Heat Sink Design Principles for Electronics Cooling

[00:00:13]until now i wanted to go a little faster because most of the aspects were sort of generic to heat transfer uh fundamentals uh now what i'll shift towards is more towards a technology focus where what are the technology type of technologies that are typically used in electronics cooling and one one that is often used is the heatsink um because most of the processes or whatever it may be the features become the way of dissipating heat from a source the heat exchanger is in occasions in but we are talking about a heat sink that means often with a heat exchanger means often it involves two fluids or three fluids and so on in this case only one fluid is used the heat is being conducted to in this picture that is shown here is a fan that is mounted on top and the heat source is underneath this heatsink here and heat is conducted first as we discussed till now is spread to a large area and then to the fins and the fan blows the air into it and it is in a jet impingement configuration that is the fan will go impinge the airflow generated by the fan will go impinge and exit through these sides so it will exit through that side and this side that is the front and the back side as shown that is often referred as the active heat sink because there is a fan involved in it there are those passive heat sinks where there is no fan involved and it is driven by natural convection and what is shown on the right hand side is a metal foam based heat sink these are metal foams are not periodic porous materials stochastic porous materials whose ligaments are whose metal parts are continuous and they have open pores so that the airflow goes through them these are some advanced heat sinks that are not commercially used in the commercial electronics world however they have been discussed and used for military electronics and very niche applications they don't seem to have entered the commercial space because these pores are on the order of two one to three millimeters and they may end up becoming more like a filter because in uh in laptops and uh desktops you see that over a period of time there's a bunch of dust that gets collected on these systems and so we will discuss the first the so-called the workhorse in the industry which is the parallel plate or the longitudinal fin heat sinks and develop a very simple guideline for even if you don't do elaborate modeling or design there is a very simple guideline that actually gives close to good uh performance we will get we'll dis discuss that aspect of it then uh we'll get into the advanced heat sinks that um tomorrow um the first part i will cover in the second part uh i'll uh there will be professor sripriya rama murphy whose background is in acoustics and noise control she will come and discuss some aspects of acoustics in electronics because we always deal with fans most of the electronics data centers and uh commercial electronics involve air hold systems whenever you have air cool system noise is a is a unwanted bike that just arises and so she will discuss the acoustic aspects of electronics and also some newer designs um tears of how to do heat dissipation as well as absorb sound within the same functional volume in the same heatsink volume can be absorbed sound that is the noise that is generated by the fan as well as dissipate heat with some aspects that she will discuss and some why we should uh study noise and so on so she will do that tomorrow and uh so as i told you discussed previously very briefly there are heatsinks can be classified in many ways however in a practical sense there are three uh situation that arises one is the so-called heatsink without any tip clearance the red dash indicates a box that is placed around the heatsink and any airflow that is going into the page this is a cross section of a heat sinks the blue is the fin the the usually the the base on the bottom plate is called a base of a heatsink and these are the heat sink fins so the flow happens between these and heat is conducted from the bot bottom and it is spread to the base and then into the heatsink phase and then when air is flown across it the conductor heat gets dissipated into the airspace and as the air is flowing through them then the air gets picks up the heat and removes the heat out of that space so that's how the process happen and as you can see there are three critical we will discuss that a little later so this is the simplest configuration one can analyze without much complexity and that's what i'll discuss today is this so called heatsink without tip clearance where if i look at a pressure drop perspective if there is a certain length of the heat sim that is the flow according to the flow direction flow length then there is a pressure drop associated with it a moderate complexity is when there is some amount of space on the top so when there is flow entering into this type of an arrangement the box is shown again as resh red dash here and you can see that now the flow has two paths to take one two between the fins one on top of it that is it has two parallel paths so depending the flow will take the least resistive path and until the point where the pressure drop across the top space and the bottom between the fins is equal that's how uh then that will be the splitting point of flow is depending on the pressure drop associated with the top and the bottom space the flow will either bypass the amount of flow that can be determined only by knowing the pressure drop in the top and the bottom so now we have a arrangement or a situation where one has to understand the impact of that gap that is present over the top of the heatsink and so that brings parallel paths in this design now becomes challenging the third complexity based on flow arrangement is that you you have flow bypass happening on the sides as well not only on the top but also on the sides this is extremely challenging situation and any improvement in hitching in such a situation is this improvement in performance in such a situation is quite difficult because the air can easily bypass and so one arrangement i'll discuss is that what is shown here is the so called heatsink thermal resistance thermal resistance we described as the temperature at the bottom as if it was the base temperature being uniform and minus the inlet temperature divided by the power that is dissipated so that is the thermal resistance that is