As we have seen in Unit 13, enhancing the conductivity of the board, or providing a heat spreader, are two ways of reducing the operating temperature of components. Where these approaches are insufficient, a common solution is to use some kind of heat sink. This lowers the temperature of the component or sub-system to which it is attached by increasing the effective surface area over which heat can escape to the surroundings.
In this Unit we are concentrating on the practicalities of using heat sinks to transport heat from device to environment, and have included a final section on improving performance, using such techniques as liquid cooling and heat pipes. Inevitably there will be some discussion on the efficiency of heat sinks in terms of coupling energy to the air, and on the limitations of that technology, but as far as possible we have tried to confine our discussion on air handling systems to Unit 15.
In its most common form, a heat sink takes the form of several thin fins of metal, each having a large surface area. Air moves through the fins, either by natural convection or forced by a fan, is heated, and carries heat away from the surface. Depending on the design, the heat sink may be attached either directly to the heat-generating components or to the board underneath the components, often using thermal vias to enhance conduction through the board.
The rate at which heat is lost depends on the rate of thermal transfer to the surrounding fluid, and is thus proportional to the total surface area presented by the heat sink. However, whilst increasing the area should result in improved performance, doing this may actually be counter-productive, as it increases the resistance to airflow. This means that in many cases there will be an optimal number of fins, beyond which the advantage presented by the increased area is more than offset by the reduction in air movement caused by the heat sink itself.
So, heat sinks have distinct limitations, as well as adding cost, and we liked Tony Kordyban's quotation below, which reminds us that all we are doing is redistributing the problem!
“The term heat sink must have been coined by an electrical engineer. It is too close in concept to the current sink used in circuit theory classes. The term sink is not to be found in heat transfer text books. When they mention those aluminium combs, they call them extended surfaces . . .
“. . . A sink is a place we can dump something and then pretend it no longer exists, such as the kitchen sink. We dump our greasy water down the drain and forget about it. But like that dirty water that shows up on somebody’s beach, heat that flows into a heat sink doesn’t just disappear, and we ultimately can’t forget about it.
“. . . Heat can’t flow forever into a chunk of aluminium and just disappear or migrate into a parallel universe. If you put heat into a chunk of anything, either the heat will flow out into something else or the chunk will get hotter.
“. . . So you attach your extended surface to the top of your component. The reason it looks like a thick comb is that all those fins pack a lot of extra surface area into a small volume. Heat energy now flows out of your component into the extended surface device, which has much more surface in contact with the air than the original component package.
“. . . The heat energy has still not disappeared. It is in the air. But keeping the room cool is somebody else’s problem . . .”
Tony Kordyban, Hot air rises and heat sinks
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Heat sinks can be broadly divided into four categories on the basis of the primary cooling method by which heat is removed:
Passive heat sinks: These are used in situations where natural convection alone is sufficient to take away the heat generated. Cooling regimes built on natural convection do not rely on a specified local air velocity in order to dissipate heat, but do require careful positioning of enclosure vents, in order to allow a steady flow of air. The advantage of such systems is that they require no moving parts and are therefore highly reliable. However, compared to other methods, passive heat sinks can only remove small amounts of heat.
Semi-active heat sinks: Whilst the heat sink hardware may be the same as for a passive heat sink, an active heat sink makes use of fans at the system level to generate a predictable air velocity at the heat sink. The fans are close enough to the heat sink to be effective, but are not attached to it. A good example of a semi-active cooling device is the fan inside a computer case, which blows air across the entire circuit assembly. The increased air velocity from such forced convection removes more heat than would natural convection.
Active heat sinks make use of a dedicated fan or blower that is fitted either to a specific heat sink or to a group of heat sinks. Fan and heat sink(s) are carefully matched, and may be designed to blow air either across the fins or directed at the heat sink. This method provides faster, localised air movement than with semi-active heat sinks, and can be used to remove more heat from a smaller area than with a semi-active heat sink. Whilst most of the active heat sinks seen will be those fitted to modern CPUs, the concept of integrating fan and heat sink is also used at a system level.
Liquid-cooled heat sinks: In cases where it is necessary to remove large amounts of heat from a system, water or another liquid can be used instead of air. Liquid-cooled systems are more effective because liquids have much higher heat transfer coefficients (typically >1,000W·m−2K−1) than gases (typically 10–50W·m−2K−1). Whilst liquids are sometimes sprayed directly on the parts to be cooled, it is more common to use a ‘cold plate’, where cooling fluid passes through channels or tubes in the heat sink. Liquid-cooled applications use a pump in order to circulate fluid past the heat source, and an external heat exchanger is usually needed to cool the liquid.
