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## Vapor Chamber Quick Calculations – Do I Need One?

In this blog, I’d like to take you through the early steps I take when determining if a two-phase device, specifically a vapor chamber, might be needed as part of the thermal solution. I’ll eventually do a complementary piece on heat pipes, but in the interest of brevity we’ll stick with a copper vapor chamber with a sintered wick and water as the working fluid.

If you’ve read some of my previous articles, you know that for the vast majority of two-phase applications where heat is being moved from the heat source to a remote condenser – heat pipes trump vapor chambers. It’s not because they’re necessarily better at moving heat. It’s because the path from the evaporator to condenser usually requires some twists and turns – not typically a strong suite of vapor chambers.

Vapor chambers, as seen above on the left, are typically used to spread heat to a local condenser/heat sink who’s required area is minimally 10 times bigger than the area of the heat source. When heat needs to be moved to a remote condenser, distances of greater than 40 or 50mm are generally required for two-phase devices to make sense.

Even before doing any calculations, I know there are several circumstances where vapor chambers are useful.

• Power densities >15 W/cm2
• Low/no air flow – requiring a larger heat sink
• Ambient temperatures above 40 oC – lowering the thermal budget
• Heat sink heat is constrained – requiring a thin base

## Step 1: Determine the Thermal Budget

Simply speaking, your thermal budget is calculated by subtracting the maximum ambient temperature in which the device will operate (Tambient) from the maximum allowable temperature of the IC case (Tcase) or in some cases the Tjunction if there isn’t a built-in spreader on the chip. Typical thermal budgets for electronic components are in the range of 30-50 oC.

Let’s assume we’ve been given a Tcase max by the manufacturer or ASIC designer of 85 oC. Further, we need our device to operate at temperatures up to 45 oC.

This leaves us with a total thermal budget of 40 oC. This means that the total of all our individual delta Ts from the case to the air cannot exceed this figure.

## Step 2: Estimate Required Heat Sink Size

Found on our website, this calculator quickly provides the overall volume of the heat sink based on heat source power, Tcase , max ambient temperature and available airflow. Obviously, if you’ve already done the detailed calcs for required heat sink size, you can skip this step.

I like to know this figure because it quickly allows me to estimate specific dimensions – allowing me to understand if the heat sink base will be substantially larger than the heat source.

We already know that our Tcase is 85 oC and our Tambient is 45 oC. This leaves a thermal budet of 40 oC.

Let’s further assume the following

Heat Source: 100W

Heat Source Size 25x25mm

Available airflow: 200 LFM

With an estimated volume of 375cm3, I can begin to make some estimates of dimensions. I’ll start by fixing the fin height to a reasonable 27mm and tacking on 3 mm for the base height. Pretty standard. Then I’ll adjust the length and wide dimensions to reach the specified volume estimate.

In this case the heat sink dimensions would be roughly 110 x 110 x 30mm.

## Step 3: Determine if you’ve got the space and airflow for a local heat sink

I can play with the dimensions mentioned earlier and compare it to the proposed system layout. Given that were talking about vapor chambers, I’m going to assume that we have the desire and space to use a local heat sink. However, if it turned out that we wanted or needed a remote heat sink whose distance between evaporator and condenser was greater than 40 or 50mm, I’d be doing a different calculation for Step 3 in order to evaluate a heat pipe solution.  As it stands for this example, we’re going to use a local sink.

## Step 4: Determine the delta-t spreading resistance in the heat sink base

First, I see that the area of the heat sink is 15 times larger than the area of the heat sink. This already suggests a vapor chamber may be in order. I also know that the total thermal budget is 40 oC. Next, I’ll use another calculator we have online to understand the spreading delta-T in the base for solid aluminum and copper as well as for a vapor chamber.

Populate the inputs with our earlier assumptions and select between an aluminum or copper base by changing the material conductivity in the calculator. Also, let’s assume the heat source is in the center of the base.

Now I’m going to use a rule of thumb to determine if a vapor chamber might be needed:

Consider a vapor chamber when the spreading resistance in a solid base is greater than 10 oC.

• The solid aluminum base in this example (not shown) has a delta-T of 34.5 o If we’ve got room we could double the base thickness, lowing the delta-T to 19 oC. But that’s almost half our thermal budget and substantially more than the 10 degree rule of thumb.
• Switching to a 3mm copper base (shown above), with a thermal conductivity of 380 W/m-K, gives us a base delta-T of 16.8 o By increasing the base thickness to 5mm, I’m within striking distance of the 10 degree rule of thumb, but it’s certainly going to increase weight and potentially decrease fin height. If these tradeoffs are acceptable later in the design process, a solid copper base might make sense.
• But, compare the 5mm solid copper base (10.7 oC) to the vapor chamber base (4.5 oC). The vapor chamber is going to be thinner, about half the weight and potentially give us other design options such as alternative TIM choices.

## Comparing our quick estimates to more lengthy calculations

As stated in the beginning of this article, this method is great for initial estimates as it gives you both the heat sink volume and a good feel for the likelihood of a vapor chamber base.

After using the same parameters as mentioned above, and fiddling with fin characteristics, I used a more sophisticated model to calculate the remaining delta-Ts.

As you can see from the above chart, using a vapor chamber puts us 3.3 degrees below our thermal budget. Note, the TIM delta-T of 4.8 oC. used thermal grease for this calculation, but I could switch to a high conductivity thermal pad (which will make the manufacturing engineers happy) and still remain below my thermal budget.

## Thermosyphons for Electronics Cooling

This blog is written to give engineers a basic understanding of an often forgotten, but still relevant two-phase cooling solution – thermosyphons.

