# Heat Pipe Modeling and Design Techniques

Welcome, thanks for joining ACT for a webinar on heat pipe design and modeling! So today we're going to be talking about exactly that, modeling and designing with heat pipes and this is actually a question we get very frequently from customers through our website and people are just very interested in I think heat pipes can potentially solve my problem how do i kind of take it to the next step and figure out on my own, whether or not it's going to solve my problem. So today we're going to go through some fairly basic steps just to give a kind of first-order approximation on whether heat pipes will work for you and from there we would always recommend contacting ACT and we can help you take it the next steps and create from concept to final product what a heat pipe solution might look like. For just a quick background on Advanced Cooling Technologies, we were founded in 2003, currently we have over 200 employees and over 150, 000 square feet. We have two office locations, one in Lancaster Pennsylvania and one in York Pennsylvania. Throughout our history our core values have been innovation

teamwork and customer care. We like to work very closely with our customers and partners on very detailed and challenging solutions with heat pipes and other thermal technologies to really solve some of the most challenging problems in the industry. That does require a lot of those three core values innovation, teamwork and customer care. Just some awards that we've

been given over the past several years product innovation awards the 2020 military and aerospace product of the year which was pump two phase-related and then the AHR green building award. Which was a heat pipe or thermosyphon based solution for energy recovery applications. So, jumping into the content here um the objectives of today's webinar are basically to provide an understanding of heat pipe operation so give you kind of some background on the heat pipe theory and how it's going to work in your system and then really just dive into some of the design guidelines so provide you with kind of those tools so you have them in your toolbox where you can design and properly say yes a heat pipe will work in my my given application. So from there we'll jump into quickly the theory of heat pipes some of the advantages and then get into some of the examples on designing them.

Very quickly, I know a lot of you joining are probably familiar with heat pipes. We'll give kind of a basic understanding of a heat pipe and what it is a passive two-phase operating closed-loop system. So how you utilize a heat pipe is anywhere where you may have conduction limitations in your system so you can't spread the heat out significantly enough to meet your temperature requirements or if you want to transfer heat from point to point so moving heat from an isolated source or electronics component to a heat sink that might be downstream from your devices. In those two operations a heap has a very nice way to achieve that goal and the way it works is at the heat input area or known in the heat pipe as an evaporator you are boiling the fluid so the heat goes in and you're vaporizing at that interface creating a vapor that creates a pressure gradient within the heat pipe itself and that pressure gradient forces the fluid all the way to wherever it's colder in your system so in the example you see here in the top it's pushing that heat from left to right and going into the condenser zone which is where it will give up its latent heat condensed back into a liquid and will be captured within the wick structure so the wick structure in a heat pipe lines the inside diameter and it captures that fluid at the condenser and then it creates a passive capillary force that pumps that fluid passively back from the condenser to the evaporator so at the end of the day you have no moving parts. A very highly reliable system because it doesn't have any real failure mechanisms as long as you kind of operate within your boundary conditions. You get very efficient heat transfer so

because of the latent heat of vaporization you have very high heat transfer coefficients at both those interfaces and you are able to achieve a very low-temperature gradient typically between like two and five degree temperature difference across end to end of the heat pipe. The benefits for for heat pipes in many cases the benefit is size weight power and flexibility so in the in the size and weight. A lot of times the alternative option for a heat pipe solution is just simply adding more heat sink volume so creating a more massive heat sink will give you some thermal performance benefits but will also eventually hit a limitation as you can't spread the heat anymore so it does have the ability to make a more compact heat sink because of the better heat spreading and then the larger benefit is typically the power so in many cases you can with the same size heat sink increase the amount of power you can output or you can increase the power and create more heat sink volume by better spreading and better heat transport in your system and the flexibility at the end of the day is primarily what our customers come back to us for because heat pipes can be bent and routed into a lot of different geometries, it is a very flexible technology for in instances where you might be retrofitting it into an existing design that just increased the power capabilities from one design to the next it does have the ability to integrate into a lot of different geometries and one of the biggest questions we get very early on in customers looking at heat pipes for the first time is the reliability and the this is a very real question but it's one that is typically mitigated fairly early on because a lot of times the boundary conditions. Power requirements will dictate whether or not a heat pipe's fit and if you can operate within those operating conditions that are suitable for heat pipes, it should be a very long life operating device. So once you properly design it into your system if you're maintaining the

