# Heat Pipe Design and Modeling

**Billy:** Welcome! And thank you for joining us for today’s webcast, Heat Pipe Design and Modeling, sponsored by Advanced Cooling Technologies and Tech Briefs Media Group. I’m Billy Hurley, Associate Editor with Tech Briefs Media Group, and I’ll be your moderator today.

Our webcast will last approximately 30 minutes, and there will be a question and answer period at the end of the presentation. If you have a question, you may submit it at any time during the presentation by entering it in the box at the bottom of your screen. Our presenters will answer as many questions as possible at the conclusion of the presentation. And those questions not addressed during the live event will be answered after the webcast. In order to view the presentation properly, please disable any popup blockers you may have on your browser.

At this time, I’d like to introduce our speakers.

Bryan Muzyka is the Sales Manager for Advanced Cooling Technologies’ defense and aerospace products group. He’s well-versed in heat pipes and other thermal management systems. He began as a research and development engineer for ACT’s aerospace group before taking on his current sales role. For the past four years, Bryan has been working with customers to solve thermal challenges in harsh environment, military, and aerospace applications.

Also on the line for the Q&A part of our presentation is Jens Weyant. Mr. Weyant is lead engineer for the defense and aerospace group at Advanced Cooling Technologies. He has designed and developed a variety of heat pipe thermal solutions for electronic devices, including power electronics, high power RF components, and other solid state devices such as laser diodes and FPGAs. He is proficient and fluid in thermal analysis and is also experienced with prototyping and testing. He currently manages the product development team, creating rugged, high performance cooling solutions for customers worldwide.

So at this time I’d like to hand the program over to our first speaker, Bryan Muzyka. Bryan?

**Bryan:** Thanks, Billy. And thanks everyone for joining us. As Billy mentioned, today’s topic is Heat Pipe Design and Modeling. And with that, we’ll go ahead and get started.

So the goals of today’s webinar is to provide you with the knowledge and tools required to implement a heat pipe solution into your system. Specifically, we will provide a basic understanding of operation and performance capabilities for heat pipes. We will provide design guidelines for integrating heat pipes into your system. And we will give you the necessary tools to run quick, easy, and effective thermal simulation. This presentation will give you confidence whether or not a heat pipe solution is right in your system and how well it performs.

The first section of today’s presentation will talk about heat pipe basics. This should provide you with a foundation and understanding of how they work and how they are effective. This includes theory and operation. We’re going to show a brief video that demonstrates the increased thermal performance over copper. We’ll get into the advantages you get when designing with heat pipes. And then we’ll talk about embedded heat pipes, known as high thermal conductivity or HiK pipes. And we’ll go over some product examples in this section.

After the background, we’ll jump into designing with heat pipes, followed by basic and detailed thermal modeling techniques. And then we’ll give a comparative example and wrap up and take some questions.

So there are many lengthy books and articles on heat pipe theory and operation. However, here we’ll just get into some of the basics to make you effective as a designer.

Heat pipes are passive, two-phased heat transfer devices, using liquid to vapor phase transition to provide minimal temperature rise across their length. A typical copper water heat pipe will operate with a two to five degree temperature difference. And that rule of thumb is a general basis for a lot of the modeling we’ll dive into later. To give you a better feel for operation and performance, we’ll show a quick video that will illustrate operation and then give a comparison on copper rod to a heat pipe.

During heat pipe operation, heat enters the heat pipe at what is known as the evaporator. The fluid contained in the wick structure vaporizes and creates an internal pressure gradient. This pressure gradient moves the vapor to the cooler region known as the condenser, where it transitions back to liquid. The liquid is then passively pumped back to the evaporator by a wick structure. This cycle is continuous as long as there is a temperature difference across the length of the heat pipe.