As we move through these categories we incur additional complication and expense, but achieve higher effectiveness. But technologies other than direct cooling by gas or liquid are increasingly found in conjunction with heat sinks. Two examples discussed later in this Unit are thermoelectric cooling, used for specialist applications, and phase-change systems, which can offer rates of heat transfer even higher than with liquid-cooled heat sinks, with fewer complications and in a smaller space.
Phase-change systems use the fact that liquids have a high latent heat of evaporation, so that boiling a liquid absorbs heat. As with liquid-cooled systems, most phase-change cooling methods are closed-loop, with the resultant vapour collected, re-condensed and returned to the hot areas, using other heat transfer methods to perform the final venting of heat to the surrounding atmosphere.
A refrigerator is one example of a phase-change system, and direct boiling of liquid at the hot spot (“ebullient cooling”) is also sometimes employed, but by far the most common phase-change system is the closed-loop heat pipe. This gives rapid exchange of heat through evaporation and condensation, and can be integrated into heat sinks to increase their thermal efficiency and flexibility of design.
The type of heat sink that is most appropriate for an application will depend on its thermal requirement. Figure 1 shows typical thermal resistance limits for different processes.
Source: Intel Technology Journal 2000 Q3 (Thermal performance challenges from silicon to systems)
This thermal technology map focuses on computing requirements, but a similar spread of thermal demands can be found in other application areas. Whilst extreme thermal challenges are most often found in communications and aerospace applications, there is a general trend towards more complex thermal management systems even at the consumer level, driven by the higher dissipation and smaller size of many electronic products, especially cell-phones, PDAs and lap-top computers.
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Before reading further, reflect on the types of heat sink you have seen, and try to develop two lists that you can compare against our text: one of the criteria that a heat sink has to meet; the second of the ways in which heat sinks can be constructed.
It may also be helpful to browse manufacturer’s web sites such as Aavid Thermalloy, Enertron, HS Marston Aerospace, ThermaFlo, Tyco Electronics, and Wakefield Thermal Solutions. There is a longer list at The Heatsink Guide under Links, Manufacturers.
Note that, in the discussion below, we have deliberately avoided showing images of typical parts, in order to encourage you to visit some of these web sites and to familiarise yourself with the wide range of heat sink products that is available.
Whilst the rest of our discussion will centre on heat sinks supplied as individual components, we should not forget that existing elements within a structure can be used as heat sinks, particularly for smaller assemblies. For example, heat-dissipating components can be attached directly to the base or other part of the housing. Such methods have the advantage of low cost, although they may bring with them unintended problems for assembly or disassembly.
There is of course the alternative approach of making a heat sink that has been specified for thermal reasons “double” as part of the final housing. For example, it is not unusual for a heat sink to form part of the back panel of a small piece of equipment, with power semiconductors visible on the outside of the case, but the connections taken through the heat sink to the circuit inside.
Heat sinks need to integrate:
All three elements, mounting area, thermal path and fins, contribute to the thermal resistance of the complete heat sink, and need to have as high a thermal conductivity as possible.
Material properties are therefore important: frequent use is made of aluminium and copper, whilst mild steel is attractive at the lower-cost end of the market. The choice of material will depend on performance requirements, but there are many other aspects to consider.
Whilst cost usually heads the list, factors such as weight may also be significant. Copper may be a better conductor than aluminium, but it is considerably more dense, so many designs use copper only as inserts for local heat spreading1. Where the weight of even aluminium becomes an issue, then ceramic composites and plastics may find use.
The selection of materials for these heat sinks is intimately related to the choice of manufacturing and assembly process. Be aware that a wide range of aluminium alloys is available, these being tailored for different processes by the deliberate inclusion of other metals; 6061 and 6063 are commonly specified for extrusion and A380 for die-casting. The description “aluminium heat sink” is thus far from indicating a single material, in the same way that the term “FR-4” embraces many different specifications of laminate.
Note particularly that the choice of material is linked to the manufacturing methods that are available, and also determines the degree of post-fabrication finishing that will be needed. Both manufacturing method and finishing process(es) can have a substantial impact on the unit cost. For example, a cost-saving can be achieved if the formed part needs no environmental protection, so aluminium is a frequent choice because it has a natural, coherent, protective (and insulating) thin oxide film.
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As well as being categorised by their cooling mechanism, heat sinks can be classified in terms of their manufacturing methods and final shape.
Stamping: Copper or aluminium sheet can be formed by stamping to give a flat bonding area and a finned outer structure. This provides a low-cost solution to low-density thermal problems. Stamped parts are suitable for high-volume production, and labour-saving options such as clips and interface materials can be applied at the factory in order to reduce the cost of board assembly.
Extrusion is a more flexible technique, applicable to aluminium alloys, in which a billet of material is forced through a die by a combination of heat and pressure, to create a complex fin structure at lower cost than machining an equivalent shape from a block of aluminium. After extrusion, the heat sink is cut to length and drilled to suit both components and mounting method.