temperature and power limits within a heat pipe it should be a very long life design. These type of systems have been integrated into very harsh environment type applications defense aerospace medical applications things that have very stringent requirements and have kind of that of that need for very long life and very highly reliable systems and the final question is kind of "when do we use heat pipes and what are the thermal performance expectations with heat pipes?" and that's where we'll get into a lot of the design and modeling work but as I mentioned earlier, that the two primary areas where you would look to improve thermal performance with heat pipes is heat spreading which is the example you're seeing here so you can see in the plate to the left you have three hot spots, really two in the top and one on the bottom where you're not able to spread the heat out as as quickly as you would want to to keep those electronics operating safely. So in this example those blue lines that you see on both sides of the plate are liquid cold rails and the objective here would just be to conduct the heat out to those cold rails and maintain a safe operating temperature at your electronics. So while the aluminum plate wasn't able to do it with the thermal conductivity of aluminum by integrating heat pipes in there you can see you're able to kind of short circuit that path out to the liquid cold rail so in the in the bottom case it was just a matter of putting enough heat pipes in there to move the full power and in the top case um it was actually a very short thermal pass so it wasn't a very long path to conduct but in this case you had such a high heat flux that you were still getting hot spots there so in this case we we routed the heat pipes in such a way that you created a long condenser area along the cold rail and that was really able to drive down those temperatures as well and just looking at some product examples you can see several here and there's many more on our website to give you some ideas of how heat pipes are used but again here we want to kind of show the flexibility in terms of applications these have been integrated into a lot of very complex systems and also the geometric flexibility you can see heat pipes of different configurations there bent routed some with many heat input zones so it doesn't have to be heat input at one end and condensing at the other end you can have multiple evaporator sections to pick up heat from multiple electronics and you could also condense to to multiple areas as well the heat pipe because it's operating in passive two-phase principles it will find an equilibrium as long as you're not exceeding one of your your power limitations so again just kind of a nice demonstration of some of the flexibility you can see in some of these designs and that's where again act could really help out if if you bring us a problem we can give you kind of a quick order of magnitude stance on yes this can be solved with a heat pipe or or maybe it's not a great fit based on the power the boundary conditions and some of the geometric limitations so now we'll dive into designing with the heat pipes and that's that's really kind of the the basis of this webinar so we'll talk about the power capacity which is one of the the major hurdles in designing with with heat pipes and then we'll also talk about the design guidelines and get into some modeling later on so the power capabilities um there's a lot of of published data on heat pipe limits and it's it's one of the um first things you need to consider when when designing with heat pipes and there's there's really several limits that's kind of bound the the power capacity of heat pipes um in many of the terrestrial applications the real defining one is going to be the capillary limit the capillary limit is is basically the wick's ability to pump the fluid back from the condenser to the evaporator and so it has to overcome all the pressure drops in the system one of the largest pressure drops would be the gravity head if it needs to pump against gravity which in most applications where it's going into things that may be variable orientation or may have to operate in in different configurations it's a requirement you have to operate in in any type of orientation so you need to overcome that gravity head when you do face with it the other option if you do have flexibility on your orientation and you can orient the condenser above the the evaporator you can move significant amounts of heat in those type of applications so those operate mainly on the entrainment limit which is the ability for the the vapor to kind of push up against the liquid shear strength sheer force that's coming down an ability to overcome that and so in those type of applications you can move a significant amount of heat but for the purpose of this today's webinar we're going to focus mainly on the capillary limit and that's usually the driving factors in in terrestrial type designs so the limits here are a function of several different items but primarily the ones listed here are what we're going to focus on because they can be used to quickly kind of approximate the the capillary limit and we have some tools to help you out as you go through that process so the main ones are diameter so the larger diameter you have the more power you can move the length of the heat pipe again how you have to overcome all the pressure forces in your system so the the longer you are the the more you have to overcome and that can become a factor orientation as i discussed and then the two driving ones are the fluid properties and the wick properties so those are fluid properties are mainly defined by your fluid selection and the wick properties are where a company like ect could come in and help you out in terms of how fine of a poor radius and and what type of permeability you might need to achieve your goals so in very quick approximations we do have a calculator online and this is a really good initial source to help you size your heat pipe and so i would recommend going on there and we'll go through an example of using that calculator later on but just to kind of keep going through the design progression here some of the the other considerations are how it's going to integrate into your system how you can bend it how you can pick up heat of various components so we do want to give kind of some sense of what's possible here and the first