Heat Pipe Modeling and Design II





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 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 220 employees and over 200, 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 year’s 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, 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 ask if a heat pipe will work in my given application. So from there we’ll jump into quickly the theory.



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 heat pipe 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, 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 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 are 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 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 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 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 basis of this webinar so we’ll talk about the power capacity which is one of the major hurdles in designing 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 published data on heat pipe limits and it’s it’s



one of the um first things you need to consider when designing with heat pipes and there’s



there are really several limits that are kind of bound by the power capacity of heat pipes in many of the terrestrial applications, the real defining one is going to be the capillary limit the capillary limit 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 it the other option if you do have flexibility on your orientation and you can orient the condenser above the evaporator you can move significant amounts of heat in those types of applications.



So those operate mainly on the entrainment limit which is the ability for 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 types 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 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 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 longer you are the more you have to overcome and that can become a factor of 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 ACT could come in and help you out in terms of



how fine of a poor radius 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 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 standard sizes there three millimeter up to eight millimeters and an eighth of an inch up to half an



inch 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 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 design points of the heat pipe



and the recommendation there is for bending it’s three times the outside diameter



so that would be a center line bend radius so if you’re bending a heat pipe as 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 guideline for bending is three times the outside diameter



for flattening we typically random recommend two-thirds the outter dimension, 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 limiting your performance but two-thirds is



a good kind of guideline to keep you moving a significant amount of heat through your system



and then in terms of integration, there are several options for mechanical fit like press



fit 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 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 it 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 of different resistances to consider here and 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 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  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 ambient going from your fins to the air so all those needs to be



considered to properly design your system to meet your maximum case temperatures make sure you



don’t exceed your maximum case temperatures but what we’ll focus on here is really



how to model the heat pipe and the conduction areas around the heat pipe



so one of the easiest ways to model a heat pipe is the basic conduction rod and this actually gives you fairly good results and would be a high recommendation if you’re looking for that first-order approximation so 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 an 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 to 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 five degree temperature difference so for instance 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 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 are 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 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 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 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 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 many benefits 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 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 in 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 xy direction to move heat and a localized hotspot that’s something that is usually very achievable and we’ve proven now 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 inside of



the heat pipe and this gives you a nice more real approximation because it does take into account



thermal interface the heat pipe wall the wick structure 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 one kind of straight shot to



give you an idea of all the various components so the first step is to go on to ACT’s website and find the heat pipe calculator under resources and

basically, input your guesswork at what the heat pipe geometry, it might look like this, so in this case we took the 25 watts there and we had it in a system you could see the geometry

there, we kind of determined what the heat by heat pipe might look like in in its configuration

based on the source and sink conditions so we



had a total length of 3.1 inches a one inch evaporator which is the heat source zone



and 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 these curves of heat pipes which is the capillary limit



for various diameter heat pipes and you can see 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 lump model method


0:26:09.760,0:26:15.440 this is where we’re going to determine the effective conductivity of several paths to get 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 can 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 for a four millimeter pipe is is twelve thou and there

you can use 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 realistic time



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 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 approximationso 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



power the effective length um and the area in delta t and again we’re putting in some values in there um for delta t where we’re saying two degrees as 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 the 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 underpredicting the 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 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 challenges 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 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!


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