Heat pipes
A Socratic walk-through of heat pipes — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #How can a sealed tube with no moving parts carry heat better than a solid copper bar of the same size?
Open a laptop and you find thin flattened tubes running from the processor to a finned block at the hinge. They are sealed, contain no pump, have nothing that turns, and weigh less than the copper they replaced. Yet swap in a solid copper bar of the same cross-section and length and the machine runs hotter.
That should be uncomfortable. Copper is one of the best heat conductors we can afford to buy. What can a hollow tube do that a solid bar of the best available conductor cannot?
Reasoning it through
REASONING #Start with what a solid bar needs in order to move heat. Conduction obeys a simple proportionality: power carried equals conductivity times cross-section, times temperature difference, divided by length. Copper's conductivity is about 400 watts per metre-kelvin (recalled, a standard handbook value). Take a bar one square centimetre in section — a ten-thousandth of a square metre — and twenty centimetres long. The conductance is 400 times 0.0001 divided by 0.2, which is 0.2 watts per kelvin. To push 100 watts through it you would need a temperature difference of 100 divided by 0.2: 500 kelvin, end to end.
So the bar is not a bad conductor. It is a conductor that charges for its service in temperature, and at this size the price is absurd. Anything that beats it must be charging less — which means dropping the hidden assumption that heat must be handed from atom to atom along a stationary solid. Suppose instead we let matter carry it. The question becomes how much energy a gram can carry, and how cheaply we can move that gram.
Here phase change earns its place. Boiling a kilogram of water takes about 2,260 kilojoules (recalled) and returns all of it on condensing. Compare warming steam: its specific heat is roughly 2 kilojoules per kilogram-kelvin (recalled), so a vapour cooling two degrees on the journey gives up about 4 kilojoules per kilogram. The latent term is some 560 times the sensible one — to carry heat while barely changing temperature, a fluid must change state.
Now the arithmetic runs the other way. Moving 100 watts needs 100 joules per second divided by 2,260,000 joules per kilogram: about 0.044 grams per second, under three millilitres a minute. That is a trickle, and it needs no pump — capillary action in a wick of sintered powder or grooves will lift it.
And what drives the vapour along? Only a pressure difference — and here is the step the device turns on. The tube is sealed and evacuated of everything but the working fluid, so the fluid sits on its own saturation line, pressure and temperature locked together. A pressure drop just large enough to push vapour twenty centimetres corresponds, on that line, to a temperature drop of a degree or two. The vapour path is nearly isothermal by construction.
Price that in temperature as we priced the bar. If 100 watts crosses the same geometry with a two-kelvin difference, the effective conductivity is 100 times 0.2, divided by 0.0001 times 2 — around 100,000 watts per metre-kelvin, a couple of hundred times copper. No better material is involved. The temperature difference simply stopped being the mechanism of transport and became a symptom of it.
The analogy
THE ANALOGY #A copper bar is a bucket chain: each person must hold the bucket a little higher than the next, so a long chain needs a steep hill. A heat pipe is a courier on a bicycle — the load is picked up at one end and set down at the other, and the road can be flat, because nothing is being passed uphill. The parcel is carried, not handed along.
the courier can be given more parcels than the bicycle holds, and then deliveries simply stop, whereas a bucket chain merely gets slower. That is the heat pipe's behaviour at its capillary limit, which no conduction picture predicts.
Clarifying the model
THE MODEL #Three tempting readings should go. The vapour is not carrying heat because it is hot: we computed that the sensible term is a few hundredths of a per cent of the job. The vacuum is not what makes it conduct — vacuum is a superb insulator; evacuation removes non-condensable gas that would otherwise pile up at the cold end and block the vapour, and it sets the temperature at which the fluid boils. And a heat pipe is not a thermal superconductor: it has real resistance where heat enters the liquid and leaves the condensate, and those end resistances usually dominate a real installation.
The account also makes a sharp prediction. If capillary return is what closes the loop, a wicked pipe should still work upside-down, hot end above cold, at reduced capacity — while a bare tube relying on gravity should fail outright in that orientation. That is what is observed, and it is why laptop pipes work in any posture. Push past the capillary limit and the wick dries out, so performance collapses abruptly rather than degrading smoothly; cool the pipe below the fluid's freezing point and it reverts to a thin-walled empty tube. A conductor has no such windows.
Where this sits next to its neighbours: spacecraft-cooling.md and countercurrent-heat-exchange.md handle the same commodity, and each differs at which term of the heat budget is manipulated. Spacecraft cooling is about the exit — radiation is the only door out, so surface and the fourth power of temperature govern everything. Countercurrent exchange manipulates the gradient, holding a small difference everywhere rather than a large one at a point. A heat pipe changes the carrier. And candle-wick.md shares the identical capillary pump; the difference is what the wick delivers to — a flame that consumes the liquid, against a condenser that returns it, one a one-way feed and the other a closed loop.
The load-bearing claim is the isothermal vapour path. If moving vapour along the tube demanded a large temperature difference, the effective-conductivity argument collapses entirely, and the heat pipe would be a poor copper bar with a hole in it.
A picture of it
THE PICTURE #How to readFollow one gram of working fluid, not the heat. Start at the hot end in the wick and go round: it boils, crosses the tube as vapour on almost no pressure difference, condenses and gives back its latent heat, then is pulled home along the wick. Three of the four transitions form a closed loop that runs indefinitely with no moving part. The fourth arrow, to "wick run dry", is the exit — not a slow degradation but the state the device drops into once the load exceeds what capillary suction can return.
What became clearer
WHAT CLEARED #A heat pipe does not conduct heat better; it stops conducting it. Conduction buys transport with a temperature gradient, and the price rises with distance. Phase change buys the same transport with a mass flow that is tiny because latent heat per kilogram is enormous, and nearly free in temperature because a sealed fluid on its saturation line changes pressure far more readily than it changes temperature. The huge effective conductivity we quote is therefore an accounting figure, not a material property — and holds only inside the window where the assumptions behind it are true.
Where to go next
ONWARD #- Why the working fluid fixes the usable temperature band, and what is used above and below water's range.
- How a vapour chamber and a loop heat pipe change the argument when heat must be spread over an area or moved metres rather than centimetres.
Key terms
TERMS #| Term | What it means |
|---|---|
| Latent heat of vaporisation | the energy absorbed in turning a liquid to vapour at constant temperature, and released again on condensing. |
| Saturation line | the locked relationship between a pure fluid's temperature and its vapour pressure when liquid and vapour coexist. |
| Capillary limit | the heat load above which the wick cannot return liquid fast enough, at which point the evaporator dries out. |
Every term the collection defines is gathered in the glossary.