thing is the standard pipe sizes so we can make a heat pipe out of pretty much any standard tubing that is available you can see some of the the standard sizes there three millimeter up to eight millimeter and an eighth of an inch up to half an inch is is very typical in copper water type heat pipes we've gone much larger than that in certain ammonia based or liquid metal based heat pipes but there's there's no real limitation it's mainly manufacturing considerations but those are very standard sizes that we use on a routine basis and then probably the more interesting thing here is the bending and flattening guidelines so this is a lot of what our customers will come and ask us is how tight can we bend a heat pipe and how flat can we make it before we're really kind of straining the the design points of the heat pipe and the recommendation there is for bending it's it's three times the outside diameter so that would be a center line bend radius so if you're bending a heat pipe like you see on the bottom right one that center line bend radius around that that 90 degree leg you see there is about three times the outside diameter and that's where you won't hurt your performance vastly if you go much tighter you have the potential to limit your performance you also have the potential to kind of crank the metal envelope and cause potential issues in the manufacturing and bending steps as well so the the guideline for bending is three times the outside diameter for flattening we typically random recommend two thirds the od again that's where you still have significant vapor space to move decent power the more you fly in the more you will impact the performance capabilities so instead of calculating your capillary limit for instance with the round diameter you're actually going to a hydraulic diameter as you flatten the pipe so you're limiting that vapor space and and limiting your performance but two-thirds is a good kind of guideline to keep you moving significant amount of heat through your system and then in terms of integration there there are several options mechanical fit like press fit type type heat pipe integration but in most cases you want some type of bond there so in many cases we'll do epoxy which is not as good of a thermal performer or mechanical properties as a solder but still gives you kind of a lower cost and you don't need to nickel plate aluminum if you're integrating into aluminum as you would with solder but in most cases solder is the the ideal choice and most of our customers prefer a solder it does give you that really nice mechanical and thermal interface and after nickel plating you can integrate into aluminum or many other base metals and now we'll talk about modeling thermally so in your thermal resistance models there's a couple different resistances to consider here and we'll we'll talk at length about how to model the heat pipe in general and modeling cutting some corners to model the system but really you want to look at these these different areas so um the case to to heat pipe evaporator that's conduction through either your your solder interface your epoxy interface or or some type of um thermal interface like a gap pad you have your your heat pipe which is as i mentioned that two to five degree delta t across the length of the heat pipe and then you have your from the point of the heat pipe to your fin structure which is again typically conduction or some type of interface there and then your rise above ambience going from your your fins to the air so all those needs to be considered to properly design your system to meet your your maximum case temperatures make sure you don't exceed your maximum case temperatures but what we'll focus on here is is really how to model the the heat pipe and the conduction areas around the heat pipe so one of the most easy ways to model a heat pipe is the the basic conduction rod and this actually gives you fairly good results and and would be a high recommendation if you're looking for that first order approximation so you can you can basically try to trick your system into showing two-phase performance with a single um conduction element and the way we recommend you do this is you start by inputting what would look like heat pipes in your system and then you assign them a effective thermal conductivity of around 10 000 watts per meter k and that effective thermal conductivity of a heat pipe is going to vary based on length so if you can meet your if you can operate as a heat pipe the shorter the heat pipe is the lower that thermal conductivity is because you have the same delta t across a shorter length than as if you're going longer distances but what we would recommend is start with 10 000 watts per meter k run your simulation and then check your delta t from hottest to coldest point along your heat pipe and then adjust that that 10 000 mass per meter k until you get within that two to five degree temperature range so if you want to be conservative maybe go to the the five degree temperature difference so for instance if you have if you have a heat pipe that's showing if you input the 10 000 watts per meter k and you're showing an 8 degree temperature difference go ahead and increase that that effective thermal conductivity so you get that 8 degrees down to the the 5 degrees and that's kind of a good approximation of what might be achieved with the heat pipe and i will say that the five degrees is fairly conservative so you can a lot of times beat that in your models but in um in a real world case where you're looking for some conservatism that's a that's a nice first order approach to modeling heat pipe the second which is even more basic is modeling the entire high cave plate so high k plate is a act's term for high thermal conductivity plates which is embedded copper water heat pipes into aluminum heat spreaders and we can make high k plates out of most geometries in aluminum surfaces if you can if you can machine in you have enough area to integrate a heat pipe we can typically turn it into a high k plate and we've done models in um going around corners so both two-dimensional and three-dimensional high cape plates have been achieved so there are there are some design variability in terms of how we can integrate