described here one second there's some noise here i'll just come back sorry for that this um so if you see here what i am plotting is thermal resistance as a function of number of fins here we i'm talking about this as one there are n number of fins here what happens is initially when there is no bypass which is this curve without flow bypass you see that as you keep increasing the number of fins initially the thermal resistance drops and after some point it reaches a minimum thermal resistance because our objective is to decrease the thermal resistance at some point it reaches a minimum value here and then it again rises before discussing flow bypass let's understand why should it decrease and then and then why is it increasing so if we look at the heat flow path when i put a heat source here there are three main paths that needs to be mean the three main mechanisms that we need to understand it needs to be that is my laser pointer so my if i have a heat source on the bottom plane here the heat needs to spread and into the fins so the conduction resistance is offered by that so you have spreading resistance and then spreading and then uh conducting through the fins itself then it needs to convert the temp and dissipate the heat into the air flow stream so you have conduction and convection on top of it depending on the amount of airflow there is only a certain amount of heat flow here there is only a certain amount of heat that it can absorb the airflow stream can move because the maximum temperature the airflow can attain is the temperature of the metal itself if i have a uniform temperature let's say 80 degree fin temperature somehow magically i have a very high efficiency fin then my fin temperature let's assume that it is at 80 degrees c and the base is also at 80 degrees then the airflow temperature the maximum airflow temperature it can attain even though it is coming in at 20 degrees c is that 80 degrees ah so if i have a fan that is dc that is generating air flow when i have the less number of fins here let's say 10 number of fins that means my pressure drop across these fins is very small that means i am able to generate more airflow that means my sensible heat rise the amount of heat carrying capacity of the airflow is higher mcp delta t that is the mass flow times specific heat times the temperature difference across the flow that is in outlet minus inlet temperatures that's the amount of heat the airflow can carry that's the maximum amount of heat so that mass flow rate will be higher because my pressure drop is good as i start to put but in this case when there is fewer number of fins the amount of surface area is smaller so my convective heat transfer h a the newton's law of only h here delta t here the delta is the surface temperature and a is the surface area of the fin surface temperature minus the reference temperature could be let's say it's similar temperature of that my convective heat transfer coefficient is is not that high because my fins are spaced far apart so my if you assume the nusselt number for the sake of discussion nusselt number is constant dorsal number is h times hydraulic diameter by thermal conductivity the fluid so the spacing between the fins is larger that means my hydraulic diameter is larger so as i put more fins my hydraulic diameter keeps decreasing that means my heat transfer coefficient because my right hand side is constant one my heat transfer coefficient keeps increasing as i add more fills and also i am increasing the surface area as i am adding more fins however there is equally the amount of airflow generated by the fan is also going down at some point they reach an equilibrium that is the amount not an equilibrium an optimum where the amount of heat convectively lost to the air stream and the amount of heat carrying capacity of air is also not is also equal so at that point you reach a minimum resistance beyond if you add more number of fins the pressure drop generator is so high that the airflow generated is also high now the amount of heat carrying capacity even though a convective heat transfer is being increased amount of heat carrying capacity of the airflow stream is reduced so the thermal resistance starts to increase again so on this side left side of this minima is limited by the convective heat transfer the right side of this minimum is limited by the sensible heat rise or the heat carrying capacity so that is without my flow bypass on the other hand yes please sir yeah so what are the mechanism that you have described this is equally true for natural convection as well uh it is true yeah okay because in the natural condition the the on the right side uh they have either increase in the heat thermal resistance that may be because of the blocking of the flow because the fins are very close and there are the this hot air is get blocked within these two consecutive fields and that causes a resistance to convection right sir yeah so as you put more fins now natural convective flow is restricted thank you sir so now now we add a flow bypass essentially a situation that happens here is that now this curve looks very similar to the no flow bypass case but the the minimum resistance for this flow bypass is higher than the minimum resistance without the flow bypass the reason being that at some point the pressure drop across this so if i'm looking at a simple situation that if i treat it as a parallel two for flow fab two parallel flow paths then at this minimum point the flow bypass effect is taking that there is more airflow uh that is happening on the top side and the amount of airflow if it was ducted can be even more higher in this case than the bottom case so the flow bypass always restricts the amount of heat that can be dissipated by the same heat sink that's why designing for flow by bypass is actually more challenging and still there are open-ended questions even though there are some correlations and others the open-ended question still exists about how to model these flow bypass effects and so that's a very simple parallel plate heatsink however you can record it from pin fin heatsinks others and so on so forth so that is the classification based on flow arrangement but there are innumerable number of uh classification based on the type and uh or like this is the longitudinal fins or parallel plate fins these are the foam based fins here again what you have is this is the heat pipe embedded heat sinks