So next in this video shows the effectiveness of a heat pipe compared to a solid copper rod. The copper rod on the left and the heat pipe on the right both have a thermal paint on them that’ll show the conduction as it changes temperature. First, the copper rod shows conduction up the length. And then as you can see, the heat pipe almost instantaneously moves the heat. When moved back to the cooler region, the heat pipe will again cool down at a much faster rate than the copper rod.

Now, we’ll jump back into the presentation.

So hopefully, our demonstration provided you with an understanding of the thermal benefits. But as a general rule, any time conduction is a large portion of your temperature rise, heat pipes can be helpful.

Some of the other benefits include normal SWaP benefits. Heat pipes are lightweight, thin-walled tube, with a very small amount of working fluid. Therefore, due to their thermal properties, you can often reduce the overall size of your heat sink or heat spreader.

Another big advantage is power. If your electronics are D-rated due to exceeding maximum temperature, heat pipes can help increase the cooling at the hot spots to allow you to increase your electronics’ temperatures. Also because heat pipes are passive, they require no additional power for your thermal solution.

The final advantage is flexibility. As we continue through this presentation, we’ll show how heat pipes can be easily integrated due to their ability to conform to different geometry.

HiK Plates are plates with embedded heat pipes. Heat pipes are pressed into grooves or drilled holes and soldered or epoxied into place. HiK Plates offer similar strength and weight as aluminum with much higher thermal conductivity. They can be manufactured as thin as 0.072 inches. And HiK Plates are often used to reduced hot spot temperatures or increase fin efficiencies for air-cooled heat sinks. The highlighted point here shows thermal conductivity range from 500-1,200 Watts per meter K. These values come from real-world applications where we went back to our models and adjusted the bulk thermal conductivity of the plate until the hot spots matched our tested results. The range provided here is mainly dependent on geometry as large form factors can achieve higher effective conductivities since the delta T across the heat pipe is not a function of length.

This figure on this slide shows a comparison of aluminum plates with a HiK Plate. In this example, the system was cooled using liquid cold rails. With straight aluminum, shown on the left, conduction gradients created hot spot temperatures exceeding maximal electronics temperatures. Going to a copper solution was not desirable due to weight concerns. So we embedded heat pipes, and using a HiK solution, we got higher performance than aluminum or copper without adding significant weight to the aluminum solution. For this program, we achieved over 20 degrees C hot spot temperature reduction.

So one of the more frequent questions on heat pipes is how reliable they can be for your system requirements. Due to heat pipe’s passive operation and known compatibility for various fluid and envelope materials, heat pipes provide very long life when manufactured properly. Twenty plus years operation is routine for heat pipes.

Next, we need to make sure that the heat pipes can operate in any environment. Heat pipes themselves are thin-walled tubing. However when integrated properly, they can withstand harsh environments, requirements such as shock, vibration, and extreme temperatures. Copper water heat pipers are typical for terrestrial applications and have demonstrated the ability to withstand freeze/thaw cycles on their own or when integrated into assembly such as a HiK Plate.

Also online, we offer a reliability guide in the Resource section of our website.

Another favorable characteristic of heat pipes is that they can be used across a large range of applications. Basically, any heat source with a temperature limitation is a potential candidate for a heat pipe. The examples we show here, starting with the one on the top left is a heat pipe heat sink for optical equipment. The top right is a heat pipe used for satellite thermal management. The central picture is an assembly used for LED cooling. And the bottom figures are conduction card frames and conduction chassis for military electronics or avionics applications.

Next, we’ll talk about designing with heat pipes. We’ll determine power capacity and also provide guidelines to help you integrate heat pipes into your system.

So heat pipes are governed by several limits. For a terrestrial application, the first limit reached in most cases is the capillary limit, which is the ability of the wick structure to overcome the various internal pressure drops created in the heat pipe. Other limits include the sonic, viscous, and boiling limits.

The figure shown here is a plot for all the various limits, and as you can see, the capillary limit determines the capacity in this case. The limits are a function of diameter, length, orientation, fluid properties, and the wick properties.

