Heat Pipe Simulation
Theory: the evaporation–condensation–capillary cycle
Overview
I hear the thin copper tubes in laptops are heat pipes. How do they differ from a plain copper rod?
Inside, it's nearly evacuated with a little water sealed in. At the CPU end water evaporates, absorbing latent heat; vapour rushes to the other end, condenses and releases it. Liquid returns by capillary action through a fine structure on the wall called a wick. Because heat moves by vapour flow rather than conduction, it passes heat hundreds of times more easily than a copper rod of the same size. But there's a ceiling on heat, set by the wick's capillary force and by orientation (gravity). Let's calculate.
Capillary limit
The bracket is capillary pressure minus the gravity head lifting the liquid. $K$ is wick permeability, $A_w$ wick cross-section, $\phi$ the tilt with evaporator upward. A smaller $r_{eff}$ pulls harder but lowers $K$, making flow harder — that trade-off is the heart of wick design.
Working-fluid quality (merit number)
Liquids with high surface tension and latent heat and low viscosity carry more heat. Water's merit number is 2.2×10¹¹ at 30 °C, 3.3×10¹¹ at 60 °C and 4.5×10¹¹ W/m² at 100 °C, rising with temperature. Water is among the best fluids near room temperature but freezes below 0 °C.
Heat pipes began with space
The heat pipe concept was patented at General Motors in the 1940s, but it drew attention in 1963 when Grover at Los Alamos built one to carry heat from space nuclear reactors — he also coined the name. In weightless space, capillary action is essential to return liquid. After use in satellite thermal control, heat pipes spread into laptop CPU cooling from the late 1990s, and the same principle now works in thin smartphone vapour chambers.
Worked example: 6 mm copper–water heat pipe
OD 6 mm, wall 0.3 mm, wick 0.5 mm. Evaporator 50 mm, adiabatic 100 mm, condenser 50 mm (200 mm total), 60 °C. Vapour pressure drop is neglected and only the capillary limit is considered.
Wick type and orientation
| Wick | Capillary pressure | Gravity-assisted (vertical) | Horizontal | Evaporator up 30° | Evaporator up 90° |
|---|---|---|---|---|---|
| Sintered (0.1 mm powder) | 6,305 Pa | 70 W | 54 W | 45 W | 37 W |
| Screen mesh | 2,207 Pa | 158 W | 84 W | 48 W | 11 W |
| Axial grooves | 662 Pa | 330 W | 84 W | 0 W | 0 W |
A 200 mm water column weighs 1,929 Pa — about three times the grooved wick's 662 Pa. Tilting just 30° evaporator-up adds 965 Pa, and the grooves can no longer return liquid.
Comparison with a copper rod
| Item | Heat pipe | Copper rod, same size |
|---|---|---|
| Thermal resistance | 0.034 K/W | 13.6 K/W |
| ΔT to carry 20 W | 0.7 K | 272 K |
The heat pipe value counts only conduction through the wick at each end (assumed 40 W/mK) and the wall — an ideal. In practice contact resistances and other effects typically make it several times larger, but it's still two orders of magnitude below the rod.
Grooves carry more than sintered when horizontal, yet drop to zero with a slight tilt.
Grooves are wide channels — easy flow, weak pull. Sintered powder has fine pores — strong pull, harder flow. Horizontally there's no gravity burden, so easy flow wins. With the evaporator up, beating gravity comes first, and only the strong-pulling sintered wick survives. So grooved wicks suit fixed-orientation or gravity-assisted equipment, and sintered wicks suit devices that move, like laptops and phones. Note the gravity-assisted 330 W: in practice other limits such as entrainment by vapour flow usually come first.
How to simulate
- First compute the capillary, sonic, entrainment and boiling limits and check margin at the operating point.
- In system-level thermal models, represent the heat pipe as a high-conductivity bar or resistance network.
- Even with such a surrogate, separately check that transported heat stays below the limits.
- At start-up (low temperature) low vapour density makes the sonic limit likely.
- Bent or flattened pipes have deformed wicks and vapour paths, lowering limits.
“Upside down, it overheated”
In an industrial control panel, a grooved-heat-pipe cooler was mounted upside down to suit the site, and the equipment overheated and tripped in summer. It had been designed with the heat source at the bottom so liquid returned by gravity. Inverted, the source was on top, and the weak-capillary grooves couldn't return liquid, so it dried out. Restoring the orientation solved it. Since heat pipe performance depends strongly on orientation, drawings must state the mounting direction clearly.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Ignoring orientation | Dry-out, overheating | Include gravity in limits |
| Only a high-k bar | Limit exceedance missed | Check limits separately |
| Ignoring bends | Limit overestimated | Use post-bend data |
| Ignoring cold start | Fails to start | Check sonic limit and freezing |
| Wrong working fluid | Out of range | Compare merit numbers |
I'd like to learn related topics.
Try the heat pipe simulator and capillary rise tool. Related pages include boiling heat transfer, condensation heat transfer, thermosiphons and conjugate heat transfer.
Related Topics
Experience the theory firsthand with the interactive simulator for this field
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