where this bottom surface bottom plane is placed on top of a heat source or a processor abridged by a thermal interface material and these are heat pipes heat pipes are fairly good conductors of heat better than even better than copper if designed well and they can transport heat more effectively than copper in this case there are these heat pipes conducting heat to the top and where there are parallel plate heatsinks many times what happens in in these air cooling enhancement is that treating these longitudinal fins becomes extremely challenging you will find uh i've been working in this area for more than uh now close to 16 years uh treating this parallel plate fins has become an extremely challenging affair not purely from a heat transfer perspective but you shouldn't allow any penalty if i want to have same pressure drop and have higher heat transfer coefficient or higher heat dissipation from a new structure you will find that parallel plate things are as good as anything else and it is a very challenging endeavor to beat the parallel platform yes there are people have shown but it is not like twice or thrice on equal pressure top basis you always get 10 percent 15 percent if you target fifty percent hundred percent improvement it actually becomes extremely challenging and i don't think there exists much work in that area anyway um coming back to this so one small question along the longitudinal fins um if you split up so there is one longitudinal fin which is uh you you can see it's a rectangular one what happens if i uh cut it out and then make it also like a fin like smaller fins placed next to each other so there is one like this oh yes yes correct yes yeah so that so what happens here is the situation that now your boundary layer sort of grows from the surface and it gets disrupted and it again starts anytime you do that there is always a associated pressure drop penalty so the pressure drop also increases so what you will end up finding is that it will show better performance from a heat transfer perspective that is you will dissipate heat slightly higher than this case from a equal velocity if i say my velocity inlet is kept constant at 4 meter per second you will find that strip these are so called strip fin heat sinks they will tend to have slightly higher or this is the so-called offset strip fin this is in line they're not changing in in occasions they smooth this in a staggering fashion we'll find that for 4 meter per second for this case it will be better however if i use if i fix the pressure drop let's say 15 or 20 pascals or 50 pascals i'll find that this actually ends up being better so it depends on whether you are accepting that penalty the slight increase in penalty for higher heat transfer but there are so many papers in this that it is very very hard to person products and so on it's very hard to judge whether it is because it is hard to each heatsink is different size it is hard to compare each of them one may claim that this is better than that or something like that but if you have to compare them equally on an equal platform it is very very hard because the geometric scaling and others that people have used for flow through people in that type of if we readily apply it's not readily applied for heat sinks because once i change my heat sink then i'm or shape or geometry i'm in a different regime so i can't compare them on equal footing um however this this so-called zipper fin is what you will you open a laptop you will find most of the fins are like this and this has become an extremely low cost in many of these commercial electronics uh cost is a bigger player than any performance improvement because they budget about a certain money and you have to fit your schooling solution within that money and they can compromise a little bit on the performance by doing some other change to it but cost becomes a real factor driving factor so many people even if there is 15 20 improvement they will settle for lower cost if the cost that one one entails for enhanced performance is much higher um then they will not be accepting 50 higher cost for 20 improvement in performance so that's why these parallel plate fins have become the real workhorse in many you will see desktop laptop servers you'll find that they tend to have even the so called heat pipe embedded fins these are parallel plate fins as you can see there are this planes again now you can classify this heatsink based on flow structures uh either they can be laminar or turbulent here's a flow over a cylinder you can see some complex flow structures [Applause] as doctor nigel pointed out if i have a strips in what ends up happening is that the boundary layer or the flow gets separated and it creates some kind of wave or wick essentially not behave and impinges on the next and that influence the previous as well and that type of thing can be observed here it's a flow visualization with water not with air but it is equally valid is that if you may have heard that in internal flow situation around two thousand dollars number you start to see turbulent flow but transition to turbulence happens in these fins little earlier than 2000 because of this uh influence effect you can see at 750 the flow is very fairly laminar that is it's not it's going straight paths there is no however at around thousand now you start to see these small wake effects and they start to mix and around thousand eight hundred now you start to see much more effect of these disturbances and you actually are in even about thousand reynolds number it actually is in the turbulent regime for these cases so there are many many options in terms of how to classify this so it is better not to get too carried away by the classification and putting a structure around it heat transfer coefficient i've already talked um so i'll skip that how do i model because parallel plate heatsinks are the longitudinal pin heatsinks or one of the workhorses people have developed lot of correlations in very simple modeling procedures and one of the simplest ways the so-called first hour model where you develop [Applause] a friction factor correlation as a function of developing flows here so there are two pressure drops that are associated with the heat sinks one is the so-called core pressure drop that is pressure drop associated by because of the flow of friction happening when the flow is going through the fins and the second because the flow from a