Heat Pipes and Vapor Chambers: Moving Heat by Phase Change

Copper is a good conductor and a poor transporter. Its thermal conductivity is about 400 W/(m·K), which sounds large until it is applied to a geometry: a solid copper bar 1 cm square and 15 cm long has a resistance of $L/(kA) = 0.15/(400 \times 10^{-4}) \approx 3.75$ K/W. At 95 W that is a 356 K rise, which is not a heat spreader but a heater. Making the bar wider helps only linearly, and a bar wide enough to carry 95 W over that distance would weigh more than the rest of the cooler.

A heat pipe replaces conduction along the bar with convection of a working fluid, and the effective conductivity of the result is quoted in the thousands to tens of thousands of W/(m·K), two orders of magnitude above copper. The mechanism is evaporation at one end, vapour flow, and condensation at the other, with the liquid returned by capillary action through a wick.

The loop, and why it needs a wick at all

A heat pipe is a sealed tube, evacuated and charged with a small amount of working fluid, lined with a porous wick. Heat applied at the evaporator section vaporises fluid from the wick’s surface. The vapour is at a slightly higher pressure than the rest of the tube, so it flows toward the condenser, where the lower temperature causes it to condense and release the latent heat. The condensate must then return to the evaporator, and it returns through the wick by capillary pressure, driven by the curvature difference between the meniscus in the evaporator, where the wick is drying out, and the meniscus in the condenser, where it is flooded.

The capillary pressure available is

$$\Delta P_{\text{cap}} = \frac{2\sigma}{r_c}$$

with $\sigma$ the surface tension and $r_c$ the effective pore radius. Water at 100 °C has a surface tension around 0.059 N/m, so a wick with 20 µm pores generates about 5.9 kPa of driving pressure. That pressure has to overcome three losses: viscous flow of the liquid through the wick, viscous flow of the vapour down the tube, and any gravitational head if the evaporator is above the condenser.

The balance is the design equation. A finer wick generates more capillary pressure but has lower permeability and therefore more liquid friction; a coarser wick has the opposite trade. Grooved wicks are cheap and have high permeability but low capillary pressure, which limits them to short or gravity-assisted orientations. Sintered metal powder wicks have small pores and high capillary pressure but low permeability, which suits thin, high-flux evaporators. Mesh wicks sit between.

The gravitational term is the reason orientation matters. A heat pipe with 5.9 kPa of capillary head can lift water about 0.6 m against gravity, and less once the flow losses are subtracted. A cooler that works in a tower orientation and fails when laid flat is failing on this term, and the specification usually states a maximum tilt or an orientation range for that reason. The condenser end is where the heat finally leaves, and its resistance depends on the airflow through the fin field as much as on the pipe.

The four limits, and which one binds

A heat pipe does not fail gradually with increasing power; it reaches a limit and its thermal resistance rises sharply, because the evaporator dries out and the loop stops returning liquid. Which limit is reached first depends on the design and the temperature.

The capillary limit is the one described above: the wick cannot generate enough pressure to return the condensate at the required flow rate. It scales with the wick’s capillary pressure and inversely with the length, and it is the usual limit for a long, thin pipe at moderate temperature.

The boiling limit occurs when the heat flux at the evaporator is high enough to nucleate vapour inside the wick structure itself, blocking liquid return. It depends on the wick’s effective pore radius and on the fluid’s properties, and it is the usual limit for a small evaporator carrying a concentrated load, which is exactly the geometry of a processor cold plate.

The entrainment limit occurs when the vapour velocity is high enough to shear droplets off the liquid surface and carry them back toward the condenser, opposing the return flow. It scales with the vapour density and the tube’s cross-section, so it matters for small-diameter pipes at high power.

The sonic limit is a vapour-flow constraint: at low pressure the vapour can reach the local speed of sound, and the flow chokes. It appears during startup, when the pipe is cold and the vapour density is low, and it is why a heat pipe can take minutes to reach operating temperature from cold rather than seconds.

The four limits form an envelope in the power-versus-temperature plane, and a well-designed pipe is limited by whichever is lowest at the intended operating temperature. Water is the usual working fluid for electronics because its figure of merit peaks in the range from roughly 30 °C to 200 °C; below freezing it cannot be used at all, and above a few hundred degrees the internal pressure becomes a mechanical problem.

Vapor chambers are heat pipes flattened into a plane

A vapor chamber is the same loop with a different geometry: a thin, flat cavity with a wick on one or both internal faces, and posts or a mesh between the faces to keep them from collapsing under the internal pressure. Heat enters across a small area on one face, spreads laterally through the vapour space, and leaves across a larger area on the other face, where fins or a cold plate remove it.

The point is that the lateral transport happens in the vapour rather than in the wall. In a solid copper base, lateral spreading has the resistance described in the thermal resistance network, and it grows as the source shrinks. In a vapor chamber the vapour space has an extremely high effective conductivity in the plane, so a 1 cm² source can feed a 30 cm² fin field with a temperature drop of a few kelvin rather than tens.

The trade is that a vapor chamber is a pressure vessel. The internal pressure at operating temperature is below atmospheric for water, so the walls are loaded by the external atmosphere and must be supported; the support posts occupy space that would otherwise carry vapour, and the wick on the condensing face adds a conduction path in series with the condensation. A vapor chamber also has a maximum thickness below which the vapour space is too thin for the flow to spread effectively, which is why very thin chambers have worse spreading than thick ones.

The failure mode is the same dry-out, localised: a hot spot that exceeds the local boiling limit creates a vapour blanket that insulates that patch, raising its temperature further. Vapor chambers are specified with a maximum heat flux per unit area for this reason, and the number is typically lower than the capillary limit would suggest.

Working fluid, pressure, and the temperature window

The fluid choice sets the operating window, because the loop only works while the vapour pressure is in a usable range. Too cold and the vapour density is so low that the sonic limit binds; too hot and the pressure approaches the container’s limit.

Water is used from roughly 30 °C to 200 °C. Below 30 °C the vapour pressure is a few kilopascals and the vapour is thin; above 200 °C the saturation pressure is well over a megapascal, which a thin-walled chamber cannot hold. Methanol and ammonia extend the range downward; ammonia is common in spacecraft because it stays fluid at low temperature, and it is toxic and incompatible with copper, which is why its pipes are aluminium. Refrigerants such as R134a work at low temperature but have poor figures of merit near room temperature. Liquid metals are used only at very high temperature.

The fluid also determines the wick material by compatibility. Water and copper are compatible; water and aluminium are not, because the aluminium corrodes and generates hydrogen that accumulates in the condenser and eventually stops the loop. That is why water heat pipes are copper, and it is the single most common materials constraint in the field.

Where the model is optimistic

The quoted effective conductivity is an average over the whole pipe and hides the two ends. The evaporator has a finite heat-transfer coefficient between the wall and the wick, and the condenser has another between the vapour and the wall, and at high flux these interface terms dominate the resistance even when the transport term is negligible.

A heat pipe also has a minimum power below which it does not work well, because the vapour flow is too small to sweep non-condensable gas toward the condenser, and any gas present accumulates at the cold end. Manufacturing cleanliness is therefore a performance parameter: a pipe with a few percent of air by volume loses a proportional fraction of its condenser area, permanently.

Finally, the transient response is slow compared with conduction. The thermal mass of the fluid and the wick, plus the time for the pressure field to establish, means a heat pipe responds to a power step over seconds rather than milliseconds. For bursty loads the die heats before the pipe has moved any heat, which is why the junction’s short-timescale thermal path is through the package and the cold plate rather than through the pipe.