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December 2005
library  >  Application Notes  >  Ake Malhammar

The Air Efficiency Concept


introduction


detailed pcb temperature calculations produce a lot of data. one might there be tempted to believe that they reveal everything that is worth knowing about the thermal status of a pcb. this is both true and false. some properties, such as component temperatures, can be directly compared with recommended values. other properties can only be surfaced if the data is treated.

a property is in this respect a value that can be put on a reference scale and thereby expose an important aspect of the design. most properties are related to reliability issues but some of them disclose more general cooling characteristics. the cooling efficiency and the air efficiency are examples of the latter. they are in addition simple to extract and can therefore easily be published within a thermal pcb program frame. 
 

this article is about the air efficiency. it is a property that quantifies how well the airflow is used for cooling. there is nothing innovative about this concept. thermal designers have used similar notions for decades. what might be new to some readers however, is that the air efficiency is helpful in many design situations and not the least for front-end estimates. the latter is important. in a way it makes the difference between thermal design as a waste handling activity and thermal design as a recycling activity.



air efficiency definition

 
figure 1 - air efficiency definition.


definition


the air efficiency is defined as the ratio of the temperature increase in the air, passing one or several pcbs, and the maximum pcb plate temperature difference. unlike the definition of the cooling efficiency, this definition is not only confined to individual pcbs. if several pcbs are stacked, it is the last pcb that counts, figure 1.



                   control volume  

figure 2 - the air efficiency definition requires a control volume.


an obvious difficulty with this definition is that it requires a control volume, figure 2. for parallel pcbs the only reasonable approach is to place the control volume limits in the middle of the free air slot. that is, slightly shifted towards the component side to compensate for the component heights. this asymmetry can some times be problematic, particularly for pcbs with high heat sinks. one must therefore always be aware that the value of the air efficiency can vary depending on how the control volume is defined.

another issue of some importance is the maximum possible air efficiency. it is not 100%. from the applied point of view it is nevertheless safe to think of it as if it was. the background for this inconsistency is that the definition is based on the maximum pcb temperature. a pcb that has a board scale heat sink with a temperature high above the board temperature could therefore theoretically produce an air efficiency above 100%. the conditions needed to realise such a design are however by far to extreme for current design practices. typical application values are therefore always considerably lower than 100%.



air efficiency - gz  
figure 3 - the air efficiency for isothermal parallel plates is a function of the gz-number. it can therefore be represented in the same diagram as the laminar flow nu-number.

isothermal surfaces

dimensionless number representation is common practice in heat transfer theory. for laminar flow between parallel plates there are two important numbers. the nu-number, which contains the heat transfer coefficient and the gz-number, which contains the air velocity and various other parameters. an interesting property of the air efficiency is that it, like the nu-number, is a function of the gz-number, figure 3.

a low gz-number signifies that the airflow between the plates nearly is stagnant. the corresponding heat transfer coefficient is therefore low but since the exit air almost takes the same temperature as the plates, the air efficiency is high. for a high gz-number the conditions are the reverse.

the region gz= 10 – 100 is interesting. this is the region where most air-to-air heat exchanges are found, simply because the air efficiency there is relatively high. it is also the typical region for natural convection between parallel pcbs and it is the region in which one dominating convection mechanism is replaced by another mechanism, which is indicated by the curvature in the nu0-curve.

an isothermal plate has a cooling efficiency of 100%. the corresponding value for typical muli-layer pcbs without heat sinks is around 70%. air efficiency values for plain pcbs can therefore not be expected to deviate radically from those found on isothermal plates.



equations  
figure 4 - the air efficiency can be calculated when the cooling efficiency is known.


calculation

there are a couple of ways to extract the air efficiency from the data generated by a thermal pcb program. figure 4 shows one way, which essentially is a heat balance. it uses the energy equation, the definition of the cooling efficiency and the definition of the air efficiency. the equations shown are only valid for single pcbs. the equations for stacked pcbs are slightly more complex. it is also worth noting that the velocity definition used, (as the virtual velocity if there had been no components), makes the equation 4 very simple to evaluate.

equation 4 also shows that the cooling efficiency and the air efficiency are closely connected. if one is increased the other one is also increased. since the maximum air efficiency is around 100% it is evident that the cooling efficiency also must have a maximum value. this value is however less apparent since it also is dependent on a group of several other parameters. 



air efficiency - velocity  
figure 5 - examples of how the air efficiency varies for a pcb without 70% cooling efficiency. n is the number of stacked pcbs



figure 5 shows a couple of examples of how the air efficiency varies with the air velocity for a pcb with 70% cooling efficiency. as expected, the general tendency is that the air efficiency decreases with velocity. for a single pcb, (n=1), it becomes painfully low already at moderate velocities. the air used must after all be both filtered and transported and most of it does not seem to do much good. for stacked pcbs the situation is better.

thermal design for electronics is often viewed as a  limbo dance in which the trick is the squeeze the component temperatures below a critical limit. this view is too limited and has always annoyed the mind of the author. there are numerous other aspects of which optimum cost design is one of the most important.