larger area is constricted to go through the fins that is called loss entry loss similar exit loss happens where the flow from a smaller channel between the fields is expanded to a larger induction so that's the inlet and exit pressure drop they're all characterized by this equation very simple this f apparent is the friction factor apparent friction factor and i x is the developing flow situation here [Music] so this then as you can see this 23.73 is fully dollar flow limit um so always uh in heat transfer and there is this fanning friction factor and rc friction factor so it has to be caffeine is a multiplying factor called four here and uh so this 23.7366 is the parallel plate limit at fully developed flow conditions but when there is developing flows then this x plus needs to be calculated x plus is nothing but uh it's the inverse of grid's number it is given here length that is the length hydraulic diameter hydraulic diameter is based on the spacing between the fins essentially you will have 2 times wc times hc divided by wc plus hc that's the hydraulic diameter and this is the so called inlet uh um this k inlet is the loss coefficient for the entry loss k exit is the last coefficient for exit losses and this is actually uh i've used it and i've verified it experimentally as well it works very well it's within 15 percent accuracy of experiments so as far as very simple calculation goes this relationship can be used if the flow conditions are correct on the other hand there is a huge confusion with this parallel flame fixing model from a first order perspective the resistance as i discussed you is the base temperature that will be the heat sink temperature heatsink based temperature at the bottom plane minus inlet air temperature divided by the amount of power or heat dissipated by the heat sink that is the thermal resistance of a heat sink and there are really bad models out there in the literature and there are they are to be carefully looked up before some well-known people who have worked in this area for more than 40 50 years also have done this mistake of using wrong models [Music] because some student may have done it however there is something called this convective resistance model what it is is given by this relationship which is one by key transfer coefficient again the confusion of what heat transfer coefficient needs to be carefully looked at a effective is the effective surface area of the heatsink this what it does is that this is a heat this model is called convective resistance model but this model as you can see is going to give a perspective that as long as you keep increasing your mass flow rate this heat transfer coefficient will keep increasing that means this resistance will always drop with increasing mass flow rate that will be the trend predicted by this equation however as i described to you when the pins become much closer and closer the effect of amount of heat that can be carried by the heatsink flow reduces so that mass flow sensible heat rise is not captured by this model that is a problem with this and there models that at the sensible tries to be added like this mcp delta t and there they call it the fluid resistance model or something mcp delta t which is the energy balance that comes from energy balance it is not a resistance it is an effect caused by the heat being dumped into that air stream so it cannot be used as as a resistance because it is the amount of heat that was dumped into the air flow stream so the air flow temperature went up from some value x to some value x plus delta x so using that x plus delta x minus x as a temperature driving force or the voltage difference is wrong but some people have done this and this is a very badly done model it is true only under one situation that the entire heat sinks is one mixed mean temperature there is one bulk mean temperature for the entire heatsink so it's thermodynamically wrong and people have done that mistake there this first model convective resistance model that correlation that is needed for doing that model is shown here i will leave it and just for your reference however one of the best way to do it is this [Applause] heat exchanger so i should do it on the board just one second i'll connect my camera to the mode oops she can you see my ball yes sir thank you yes sir so if i uh have a heat sink sorry for bad drawing but nevertheless if i were to draw the temperature profile of this temperature as a function of x let's call this x direction i find that my temperature of the solid pin will look something like this however right temperature of the air flow will look like this that means the airflow will see a large temperature rise is not thermal resistance but keeping is not this model of this is valid only when the things are far apart that one can treat it as if they were you know the density of things is not high when you get into higher density pins then one has to do what is called the heat exchanger theory one has to make use of the heat exchanger and this time we're reaching the systems as one by m cp times epsilon epsilon is the effectiveness and effectiveness of a single stream heat sink as we all know effectiveness is defined as q max by q actually because we have only one fluid that is going through this we have m dot cp times temperature of air at the outlet minus temperature of air inlet divided by m the q max is usually m dot cp times the base temperature is a maximum temperature which is the surface temperature of the solid minus the air the minimum this should always be this so-called minimum if you look at it you will find that this temperature profile this is for the solid and this is for the air and am i recording you see there is the stream that undergoes lot more temperature change than solid that means that has the minimum capacity relative to solid that means this m dot cp must be error so if i write it this way then these two get cancelled so my effectiveness is nothing but e air outlet minus e however we know the resistance of fixing i have described you earlier as p surface minus p inlet or e air inlet divided by the amount of power you can see that you know that by purely energy balance q is equal to m dot cp times so from here using the definition of epsilon i can write it as t surface minus e air in is equal to so if i substitute for oh so if i substitute that so now i can define r as p surface minus e f in divided by q which is nothing