A single extrusion tool can make a range of different lengths of heat sink, but the tool is costly, and needs to be amortised over a significant volume. The piecepart price will reflect this as well as the costs of material and processing, together with any subsequent surface treatment, such as anodising.
The extrusion process requires fin designs with a tapered cross-section and relatively robust dimensions, and has limitations on the height-to-gap aspect ratio:
Particularly when the airflow can be directed down onto the heat sink, an improvement in performance can be achieved by using a cross-cut profile. Sometimes this is made by machining across an extrusion; in other cases, a billet of aluminium is milled in two orthogonal directions, creating a profile that resembles a bed of nails. This style of heat sink is usually referred to as a “pin fin” design.
Pin fins are popular, and one of the reasons for this is that they have the advantage of working equally well with airflow from any direction. Since mechanical restrictions in computer cases result in air flowing from an uncertain direction, pin fin heat sinks are generally recommended for this application. However, the user must bear in mind that the effectiveness of the profile depends both on the overall surface area (which may actually be less than for an extruded equivalent) and on getting intimate contact between airflow and heat sink.
From the manufacturing point of view, making a pin heat sink by machining means removing material as swarf or dust, and this adds to the cost, as the waste has to be retrieved safely and recycled. There are however, several alternative methods for producing complex, high-density, pin fin heat sinks in aluminium or copper/bronze:
In all of these methods, the waste is almost eliminated, but the processes themselves can be more expensive, especially where tooling costs are involved and manufacturing quantities are low. However, whilst all these approaches have limitations in design and surface area, they can be more flexible than extrusion, for example making it possible to stagger fins rather than have them in a straight line. And injection moulding will make complex parts as readily as simple geometries, allowing increased freedom of design, and can use specialist materials, such as tungsten-copper and molybdenum-copper.
Johnson and Tan, Metal Injection Molding Of Heat Sinks
European Powder Metallurgy Association booklet, Metal injection moulding (archived copy)
For higher-specification (and higher-cost) heat sinks, the range of options is extended by a range of fabrication processes.
For example, the overall thermal performance of an air-cooled heat sink can be improved significantly if more surface area is exposed to the air stream, even though the conduction paths to the fins may be of higher thermal resistance. To achieve this, a wide variety of bonded/fabricated fin heat sinks have been developed. A typical manufacturing method is to bond flat fins onto a grooved extruded base plate using a thermally-conductive epoxy resin. This allows a much greater fin height-to-gap aspect ratio of between 20 and 40, greatly increasing cooling capacity within an unchanged volume. An alternative is to use brazing techniques to assemble fins to the heat sink body. This technology is already well-established (originally using brass alloys) for heat exchanger applications such as car radiators.
Another type of assembly, generally offering a lower profile, is the folded fin construction, where a sheet of aluminium or copper is first corrugated and then bonded using epoxy resin or braze2 either to a base plate or direct to the hot surface. The depth and pitch of the folds determine both the surface area and the resistance to air flow of the heat sink. A folded fin can be made of relatively light-gauge material and still create a robust structure. And, as with the fabrication method, it is possible to select different materials for base and fin.
Most of these more complex structures, though having a larger surface area, also have a higher impedance to airflow, so are frequently used in combination with a matched fan. Such heat exchangers are often used on a small scale for the active heat sinks associated with high-power components, but are also important elements in larger units designed to remove heat from whole systems, where methods such as liquid cooling and heat pipes have been used to remove heat from where it has been generated.
Christopher A. Soule, Future trends in heat sink design.
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As indicated in the previous discussion, there are many aspects of cost other than that of the purchased piece part, and a significant portion of this cost relates to the assembly process.
There are usually two aspects to assembly, mounting the heat sink to the heat generating component or module, and fixing the heat sink within the overall equipment. Depending on the type of heat sink, this might be carried out as a single operation, but more typically heat sink and component will be assembled first, and then the whole sub-assembly secured.
The thermal quality of the connection is always important; the extent to which mechanical security is important will depend on the mass of the heat sink and other components, and on the mechanical environment that the assembly has been specified to survive.
Primary methods of assembly include nuts/washers/bolts, self-tapping screws, rivets, spring clips and adhesives. The choice of method will depend on the requirement for rework, the application life, the preferences of the assembler and the equipment available to them. General design for manufacture guidelines are appropriate here, such as making parts self-aligning, designing out the possibility of error, using as few components as possible by combining functions, and using standard components (especially fixings) as far as possible.
Where multiple heat sinks are to be fitted, or there is potential interference between the heat sink and other elements in the assembly, care should be taken to keep access to fixings as free as possible – most service personnel have “horror stories” of assemblies that needed to be disassembled and assembled in a specific and awkward sequence in order to make the task possible.