Recently, I visited the Henry Ford Museum in Michigan. A fabulous place that’s steeped in the kind of history that reminds one that the ‘tech revolution’ started well over one hundred years before our modern use of the term.  I’m talking about more than just the innovation that allowed the Model-T’s assembly time to be cut from 12 hours to 2.5 hours. It was an effort in materials innovation coupled with a desire to keep things as simple as possible, in some cases eschewing innovation for less costly, more dependable solutions.

The decision to rely on an atmospheric radiator cooling solution is one such example of simplicity in place of innovation. Although pumped liquid cooling was in use by Daimler at the time, Ford decided he didn’t need the added cost or point of failure.  The solution is known as a thermosyphon, which is a simple open or closed loop self-pumping mechanism that relies on the fact that hot water rises while cool water sinks. As the water in the engine block channels is heated, it’s forced up and into the radiator, where it is cooled and sinks to the bottom of the block where the cycle is repeated.

Thermosyphons are still used today in solar heaters and furnaces, but it’s their use in electronics cooling that I want to focus on today, albeit in a slightly different form. Certainly, the first step in the discussion should be to understand what’s generally known as a heat pipe thermosyphon. Let’s compare them to standard heat pipes in terms of design, limitations, and benefits.

## Differences Between Thermosyphons & Heat Pipes

Thermosyphons can only be used when gravity is used to move liquid back to the evaporator

Thermosyphons used for electronics cooling are known as “Heat Pipe Thermosyphons” (HPTS) because they mimic their heat pipe counterparts in all but one way: the wick structure is fully or partially removed. But, why is this important and how do they work without this seemly critical component removed?

As you know, the wick structure inside a heat pipe is used to move liquid from the condenser to the evaporator after is has changed state from vapor to liquid at the condenser (fin stack). This capillary action allows efficient liquid transport even if the heat pipe is in an orientation that is neutral or against gravity. Without this built-in liquid transport mechanism, HPTS must rely on gravity to move the liquid back to the heat source (Fig 1 – Thermalfluidscentral.org). For this to occur, the angle should generally be greater than +5 degrees with the evaporator below the condenser.

For a given diameter, thermosyphons have a higher Qmax than heat pipes

The sintered wick lining the walls of a heat pipe reduces the available vapor space, a key component to determining a device’s Qmax. This isn’t a problem for heat pipes as it’s the capillary limit that determines its ability to transport heat. The chart below shows Qmax for various heat pipe sizes where the evaporator is directly below the condenser (+90 degree orientation).

Wickless thermosyphons of the same diameter as heat pipes have 100-200% higher Qmax than the heat pipe counterparts, all because of the additional vapor space. See Celsia’s heat pipe performance calculator.

Thermosyphons can carry heat farther distances than heat pipes

The simple reason thermosyphons operate more effectively over longer distances has to do with the ease with which liquid can travel from the condenser to the evaporator. With a heat pipe, the water is transported through the wick structure which is usually porous sintered metal.  In a thermosyphon, water easily flows back to the evaporator along the smooth or grooved inner walls. While a heat pipe’s practical heat transport limit is on the order to 1 to 2 meters, a thermosyphon can easily carry heat distances over 10 meters. This usually isn’t an issue with electronics cooling as most applications will use these devices in distances less than a couple of meters, but worth mentioning nonetheless.

Thermosyphons are susceptible to damage caused by freezing

The fluid level required for a thermosyphon generally covers between 20-80% of the length of the evaporator, assuming the vessel is in a vertical orientation. This is significantly more than traditional heat pipes and can be problematic if water is used in conditions where they are exposed to freezing temperatures. After repeated freeze/thaw cycles, the expansion of water will form bulges in the pipe, eventually fracturing the tube wall.  For HPTS designs using other fluids, freezing is generally not a concern.

Water (used in a copper system) is the highest performing fluid for most electronics temperatures followed by alcohols and then refrigerants. The advantage of non-water based working fluids is their ability to operate below freezing temperatures. Common combinations with proven life are copper/water, copper/alcohol, aluminum/refrigerant.

## Thermosyphon Variations

There are several variations of this basic design that can improve thermal performance and/or reduce the possibility of structural damage due to freezing.

Add a wick to the evaporator section

A grooved or mesh wick will reduce thermal resistance, enabling higher power densities in the evaporator. However, this solution will do nothing to prevent damage caused by freezing as the same amount of liquid is required.

Sintered wicks will lower the thermal resistance to the greatest level. It also allows optimization of the fluid charge, effectively reducing the required liquid. This all but eliminates the possibility of damage caused by freezing. In the bottom portion of the above figure, note that the wick is only used at the evaporator section of the thermosyphon.

Create separate loops for the vapor and liquid

Lastly, a looped thermosyphon can be used to separate the vapor flow from the liquid flow, further increasing Qmax. The vapor flow leads directly to the condenser where it cools and returns to liquid which travels back down to the evaporator. In the configuration to the right, the hollow evaporator at the bottom of the device uses a mechanism to prevent vapor from traveling up the liquid flow section, but still allowing liquid to flow in. The addition of a sintered wick to the evaporator allows less water to be used, decreasing the risk of damage caused by freezing.

## Using Thermosyphons to Cool Electronics

Taking into account both the advantages and drawbacks of thermosyphons – when should they be used in electronics environments? Historically the number one use for these are in power electronics applications and recently some use in data centers. Power electronics would include stationary motor controllers in places like steel mills, mining etc. Also moving applications such as light rail and subway systems. Recently there has been renewed interest for data center applications as they move towards higher ambient temperatures and a reduced number of fans. Cooling in data centers accounts for about 33% of the operating costs, with cooling fans accounting for almost half that figure.

In summary, thermosyphons are still a relevant technology for cooling high power applications where the evaporator is below the condenser. Applications include power electronics such as IGBTs as well as radar systems, transmitters, and alternative energy generation.