but 1 by m dot dt so this is the accurate model for zinc because one can also obtain from this expression but can also obtain uh the expression of the so-called convective convective resistance model which is this from the heat exchanger theory we can write for a single stream heat exchangers epsilon is equal to 1 minus exponential of minus ntu npu is number of transformers this comes directly from a gene exchanger here from there you can write it as 1 minus exponential of minus h times a divided by m dots so using taylor series expansion of exponential of minus x is nothing but 1 minus x plus x square by 2 factorial and so on so just using the linear terms if i substitute that this is a taylor series expansion epsilon is nothing but 1 minus of minus 1 plus h a by m naught c sub e ignoring all the higher order so epsilon is written as m naught if i go substitute it here what this is saying is that only at very low limits of this ntu that this convective resistance model works whenever the ntu starts to become larger and darker resistance model doesn't work so so for future purposes it is always better to use this even though you will find that very common micro channel is that most people use this one which is absolutely wrong and one should be very careful because the same idea of heating that where air is going through is equally valid for water flowing through a microscope it doesn't matter and so most of the literature is full of these type of models or there's this new one that is one by m this is even worse because that is thermodynamically wrong so i just thought it is probably better to just this on board rather than two slides so i'll come back to my slides now so that's what i have discussed here and the error associated with using you can see the ntu which is h a by m dot c sub p that i had described on the board here if you see that my ntu is small then the error between the the two models which is the one by m c is a heat exchanger theory based model that is htx and the convective resistance model is very small as the ntu starts to grow to bigger number the error between the two also grows it is important that we use the right uh theory for modeling these things and code breaks so that's the first order model the if you use the right proper relations for heat transfer equations and the friction factor then they actually predict heat sink performance well within 15 to 20 percent if the right performance uh if the right uh you know if you use the right correlation in terms of whether the flow is developing or fully developed then you will get really good prediction from just doing a very simple calculation however when you have fans uh then one has to understand the impact of fans which is whether the fan is centrifugal axial or whatever there are many varieties of fans that are used and in laptops it is very common to see the so-called centrifugal fans and in servers you see most commonly the so called axial fans or the tube axial fans servers and desktops laptops because you your wind went for cap catching the air from is on the back side of your laptop and it pushes the air out through the side so you you see mostly centrifugal fans there on the other hand as i mentioned you you can see here this side will be the side that faces your lap and this is your vent and the heat will blow across these heat pipes here right here there will be a heat sink underneath this board and it pushes it out through this vent this is your vent of a laptop this is a tube axial fan that is often used for uh you know your servers and desktops so one has to understand this i've already described to you the fan curve so i won't spend the time again our fan selection is a very critical parameter and as you may notice that whenever you start a computer the fan makes a lot of noise and the reason for that is that they one of the simplest way because in many um especially in india we have very dusty mumbai is so dusty sometimes i don't understand where the dust is being generated however these dust gets collected into our heatsinks and fans and some of them look like this the reason for the whenever you start the laptop uh there is a the fan makes a lot of noise that is because they tend to spin the opposite direction that they typically do that is to push some of the deposited particles out that's why you see it is spinning in the uh the polarity is changed at the beginning to push any of the dust that was collected over a period of time out of the laptop system so that is a and then only after that it changes its direction and starts to pull air back into the system so uh that is used to you know sort of prevent or reduce the amount of dust collected over a period of time for fan selection however there's so many parameters in factors that one often looks into before one picks a given pan and you will find that most of the manufacturers once said they'll select a fan it is uh they don't tend to change the fan at all for unless it is they are compelled to stage it so depending on the volume flow rate required static pressure required space limitation because in laptops your height is fixed or they may be to a certain noise generated what is the operating temperature whether the heated air is going to enter the fan or not so on so forth so so there are so many parameters that one has to look into selection though it becomes extremely challenging um once you change you select the fan to change it so um so there are fan lots i'm sure you are well aware of it i am listing them is if the pan is if there is not big change and you are just changing the diameter of the fan and so on then these fan laws are quite useful i'll skip these fan loss and as you all know if the two fans are placed in series the amount of pressure it can sustain the back pressure it can sustain can be high and if the two fans are put in parallel then the amount of air flow rate generated becomes higher so with that we can now discuss about how to optimize these heat sinks so there are four possible optimization constraints for heat sinks one is fixed mass flow rate of air that is uh i supply a certain amount of mass flow rate and i'm trying to explore uh is there a optima second is fixed pressure drop third is fixed pumping power and the fourth one is described and for the fixed mass flow rate typically when there is no tip clearance there is no optima because as the amount of air carrying a heat carrying capacity