to compare a pcb with a heat exchanger might seem somewhat strange to non-thermal engineers but it is actually quite relevant. in both cases there are costs associated with the convection surfaces, the air ducting, the fans and the energy consumed by the fans. an evaluation of all these factors have made manufacturers of air-to-air heat exchangers conclude that an economically optimised heat exchanger should have an efficiency in the range 50 – 80%. even thought the cost image for electronic devices is quite different, it is nevertheless difficult to believe that an air efficiency on the 10% level could represent some kind of economical optimum.

heating and refrigeration equipment has been designed on the bases of economical criterions for more than 30 years. the engineering literature for this branch therefore also covers economical issues and terms such as optimum heat exchanger surface and optimum flow rate are quite common. thermal design for electronics has not yet reach that level. this has to change and the air efficiency concept might have an important part to play in future optimisation theories.


 
heat sink on pcb    
figure 6 - when the air efficiency is high it is important that eventual heat sinks are designed to capture as much as possible of the air flow.



heat sinks

a heat sink is usually looked at as device that can decrease the chip temperature of a critical component. this is of coarse true but this view is somewhat narrow. increasing the air velocity could alternatively solve the chip temperature problem, at least as long as the velocity is within the sub sonic region. another way to look at a heat sink is therefore as a device that saves airflow, or differently expressed, as a device that increases the air efficiency.

a heat sink operates just as any other heat transfer device in the sense that its capacity increases with the available temperature difference. heat sinks are therefore most effective when the air efficiency is low. it is subsequently difficult to make them perform well when the air efficiency is high. natural convection and stacked pcbs are examples of conditions that generate the latter problem. 

a heat sink must evidently be made large to operate well in an environment with a high air efficiency. this is however not enough. it must also be designed to capture as much of the airflow as possible. designs such as in figure 6 are therefore some times inevitable. it can in addition be noted that it is difficult to make heat sinks contribute significantly on natural convection cooled pcbs. the gain of the increased surface is often consumed by a loss of airflow, particularly if the pcb pitch is low. the author has actually seen a case in which a heat sink increased the temperature rather than the opposite.



colling efficiecny at 50% air efficiency  
figure 7 - the cooling efficiency for a pcb when the air efficiency is 50%.


front end application

on way to enhance the cooling properties of a pcb is to use heat sinks. the first step on this roadmap is to apply heat sinks on individual components. the next step, which currently is under way, is to use large pcb scale heat sinks that thermally are connected to several components. a great advantage with this type of design is that the air efficiency can be tailored to a much larger extent than else would have been possible.

it is still too early to know towards which limit the air efficiency for pcbs with board scale heat sinks can be boosted. a rough guess is that 50% can be reached without too much pain. 

a plain multi-layer pcb typically has a cooling efficiency of 70%. this value could be substantially increased if the pcb was equipped with a board scale heat sink. figure 7 shows the cooling efficiencies that could be attained if the air efficiency was raised to 50%. the gain is rather small at low air velocities but at 1.5 m/s it is a factor 4! no wonder that thermal engineers are interested in board scale heat sinks.

the use of the air efficiency concept for front-end purposes is currently limited to the type of diagram that is shown in figure 7. that is, slightly speculative predictions of what could be done, all efforts made. the speculative part will rather soon fade away. in this new situation it is possible that front-end predictions based on a qualified guess on the air efficiency could become quite relevant. 

whether front-end estimates best are made with the air efficiency method or the cooling efficiency method, must be determined from case to case. the cooling efficiency method is surface oriented and therefore works best for plain pcbs. the air efficiency method is volume oriented and therefore works best when a volume around a pcb is filled with heat transfer surfaces. 



conclusions

the air efficiency can be extracted from detailed thermal calculations made for a pcb.

there is no radical difference between the air efficiency for isothermal plates and the air efficiency for multi-layer pcbs.

thermal design for electronics is far behind other thermal branches in the domain of optimum economical design. 

it is difficult to make heat sinks perform well when the air efficiency is high.

the air efficiency concept could become a common front-end estimation method when pcbs with board scale heat sinks become more common.



about ake malhammer



ake obtained his master of science degree in 1970 at kth, (royal school of technology), stockholm. he then continued his studies and financed them with various heat transfer-engineering activities such as deep freezing of hamburgers, nuclear power plant cooling and teaching. his ph.d. degree was awarded in 1986 with a thesis about frost growth on finned surfaces. since that year and until december 2000 he was employed at ericsson as a heat transfer expert. currently he is establishing himself as an independent consultant.


having one foot in the university world and the other in the industry, ake has dedicated himself to applying heat transfer theory to the requirements of the electronic industry. he has developed and considerably contributed to several front-end design methods, he holds several patents and he is regularly lecturing thermal design for electronics.


to read ake's web site for more thermal information and software tools he has developed, please visit http://akemalhammar.fr/ - see more at: https://www.coolingzone.com/library.php?read=534#sthash.y3rcxrow.dpuf

to read ake's website for more thermal information and software tools he has developed, visit http://akemalhammar.fr/.

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