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## How Does Bending Affect Heat Pipe & Vapor Chamber Performance?

The majority of applications for heat pipes, and to a lesser extent vapor chambers, require these products to be bent. Below are respective examples for high-performance graphics card, semiconductor equipment and networking applications.

Figure 1: Heat Sinks Using Bent Two-Phase Devices

But what effect does bending a heat pipe or vapor chamber have on their performance? To answer this, let’s first talk about bend parameters then we’ll move into the meat of it and discuss both evaporator and vapor resistances.

Although smaller bend radii are possible, heat pipe guidelines almost universally put their c/l (centerline) bend radius at 3X the diameter of the heat pipe being bent. In other words, for a 5mm round heat pipe bent into a U shape, the resulting OD would be 35mm.

Bend radius for a 1.5-3.5mm thick vapor chambers are about 10mm. For instance, for a 2mm thick vapor chamber the OD of a 180 degree bend would be 22mm. While these would have to stamped into place for a traditional two-piece vapor chamber, one-piece designs can be bent post production, even into a U-shape.

Figure 2: Bending Examples

Two areas of thermal resistance in these devices must be closely examined. The first is evaporation resistance which is the deta-t due to conduction through the device wall and wick structure as well as phase change of the working fluid into vapor.

In the vast majority of applications, the evaporation resistance is the dominate resistance; therefore, making these devices somewhat length independent. This means that a two-phase device with a transport distance of 75 mm will have almost the same Tsource -Tsink as one with a 150 mm transport distance. This, in effect, doubles the effective thermal conductivity for the longer devices. For a typical water/copper heat pipe with 0.5mm wall and 0.4mm sintered wick, thermal resistance has a nominal value of about 0.1 oC/w/cm2

Figure 3: Heat Pipe

The second is vapor transport resistance which is the temperature loss in the transport region due to pressure drop and condensation delta-t’s. This resistance is typically a function of the power density in the vapor space – nominal power densities are 300-400 w/cm2 with a typical maximum of 800-1,000 w/cm2. The nominal thermal resistance of vapor transport is about 0.01o C/w/cm2. Because of the correlation between cross sectional area of the vapor space and vapor resistance, smaller diameter heat pipes or those that have been flattened increases vapor flow thermal resistance.

So how are these two key resistances affected by bending a two-phase device?

Because the evaporator is almost never placed at the arch of a bent two phase device, we would expect relatively little to no increase in its nominal value when comparing straight and bend two-phase devices. When testing a 3mm thick U-shaped vapor chamber with a 10mm bend radius we see this to be true. Test data showing the evaporation resistance before and after bending is shown in Figure 4. The results are identical within measurement error.

Figure 4: Evaporator Resistance

Now let’s look at vapor transport resistance. Due to the pressure drop induced by bending the vapor chamber, we would expect vapor transport resistance to increase due to an increase in pressure drop, thus decreasing the thermal conductivity of the device. Again, testing supports this claim and is relatively consistent between heat pipes and vapor chambers. Bending a two-phase device 180 degrees increases vapor flow resistance by around 50%.

Figure 5: Vapor Resistance

It’s important to note that while vapor transport resistance is significantly affected by bending, its relative contribution to overall thermal resistance is often small. Remember that for an un-bent part, evaporator resistance is a full order of magnitude greater than that of vapor flow resistance.

So, when we examine the overall thermal resistance, we see that the net effect is between 18-40%. You will also note a decrease in the total power. When relying on capillary pumping in the wick structure to return the fluid the bending affects the pore radius and porosity in the bend region. This has about a 10% effect on the Qmax post bending.

Figure 6: Total Thermal Resistance

Given that one should generally design a two-phase device to operate at 70% of its Qmax (we’ll use total power of 70W), we see that the thermal resistance of an un-bent device from 0.047 degrees c/w (3.3 °C) to 0.063 (4.4 °C) for a device with a U-shaped bend. This translates to a delta-T of only 0.9 degrees Celsius.

Based on this we can extrapolate some rules of thumb.

• Spec a straight heat pipe or vapor chamber with 30% thermal safety margin.
• Example: A lead load of 70w should use a heat pipe designed with a Qmax of no less than 91w.
• Add total bend radius of the heat pipe/VC. While not perfect this will get you very close to actual.
• Example: one 90 degree bend and another 45 degree bend = 135 degrees of bend
• For each 10 degrees of bend Qmax will decline by .56%.
• In our example from above: 135 degree total bend divided by 10 multiplied by 0.56% = 7.6% decrease in Qmax.
• So for our 70 w heat source with two bends totaling 135 degrees we’ll need a heat pipe with a Qmax of 70*(1+(.3+.076)) = 96.3w.

## Dust Bunnies are Choking Heat Sinks to Death

My current notebook is about 18 months old and had been running slower and slower for a few months. It was also noticeably hotter causing the fan to run almost continuously. I knew it was that time. About every year and a half I have to take apart my PC to clean out dust from the fin stack and to replace the thermal grease if I want it to run at peak performance. When I mention this to friends they always look at me strangely. Here’s what I found, and expected to find, when I opened it up.

Notebook Heat Sink After 18 Months

Yes, that’s the heat sink. And, for the most part this notebook is used on my desk and most people think I am anal about keeping things neat and tidy. So, this is not from a harsh environment!

And since the processor has been running hot for a few months the grease has started to harden so that needed replacing as well. Whoever put the grease on in the first place used enough for three processors!

Thermal Grease

This reminds me of several papers I saw presented some years ago. David Moore of HP showed results in both desktop and laptop systems with failures showing up in less than 1 year1&2. The process begins when hair, and/or thin fibers of fabric or paper begin to layer on top of one another forming an intertwined network. Smaller flakes, usually skin, are then trapped by the matted fibers. Here’s what the process looks like2.

Long Fibers Intertwine then Small Particles Become Trapped

Wanting to understand more about the process he and an HP team created a “Dusty Environment Simulator”, complete with manmade dust – a combination of finely shredded and ground recycled newspaper and attic insulation, with a fire retardant added. The material would be introduced into an enclosed test chamber using a standard flour sifter.

The next step was to test small form-factor desktop systems, each with a different CPU heat sink design. The two I’ll touch on here are a folded fin radial heat sink with a top mount fan and an extruded straight fin heatsink, also with a top mount fan. I pulled these pics off the web for illustrative purposes so show roughly what these sinks look like.

Folded Radial Fin and Extruded Straight Fin Heat Sinks

His results bowled me over. The radial heat sink had a delta-T which was 3 degrees Celsius better than the extruded fin sink when the systems were tested without dust. However, the radial sink became more quickly clogged with dust causing its delta-T to rise above that of the extruded sink1.

Heat Sink Fouling Test Results

David concluded that while environment is a significant risk factor in heat sink fouling, heat sink design also plays a key role. Here are some of the non-environmental factors that increase vulnerability.

• Finer pitch heat sinks – provide a shorter distance for fibers to bridge
• Sheared fin construction – sharp surfaces retain fibers
• High impingement velocity
• Close proximity of fan

Hopefully, every one of you is not only reaching for a screwdriver to take apart your own system, but also thinking about these killer dust bunnies when designing your next thermal solution.

Sources

1. Moore, David A. “The Dust Threat” Presentation to the IMAPS Thermal ATW, October 23rd, 2003
2. Moore, David A. “Characterization of Fiber Accumulation Fouling in Fine Pitched Heat Sinks” Paper for 25th IEEE Semi-Therm Symposium.