the heat pipes but in most cases if if you have enough thickness to get the heat pipes in there we can turn it into a high k plate and this creates a really nice approach to very easily model thermal performance improvements so in aluminum 6061 is what most designers use as their heat spreaders that's a thermal conductivity of about 167 watts per meter k so changing from aluminum to a high k plate will increase that that thermal conductivity dramatically and in real world results what we have seen is between 500 and 1200 watts per meter k so when i say real world i mean we're not kind of tricking the the system to put a heat pipe in the most favorable condition and put a heat heat source at one end heatsink at the other end we're looking at real world applications where you may have multiple components and multiple heat sinks and you're designing a heat pipe network to achieve the desired results or best case results and then what we'll do is go back into our models after we've performed thermal performance testing and we'll just increase the thermal connectivity until we match our performance testing so it's it's a very fair comparison to say somewhere in that 500 to 1200 watts per meter k range is where you'll land and again that variability or that range is based on how much work the heat pipe is doing so how long the heat pipe is and how much benefit you're getting from the more or less short-circuited thermal path of the heat pipe so we'll talk about some examples later on but for for one quick example that most of our customers are familiar with a 6u conduction card which is around um like nine by six inches that that is typically in the six to seven hundred watts per meter k range so could have components located various places along the surface but we can usually achieve somewhere kind of in the middle of that range to give you a sense so again here to kind of make it easy on you we're going to suggest using a thermal conductivity of 600 watts per meter k so again if you have any real distance or or xy direction to move heat and a localized hotspot that's something that is usually very achievable and we've proven now with with many types of these designs and the next one and i guess the most complex to model um is the what we call kind of the the lumped approach where we uh more or less lump some of the resistances of getting the heat into the vapor space and then use a very isothermal vapor space along the the inside of the heat pipe and this gives you a nice more real approximation because it does take into account thermal interface the the heat pipe wall the wick structure and and some of those more granular resistances that you would experience in a real world system but it does take some of the detailed modeling as from those various resistances out of the equation so you don't need to model two phase flow you don't need to model very high heat fluxes that have very small wick structures and things like that so it's a way to kind of get a little more detail but provide a realistic and accurate prediction without kind of taking significant computational time to run these models so with that model we'll talk about in a little more detail as we go through so this example is trying to transfer 25 watts against gravity at room temperature so now we'll kind of run through all the steps of the lump model in in one kind of straight shot to give you an idea of all the the various components so the first step is to go on to acts website and find the heat pipe calculator under resources and basically input your your guesswork at what the heat pipe geometry might look like so in this case we took the 25 watts there and we we had it in a system you could see the the geometry there we we kind of determined what the heat by heat pipe might look like in in its configuration based on the the source and sink conditions so we had a total length of 3.1 inches a one inch evaporator which is the the heat source zone and a um a very small condenser less than one inch on the condenser which gave a 1.32 inch adiabatic

zone so with those inputs and you can see the figure over here to the right those inputs actually output this these curves of heat pipes which is the capillary limit for various diameter heat pipes and you can see the the red numbers there are the only inputs required in our in our calculator and then you can use those curves to figure out exactly where you're going to be operating and what performance you need so in this case we had an operational range of a little under 20 degrees to about 100 degrees c and so we needed to operate across that entire um curve and so there we're showing that a four millimeter heat pipe is needed so now you know the kind of the diameter of the heat pipe you can go into your your modeling approach so now diving into an example here with the the lump model method this is where we're going to determine effective conductivity of several paths to get the the heat into the heat pipe and then there again we don't want to model each of these individually because they're going to be very thin it's going to bog down your computational time so what we are trying to do here is create a sum of all the resistance is in there so you can see the calculations there as you go through your resistance you have a resistance through a solder so you you approximate that based on the thickness the the length that you need to transfer heat through that solder and the effective um or the actual thermal conductivity of that solder itself so then you can approximate the resistance of that solder again same thing for the copper wall the copper wall for a four millimeter pipe is is twelve thou and there you can use the the copper thermal conductivity and output of resistance for that as well and then the wick material and evaporate evaporation and condensation areas we give an approximation here of a very low thermal resistance in those areas and lumping those together we want to create a model that again you can calculate in in realistic time to to create that first order approximation so we're recommending that you model them as um 40 000 so that that won't create too thin of a surface to allow you to model it and basically to create that effect of connectivity you take all