of air is fixed when you fix them right there as long as you keep adding a pin it will keep because you are anyway generating you are not fixing the pressure drop you are saying i am going to give you a certain amount so what will happen as long as you can add fins it will keep increasing its performance so literally there is no real value in in uh in doing any optimization or a mis fixed mass flow rate and that will always depend on how many number of things that you can put the second one is the fixed pressure drop when you have a fixed pressure drop then you should expect an optimize when you do the optimization you will expect that that there will be a resistance like we discussed for the case of the initially the mechanisms of the heatsink design is that initially it will be limited by the conductor heat transport then it will be limited by the amount of heat carrying capacity of the air so the fixed pressure drop will generate uh this versus number of fins or whatever parameter cell size and the spacing between the frames or something like that uh if you do any of the optimization then you will find that initially the resistance will drop because you are increasing the surface area and the mass flow rate is not um is not limited to the amount that will dump into it after that after it reaches a minimum it starts to rise the same behavior can be expected for pumping power constraint as well as fan curve so one of the very simplest methodology that one can use and can quickly get a very good estimate of heating uh geometry is this work by professor bejan and back in 1992 and they used them the so-called method of matched asymptotes that i discussed for natural convection but here used for [Music] force convection um however they have developed this initial work was based on hydrodynamically and thermally developing flow uh you can look into it for in any type of flow situation that you are interested so what they looked at is a two dimensional geometry they didn't look at the 3d part but you can add the 3d part by doing numerical simulation so if i have a flow going through a stack of fins and the width of the heatsink is h and the length of the heatsink is l then as we discussed previously there are two limits that one can look into for a fixed pressure drop is that one is the limit where the fins are placed so closely that right from the beginning you see fully developed on the other hand you see a limit where the spacing between the fins are so large that the boundary layers do not merge even at the exit somewhere between the two limits is where the optima exists and for the sake of discussion what we're going to ignore is the thickness of the fin thickness of the fins that are found in laptops and desktops these days is about 0.2 millimeters 0.2 to 0.3 millimeters and so they are quite thick these days but any if they can be easily incorporated so the first as we discussed is the so-called depending to 0 right fully developed flow limit where the fin the blue is the and we are looking at from the top as the flow enters it quickly becomes fully dollar flow essentially you just and the boundary layers have merged and so they have become a fully developed then the average velocity can be found using a puzzle flow model and that is what is given here once you know the velocity because as you can recall that we have fixed the pressure drop across the heat sink as a concern once you find the velocity because we know the pressure drop now we know at this small spacing d is known mu is the dynamic viscosity l is the length of the fin the mass flow rate per unit depth depth is going into the page is given by rho times velocity times h this h that is given by the that gives the total mass flow rate per unit depth once i know this because i have reached a fully developed flow what i am going to assume is that the fins are at uniform temperature t wall that is fin efficiency is assumed to be 100 for this so usually when you design a reasonably good heat sink fin efficiencies tend to be on the order of 90 percent or higher so assuming 100 fin efficiency is not such a bad assumption however we fix the temperature of the fin to be t wall and because it is fully developed flow what will happen the wall temperature will imprint itself on the air the air flow will attain the maximum temperature t wall before the exit so or at the exit so the overall heat transfer from this system is given by mass flow rate times specific heat times the delta t across the air p wall is the maximum temperature air can attain so p wall minus t infinity is the total mass transfer uh total heat transfer transfer and that is one limit and you can set the total heat transfer rate from this stack is proportional to d square that is the spacing between the two fins the other limit why is this the other limit is d tending to infinity that is the spacing between the fins are so far apart that the boundary layers that are generally uh developing they don't even merge so in this case he uh processor beijing and cuba they had used flat plate correlation however we have to keep in mind that there is accelerating flow effects in a internal flow situation so what they did was to use flat plate correlation to calculate the amount of heat transfer from these fields since there are two things they have used two and n is the number of fins in the stack then they calculated total heat transfer rate from all the fins and they where they the total heat transfer heat transfer rate at this limit is 1 by d raised to the power 2 by so if we plot d as a function of q then for one limit it increases with that is the fully developed flow limit the amount of heat transferred increases as of as proportional to d square on the other limit it decreases like this and the point where this crossover can be deducted by equating the two heat transfer rates and that is how you obtain the optimum spacing between the fins and that turns out to be however if you really look at this and finally plotted what you will end up seeing is that the best solution is what they what the final outcome comes from this whole discussion is that if you place your fin such that the boundary layers merge just before the exit like this that turns out to be optimal if you merge the boundary layers very close that means you have choked the flow that is you can't carry any more heat if you if you if your boundary layers do not merge even before they exit that