So in the first step, when you’re looking to design with heat pipes, you need to make sure that the heat pipe or multiple heat pipes can move your total power. To do this, ACT offers a free calculator on our website that can be used for copper water heat pipes. This calculator makes assumptions on the wick structure but is a good initial tool to predict heat transfer capacity. And if you’re close to the values, you can call us, and we can optimize the wick structure to get a little better performance.

Now, we’ll go to the website to give a brief example on how to use the calculator.

As we mentioned, the calculator is located in the Resources page. And this figure here gives you an idea of all the inputs you’ll be looking at, evaporator length, condenser length, and the height against gravity will all be used.

So in this application, we’ll use a six-inch long heat pipe. We’ll use a one-inch long evaporator. And we’ll use a three-inch long condenser. The evaporator length can be estimated by the length contacting your heat source and the condenser end as the length contacting your heat sink. So in this case we’ll assume that the orientation is horizontal, which would be zero inches against gravity. And then we’ll submit the form and the calculator will output curves for different diameter heat pipes. One thing to note here is that if you’re designing with heat pipes, the power requirements are additive. So for instance, at 80 degrees C, a three millimeter heat pipe can move 34 watts. So if you have two 3-millimeter heat pipes, you can move 68 watts.

Hopefully, that gives you a feel for the calculator. Now, we’ll jump back into the presentation.

So the next step is to integrate heat pipes into your system. The key points here are bending and flattening guidelines. If you can keep a bend radius greater than three times the outside diameter and a flatness greater than two-thirds the outside diameter, the heat pipe can be manufactured accordingly. If you’re close to these values but need a slightly tighter profile, give us a call and we can give you some advice on feasibility. As far as attaching your heat pipe into your system, most heat pipes are epoxied or soldered into the assembly. Solder provides a thermally and mechanically superior joint. But oftentimes, if your heat flux isn’t critical, epoxy can be used.

So now that your heat pipes are in place in your assembly, it’s time to predict performance. We’ll start with some basic modeling techniques that are very quick and easy to use. And then we’ll get into some of the more detailed models.

So most programs start with some quick feasibility and hand calculations. One method to do this is to create a thermal resistance network and calculate temperature rise at each level. For a heat pipe, this is very straightforward, and you can easily integrate a two to five degree temperature rise for that component.

So to actually calculate temperature rise through the entire system using hand calcs is very difficult. A lot of times, you’ll use finite element analysis software to get better accuracy in these types of systems.

So in here, the first method we’ll look at is a basic conduction model to simulate heat pipe performance. So after proving your power and using the design guidelines to layer heat pipes into your system, you assume the heat pipe is a solid component.

From here, there are three easy steps to consider. First, you start with a bulk thermal conductivity. We suggest starting around 10,000 watts per meter K. You run these models and check the temperature extremes on the heat pipes. And finally, you iterate that 10,000 watts per meter K until your max temperatures across the length of the heat pipe are within two to five degree of the temperature range. This temperature range has been validated with a lot of test data.

So now, looking at HiK Plates, a similar approach can be used so you don’t have to model each individual heat pipe or even figure out a complete layout for your heat pipes when using HiK Plates. As we discussed earlier, test results have shown a 500 to 1,200 watts per meter K thermal conductivity for HiK Plates. So to quickly model HiK Plates, simply replace your aluminum or base material conductivity with a 600 watts per meter K. If you get favorable results here, that’s something that we can usually hit with an optimized heat pipe design.

So in the following section, we’ll go into a little more detailed modeling scenario.

So in this model, we’re using two components. The first component is an envelope which captures the thermal interface material such as solder or epoxy. It captures the heat pipe wall, the wick structure, and the evaporation and condensation zones. This area would have a relatively low thermal conductivity. But really, it only acts as the radial conduction element, which is a short thermal path into your vapor space.

The second component then would be your vapor space, which simulates the effects of two-phase heat transfer through the center of the heat pipe. So in this area, there are a lot of thermal dynamics occurring. However, we can significantly simplify this model to basically use it as a effective conductivity range.