those different areas and you output your effective connectivity and with those results you get 26.7 watts meter k as your as your effective conductivity through that interface so that's again getting the heat into the the vapor space at the evaporator surface and getting it out of the vapor space on the condenser surface so that's an approximation that can use as your lumped envelope material that can take into account the solder the wall and the wick structure and then from there we want to put a value in for the effective thermal conductivity of the vapor space and the vapor space is going to be nearly isothermal because of the the um properties of fluid vapor it's going to be very very low thermal resistance across the vapor space so the approximation we're using here is 4a's law and going across that length i will say this is a fairly conservative approximation so in most cases you'll you'll see even a lower delta t than this across the vapor space specifically but as a nice approximation you could use fourier's law which takes the the power the effective length um and the the area in delta t and again we're putting in some some values in there um for delta t where we're saying two degrees as your your delta t which again is very conservative but should give a nicer approximation of what the effect of conductivity and that value is going to be very high because again it's very isothermal in that vapor space so going from there you have all the inputs to to run your model so what we did there again just to recap is will a heat pipe transfer the required power so that's your first thing you can have a no go no go on if a heat pipe can move the amount of heat and what size heat pipe you might might need once you have the size of the heat pipe you put it into your model say do i have enough thickness here can i manipulate it within my model to get the desired results and again if there's any challenges there let us know a ct can certainly help out in some of the practical considerations for integrating heat pipes and then from there we determine the effect of conductivity of the various inputs so the summed model of getting the heat into and out of the heat pipe or into and out of the vapor space and then the vapor space itself which is a very high effective thermal conductivity and from there you can input your your heat loads into your cfd model or or basic conduction model and you can put your sink condition so your ambient air temperature or just the heat transfer coefficient to simulate your heat sink and from there you can run your model and hopefully get the desired results you're looking for and just one example of where we went through the steps on a fairly small conduction card and and this was actually a fairly good approximation for the inputs we used in this case we we had the actual hardware where we we tested so we put in the 25 watts at that interface and we tested and got the results of about 80.3 degree interface temperature there and then we ran the model in in both ways so the more detailed model was um was fairly accurate so it got us within um within a 1.2 percent error and again because some of the vapor space um approximations were somewhat conservative we were actually under predicting performance of the heat pipe solution there and then looking at a model using the effect of conductivity of 500 watts per meter k again um a little under predicting the performance there which is why we typically say 600 watts per meter k i think we use 500 watts per meter k in this model because the distances were a little shorter than than a typical high k plate but in general no matter what k what you're using you can get fairly close to the results and if you're within you know a couple degrees or within somewhat margin of error that's when you call act and we can help kind of guide you through the steps in getting a very detailed and accurate model so then you can say do we want to go through the steps of prototyping testing this and going forward with the heat pipe solution so again just to wrap up heat pipes are highly reliable and they can be effective components in thermal design they are used in a lot of real world applications for electronics cooling avionics type applications so there's not really many environments which heat pipes have not successfully operated but there are a lot of practical considerations in in each environment um so thermal performance is one of many considerations and those type of things but if you have a functioning heat pipe operating within its ability they are very reliable and long-lasting devices they can be easily integrated into new and existing designs so if you know early on that you're going to have a thermal challenge that can be alleviated with advanced conduction or point-to-point heat transfer going forward with the heat pipe solution off the bat is often a great approach but there's many cases where maybe your component power goes up from one design to the next and you need to retrofit heat pipes into an existing system that's also a really good opportunity to easily integrate them without going through major changes to your heat spreaders or heat sinks there are several ways to effectively model heat pipes we talked about several today and there's even more complex ways out there so again hopefully this gives you some tools in the toolbox to give a first order approximation of how a heat pipe heat pipe might perform for you and then the final is is act your trusted partner we're here as needed so if you run into challenge running any of the models or thinking about some of the practical considerations with heat pipes give us a call we have engineers on standby ready to kind of walk you through the process and and help you out as you are thinking about heat pipes and the final slide here just wanted to talk about act your success is our success so we do take um our partnerships very seriously and we have received a lot of very good feedback over the years so again reach out to us no matter where you are in the process and we'd be happy to work with you and see if a heat pipe solution is right for your design thank you all appreciate your time and please give us a call we look forward to working with you you

*2021-06-27 17:45*