means you are not using the cold flow that is coming here so a situation where the boundary layers merge just before the exit of the heatsink is the optimal spacing between the fins that's what emerged out of this discussion and it makes intuitively correct [Music] so this is a very good starting point for any of the parallel plate heatsink models and that one starts with is to keep the space facing as as equivalent to the thermal development length of that so one puts that then for a fixed pressure drop you really see a performance improvement without doing a lot of calculations or doing numerical modeling so that was one of the important outcomes and i i i have used it and many of my friends and they always find it very very good point and once you starting guess correctly then the number of iterations to get to the final design becomes much simpler okay so that parallel plate design is quite it can be used for heated cngs and others as well so if you look at manufacturing perspective because uh heat sinks are manufactured by many many methods the most common ones are the extrusion processes die casting and the so-called folding and bonding this type where they fold the fins like this or they have extruded fins like this and they get bonded so this is a method this folding and bonding method is the most commonly uh used method these days for they don't do this type of folding but instead a c type fin so they make lot of c type and then they just bond it to a base plate so depending on the manufacturing process uh you may or may not be able to achieve all the fin um the spacings and so on so one has to when you're designing heatsink one has to keep in mind the design for manufacturing in mind to actually ensure that the heatsink design that you have come up with this can be manufactured for example in an extrusion case there are certain limits of what can be what needs to be the delta or the thickness of the fin itself what can be the height of the fin to spacing between the fins the aspect ratio should be so these are limited by the processes themselves for extrusion the fin thickness cannot be less than 1 mm the height aspect ratio the height of the fin 2 spacing between the fins cannot be more than this 8-ish to 1. similarly the spacing between the fins needs to be at least 6.6 millimeter so on so far so now there are many of these things and so you when you draw a thermal resistance versus fin density number of fins per centimeter you will find that there are very few modern manufacturing processes like bonded fin technology and the skype fin technology are the very few things that can give you very high density so that's why you find that most of the current currently existing pins in the laptops and desktops are tend to be this folded fin technology that can even go to higher intensities but one has to keep in mind the manufacturing to ensure that the design becomes realizable and that's why i discussed this very briefly and then we will discuss about the acoustics tomorrow um but the acoustics also plays an important role in all these things so because the noise cannot exceed a certain maximum going to occupational health safety and osha and process sheep we will discuss tomorrow about that but the if i have if i'm designing a heatsink for a laptop then the laptop needs to operate in air at higher altitude as well so there is a change in density you need to ensure that the or if it is being used in a modern day submarine or something then it has to offer that as well so this heatsink has to keep in mind the altitude effect as well and the factor that needs to be there are some very simple factors that people have come up with and for example here is an example at sea level 3000 meters then if you calculate a resist resistant heatsink resistance at sea level then you divide by that factor so the resistance keeps increasing as you go to higher and higher altitudes for example if you go to 3500 meters then your heatsink resistance will be divided by 0.75 that means the resistance went up significantly so one has to ensure the altitude effects are taken into account when someone designs these heat sinks as well in practical situation there are so many parameters that come into picture uh as these are the prescribed parameters we know how much heat dissipation what the ambient temperature needs to be maximum heat sink temperature velocity all these things so one is always required to calculate fin height thickness spacing length base plate thickness what is the material of the heatsink and the complicating factor is whether the flow is turbulent low this flow that flow fouling falling is one of the real challenging situation how much of the it degrades as you collect dust is very hard to predict our people have done some experiments by doing particle loading and but prediction is still lacking in in those areas so we've discussed this uh bypass effect and so on so i'll so the next is to go to somewhat on the complex side i'll take a break here and just ask you if there are questions about what i've covered no sir you have any questions for me i'm assuming none so i will proceed and there's about only 20 minutes i'll spend a few minutes on this oh thank you i will spend a few minutes on the advanced uh complex structured heat sinks uh and maybe pick up more on the details in the next tomorrow essentially so once you get out of this parallel plate teaching domain there are innumerable number of designs as we discussed there are so many options so many people have investigated this area some of these pictures are some of my own work that you can enhance heat transfer in in a number of ways using heat pipes here the challenge is the vertical space is quite high that the fin conduction in the particularly by using thick pins is avoided by using these heat pipes for example and the heat pipes carry the heat all the way to the top and you put so many parallel plate fins to dissipate the heat so then here are some micro honeycomb type heat sinks these are the foam heat sinks then these are honeycomb type structures where we have increased the surface area but once you have a lot of surface area and if you don't have these so called slots that are shown here if it is all closed ducts array of ducts then what happens is the dump that is closer to the heater which is on the bottom the closer to the heater it's hotter the air gets hotter there and these ducts are much cooler