So using the equation shown to the right there, we have known variables that include length, power, and cross-sectional area. And we can estimate temperature rise for this section.

So now, we’ll take a walk-through of a design guide showing you the detailed modeling approach and giving you some comparison data. The requirements for this heat pipe is that it needs to move 25 watts fully against gravity at room temperature. This geometry was based on the profile of the electronics and the sink conditions that we were given.

So first step here is to use the calculator. And you can see the plot to the right there, shows that a four-millimeter heat pipe will easily work in this system. There’s plenty of margin there. Again, if you needed a smaller heat pipe, you can go with two smaller heat pipes and add the power together to make sure you have margin for that 25 watts.

So now, going into our detailed modeling, shown in the figure to the top right is the lumped model. So we’re assuming the radial conductivities of the solder, copper wall, wick, and evaporation-condensation zones are lumped into one lumped envelope material.

For solder and copper, they have known thermal conductivities, which can be used to solve for a thermal resistance in these areas. The only value really needed here is the resistance through the wick material and the evaporation and condensation areas.

So here, we can estimate this as 3.195 times 10 to the minus fifth degrees C meters square per watt. And this is an assumption that we back-calculated out of test data but is a good approximation for normal-sized heat pipes. So from there we also want to keep the model to a thickness that is easy to mesh in your finite element analysis software. So we want to assume a 0.040 thick lumped envelope material.

Using the thermal resistances and accounting for the 0.040 wall, we can then calculate the effective conductivity, which comes out to 26.7 watts per meter K. Typically, this value is between 25 as far as a four-millimeter heat pipe would be concerned.

So next, we use Fourier’s law to determine the effective thermal conductivity for the vapor space. In this example, we’re attempting to move 25 watts, which can be plugged in as the Q value in the equation. We can estimate the delta T here to be very small. Conservatively, we used a value of two degrees C. The effective length of the heat pipe is determined by the average length of the evaporator and condenser plus the adiabatic length. In this case, it’s about 2.21 inches. And the vapor area can be solved for by removing the 0.040 lumped envelope from the total heat pipe cross-sectional area. So plugging these values into the equation at the bottom gives us a result of 233,000 watts per meter K conductivity.

So just as a quick recap before showing the results, we know that the heat pipe can move the power from the online calculator. We incorporated the heat pipe into the 3D model. We solved for the effective thermal conductivity. And now, we have all the tools and assignments to put on our boundary conditions and simulate performance for this system.

So here are the results for that part we mentioned. This part was roughly two and a half inches by four inches. Therefore, as a quick modeling tool, we selected a thermal conductivity from the lower end of our HiK range, and we used this to run a quick model and get a feel for the performance.

So running a 500 watts per meter K as the total base material thermal conductivity, we showed a 83.7 degrees C hot spot temperature. Since this was within the range of our maximum electronics temperature, we went ahead with the detailed modeling approach. We laid heat pipes in there. And we determined boundary conditions from the model. And implementing those into a detailed model, we got 81.3 degrees C as our hot spot temperature.

Finally, as shown to the right, we built the part and tested it with the heat pipes in. And we showed a test result of 80.3 degrees C. So across the board, the error was not extreme. And due to some conservative assumptions, performance actually beat the simulator results.

So now, we’ll go through just some quick takeaways. And then Jens will answer any questions you might have on modeling or heat pipe theory.

So today, we covered operations and reliability to show how powerful heat pipes can be. We provided you with the design guidelines allowing you to easily integrate heat pipes into your system. And finally, we provided techniques to model whether you’re looking for a quick [inaudible 00:21:57] check or whether you’re looking for a nice detailed design.

So hopefully, at this stage, you’re all ready to introduce heat pipes into your thermal solutions. And at this time, I’ll pass it to Jens Weyant who is our lead engineer. And he’ll field any questions you may have.

