon
Example 1: flooding limit
| Bore | 40 °C | 60 °C | 80 °C | 100 °C |
|---|---|---|---|---|
| 10 mm | 188 W | 281 W | 393 W | 521 W |
| 20 mm | 1,066 W | 1,592 W | 2,225 W | 2,945 W |
Same tube, yet 40 °C and 100 °C differ by a factor of 2.8.
Water vapour density is 0.051 kg/m³ at 40 °C and 0.60 kg/m³ at 100 °C — twelve times different. Thin vapour must move faster to carry the same heat, and more easily pushes back the liquid. So a thermosiphon run at low temperature carries less heat for the same bore. Doubling the bore quadruples the area and the $\sqrt{D}$ term adds more, for about 5.7 times. The basic step is sizing the bore from operating temperature and required heat.
Example 2: thermal resistance versus a copper rod
A 10 mm-bore tube with 0.15 m evaporator, 0.2 m adiabatic section and 0.15 m condenser carrying 100 W at 60 °C was computed. The condenser uses Nusselt's formula; the evaporator coefficient is assumed at 5,000 W/m²K:
| Item | Value |
|---|---|
| Condenser coefficient | 14,929 W/m²K |
| Condenser ΔT (resistance) | 1.42 K (0.014 K/W) |
| Evaporator ΔT (resistance) | 4.24 K (0.042 K/W) |
| Total ΔT | 5.67 K |
| Effective conductivity | about 79,000 W/mK (about 200× copper) |
| Copper rod, same size and ΔT | 0.51 W |
Most resistance is in the evaporator; the temperature drop along the vapour space is tiny, so lengthening the tube barely increases ΔT. To improve performance, work on evaporator heat transfer (internal surface treatment, fill amount).
Design workflow
- Confirm heat load, operating temperature, and that the heated end is below the cooled end.
- Choose the working fluid (water from room temperature to about 200 °C; ammonia or refrigerants for lower temperatures).
- Size the bore from the flooding limit with margin.
- Estimate temperature difference from evaporator and condenser heat transfer.
- Set the fill amount (too little dries out; too much causes geysering and reduced performance).
“It stopped cooling when tilted”
A thermosiphon mounted nearly horizontal inside equipment cooled well in the prototype but barely carried heat in production. The prototype stood vertical; production tilted it less because of the enclosure shape. With gravity returning the liquid, a small tilt slows the return and the evaporator dries out — and with the heated end even slightly higher, it doesn't work at all. For horizontal or upward heat transport, choose a heat pipe with a wick.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Assuming high-temperature limits at low temperature | Flooding cuts performance | Use properties at operating temperature |
| Ignoring inclination | Liquid doesn't return; dryout | Keep the heated end low |
| Arbitrary fill amount | Dryout or geysering | Test several fill amounts |
| Non-condensable gas | Condenser blocked | Control degassing and sealing |
| Estimating resistance by tube length | Real cause missed | Evaluate evaporator and condenser |
I'd like to learn related topics.
Check boiling and properties with the boiling curve simulator and steam tables. Related analyses include heat pipe simulation, boiling heat transfer, condensation and cryogenic thermal analysis.
Related Topics
| Format | Extension | Type | Overview |
|---|---|---|---|
| STEP | .stp/.step | Neutral CAD | ISO 10303 compliant 3D CAD data exchange format. Supports geometry + PMI. |
| IGES | .igs/.iges | Neutral CAD | Early CAD data exchange standard. Has issues with surface data compatibility. Transition to STEP is progressing. |
| CGNS | .cgns | CFD Data | CFD General Notation System. Standard exchange format for CFD results. |