so in order to allow some amount of mixing uh these vertical slots have been inserted and then you can do periodic focusing and these are called swatch structures or heat sinks where we try to do what is called the trigger instabilities in the heatsinks i will discuss that in little bit more detail uh in the by probably tomorrow and there we try to make use of instabilities we want we know that laminar flow has pressure drop compared to uh turbulent flow however turbulent flow has higher heat transfer coefficient of course it has higher pressure drop as well so the idea here is to make use of instabilities flow in stabilities [Music] and this is one of those flow instabilities to obtain very close to turbulent heat transfer rates but keeping close to the laminar flow rate so we induce what is called flow unsteadiness we sustain flow and steadiness self-sustained oscillations is what is done here and those flow and steadiness essentially keeps the flow regime close to the laminar range and even though there is a minor penalty of pressure drop increase the performance the heat transfer performance increases by three to four times this is one of those methods by which people have shown that one can obtain three to four times improvement in a transfer four times not uh four percent uh four times increasingly dragged and we'll discuss that so if you really look at the high performance heatsinks and what you see is that at very low end uh where the powers are low usually die cast or or depending on the application you have extrusion or die cast type heat sinks and as as power increases then the bonded pins folded fins then the so-called thermosyphons are vapor chamber attached heatsinks and water cooled plates come into picture so we will discuss some of these aspects here so what is the real challenge in this is that we all know that heat dissipation increases with surface area the same surface area is responsible for fluid frictional loss as well so if you increase one thing yes guy goes up so the challenge is how to improve heat dissipation by not increasing the root frictional losses is the real question that we are trying to address and why should we do this is because if i look at a processor thermal budget they usually call it a thermal budget because the temperature of the die minus ambient divided by the total power dissipated by die can be split into these parts this is the so-called package part that we don't have access to but what we have access to is the thermal interface material too and heatsink design these you can see that 42 percent of the overall thermal resistance is contributed by the heat sink alloy so improving even a good 10 for percentage of this means a tremendous improvement in the performance and is there a general principle there is no general principle that allows us to tell you know how to design a heat sink from so that um pressure drop can be reduced while increasing the heat transfer one such thing is reynolds analogy and recently there is some new analogy has come up which is the lava analysis this reynolds analogy often in the in our classes we teach as if it is we use the flat plate and we say that uh what it is is actually um it is it's an anonymous case in the case of a flow over a flat plate laminar flow or a flat plate case it is some sort of uh serendipity that it works for that case because the pressure gradient for a flow over a plasma is small metals analogy in reality is valid only for mixed turbulent flows what it says is that the effective turbulent eddy viscosity is equal to the eddy diffuses that's all it says that is the turbulent prandtl number is one that's what the reynolds analogy says however we tend to teach as if it is equally valid for any flow situation because we make use of the flat plate keys so without going into the in details it is as i i've stated here energy is anomalously valid for laminar platforms because the pressure gradient is lowered so vana's analogy what it does is that gives you a relationship between this the coefficient of friction and the stanton number or no cell number however you want to write it so this so essentially knowing pressure drop means you can predict heat transfer that's what it means that if i know my pressure drop then i can predict heat transit so if i reduce my pressure drop then i can reduce my heat transfer so that's so knowing one thing predicts the other so reynolds analogy sort of tells you what best you can do for a given situation there is something new that is coming up which is the levac analogy however i won't get into that um so you can use this to sort of get it but this doesn't tell me how to design my heatsinks and so on so that is the only way only analogy that gives us some idea of what may happen in terms of pressure drop once i know pressure drop if this is the budget i have a pressure drop of hand curve then then i can figure out what is the maximum heat answer i can i i can obtain from reynolds analysis so um i think um so what we'll discuss in tomorrow for tomorrow's class is that for high performance heat sinks there are uh you know two main teams that people have addressed one is geometrical modification the other one is flow modulation it is the inlet flow is modulated or it is given some oscillatory signal so that the heat transfer performance is improved so in the next tomorrow's class i'll discuss the array of ducts as a way of improving heat transfer porous media is another way of improving heat cancer and the so-called laminar flow instabilities as the third week i'll stop at this point because it just starts to get to the details and pick it up tomorrow if you have any questions i'll be glad to uh how we handle um yeah so this uh ice pack i am sorry i just looked at this looked at this question this ice pack does have turbulent flow models what i'll do is i'll bring up icepack again tomorrow and i will show an example of how to build a pcb there it can be done very easily if you have the so-called board files it can be done otherwise i'll show you put a board then put key sources there that type i'll show one quick example um is there a if there is no other questions uh i have shared this link i will send it through moodle as well i will upload i have just put one lecture there i will upload other lectures as well and share them across through that link okay if there is nothing else uh thank you for the time and i'll talk to you tomorrow you