**Billy:** Thanks Bryan. This is Billy Hurley with Tech Briefs. At this time, we’d like to begin our Q&A. And I’d like to welcome to the line Jens Weyant, who is lead engineer for the defense and aerospace group at Advanced Cooling Technologies. So if you have a question out there, you can submit it by entering it in the box at the bottom of your screen.

Jens, we already have some questions that came in. The first one here, how thin of a bond layer is required? And what is the approximate conductivity of that layer?

**Jens:** Sure. That’s a question we get pretty common. Typically, we like to see 0.002 to 0.004 of an inch clearance on the radius of the pipe. So for example, for a quarter-inch diameter heat pipe, 0.25 inches, we would like to see a groove about 0.255 inches. And as for the conductivity, solders range about 40 watt per meter K. Whereas, a lot of epoxies are about 1.4 to four and a half Watt per meter K.

**Billy:** Does bending or flattening of the heat pipe effect performance?

**Jens:** As Bryan mentioned earlier in the presentation, the capillary limit is driven by the pressure drops within the system, which include the gravity head, liquid and vapor pressure drops. When you flatten the heat pipe, you do increase the vapor pressure drop. But if you stick with our guideline of flattening it to about two-thirds, we typically don’t see large impacts. Our online calculator does not take that into effect. But we do have in-house code that does. So if you have a specific application where you need a extra thin heat pipe, feel free to contact us, and we can help you out.

**Billy:** Here’s another question. Do vapor chambers offer similar benefits to HiK Plates?

**Jens:** Yeah, I think the short answer here is yes. A vapor chamber is very similar to a heat pipe except that it does a better job of spreading in multiple directions. Whereas, a heat pipe can only transfer it actually [SP]. When heat pipes are embedded into aluminum, we see a very similar effect. When you have a high-performance application, vapor chambers are thermally a little better. However, when you account for the weight and the cost, we see HiK Plates as a very good alternative.

**Billy:** Here’s another question from an attendee. In a HiK application, do the heat pipes need a thinned heat sink on them to provide the condensation?

Jens: I think this goes back to another point Bryan had during the talk that the heat will be transferred wherever it’s warm on the pipe. So as long as you have a delta T, you’ll be evaporating somewhere on the pipe and condensing someplace else. So it doesn’t necessarily need to be a thinned heat sink, but you do need some place to reject the heat. Heat pipes are excellent at moving heat from one spot to another. But you still need the ultimate heat sink. It’s just the physics of it.

**Billy:** Does the plate thickness include the embedded heat pipe?

Jens: Correct. I think Bryan mentioned 0.72 inches as the thinnest HiK Plate we’ve made. That does include the plate thickness.

**Billy:** Let me pull up another question here. How does the heat pipe work under zero gravity due to surface tension effects?

Jens: So going back to the factors in the capillary limit, we have the gravity head, the liquid, and the vapor pressure drops. In a zero G environment, that gravity head goes to zero. Well, we still have the liquid and vapor pressure drops, so the end result is a much higher capillary limit. The heat pipes are often used in space and work quite well actually.

**Billy:** We have time for one or two more questions. How are these heat pipes embedded into metal? What is the manufacturing process that is followed?

**Jens:** So in solder applications, we can embed it into any metal that has a surface that weds to solder. So a copper heat pipe can be soldered directly to a copper heat sink. We can solder a copper heat pipe to a nickle-plated aluminum heat sink. A lot of times, we see nickle-plating used to provide that wedding. For other applications such as thermal epoxies, we can use other coating such as chem film aluminum or anodized aluminum. So as long as the heat pipe groove is the correct diameter, there’s a lot of flexibility.

**Billy:** All right, we’ll end it there. That’ll conclude today’s webcast. Again, if we did not get a chance to answer your question today, our sponsors will do their best to address them after today’s presentation.

So our thanks to Bryan Muzyka, Jens Weyant, and everyone out there for joining us. Have a great day.