In Unit 6 we discussed the need to manage the interface between surfaces, as contact takes place only between the high points of what is always microscopically a rough surface, despite its smooth appearance. Lack of intimate contact results in increased thermal resistance, often unstable in value. For this reason, a range of different interface materials in employed, ranging from oils and greases, through compliant filled rubbers, to shims of soft metal.
In some cases it is not practicable to take all the heat through the board, but the unevenness of the top surface makes it difficult to attach a heat sink directly. One way of aiding the transfer of heat to a cover or other structural plate is the Bergquist Gap Pad material, which is designed to be sandwiched between the assembly and chassis. [A 1990s approach, the 3M Liquid Heat Sink, used flexible plastic bags filled with Fluorinert liquid to carry heat away from hot components, but this idea seems to have been consigned to oblivion.]
The choice of material and method will depend on assembly considerations as well as the environmental specification of the assembly, the design life of the equipment, and the environmental conditions to which it is subjected. With any assembly, it is good engineering practice to think in advance of the ways in which the assembly will deteriorate with time and use, and carry out at least an informal failure modes and effects assessment. For example, a riveted assembly may function well initially, but the compressive force applied to a filled rubber used as an interface material may reduce if the rubber creeps or becomes more brittle with age.
Christopher Soule in his Heat sink attachment methods optimise thermal performance (PDF, 120Kb) tells the cautionary tale of a computer that gave intermittent problems because of the failure of a single-fan extruded cooler for a socketed microprocessor. The failed heat sink had a Teflon-like interface material which had become shiny in patches, indicating that the microprocessor had overheated. The cure was a different model of heat sink, with a dielectric thermal compound. Soule’s paper is worth reading, if only for its decision tree selection guide for a thermal interface material.
The EPPIC Faraday Partnership paper An Introduction to Thermal Management contains a lot of information on the properties of interface materials. This is available upon (free) registration at their EPPIC Eye web site.
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The choice of heat sink for an application will depend on the thermal parameters required, the external conditions, and the mechanical constraints. Lee’s list of design criteria for a heat sink includes the following parameters:
The heat sink needs to give the best possible performance within the envelope of a given set of design constraints. Typically the designer has some control over fin height and length, fin thickness and spacing, fin shape and profile, the number and density of fins, the base plate thickness, and the heat sink material.
“The impact one parameter has on the performance of a heat sink cannot be generalised, or even foreseen, without concurrently considering the consequences exhibited in the other parameters.”
This example Lee gives is of a fin, where increasing its length or height to give additional surface area should improve overall thermal performance. However, if the available flow rate is fixed, the overall performance may actually deteriorate if the height goes up. Similarly, if it is the available pressure drop that is determined by the fan, a heat sink that is longer in the direction of flow may decrease the velocity over the fin surface.
Kaveh Azar’s Comparison of Heat Sink Designs and Their Respective Thermal Performances contains a selection of modern heat sink types, and a good description of how these might be measured and compared practically. Azar shows significant variations in performance, particularly at low values of air velocity. Although he might be criticized for commercial bias, his emphasis on the importance of airflow management for enhancing thermal performance is both valid and important to bear in mind.
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We asked you to look at Azar’s paper to give you some background to the next sections, in which we are considering the elements that come together as a heat sink specification, after which we have more to say on calculation and simulation and on the approach to making an appropriate choice from the many heat sinks available.
The advantage of representing all heat transfer processes in terms of their thermal resistances is that they can then be combined to obtain an overall thermal resistance representing the total heat transfer of the system.
Figure 2 shows a heat-generating integrated circuit mounted onto a heat sink using thermal paste or a pad, together with a simplified view of the various thermal impedances involved. Note that we have ignored for this purpose the heat transferred to the environment through other parts of the case, making the (probably reasonable) assumption that most of the heat will take the path of least resistance. This figure is of the order of 90%, as we will see later in the quotation from Cathy Biber.
We can break down the total thermal resistance from the junction to the surrounding air into a sum of thermal resistances:
ΘJA is the junction to ambient (or total) thermal resistance
ΘJC is the thermal resistance of the junction to the component casing
ΘCS is the thermal resistance of the thermal pad or paste between the component case and the heat sink
ΘSF is the thermal resistance of the heat sink base to the effective point at which the fin transfers heat to the surrounding air
ΘFA is the thermal resistance between the fins and the surrounding air
These last two resistances are the most uncertain and dependent on the conditions:
ΘSF can be calculated from a knowledge of the heat flow within the heat sink and its thermal conductivity. However, its value will depend on the route through which heat flows into the surrounding air, so will exhibit some variation with the local air flow.
ΘFA is the most difficult element in the equation, as its value is highly dependent upon a number of factors, the major ones being the heat sink surface area and the rate of air flow across the heat sink fins.
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For the convection process from the surface of the heat sink at temperature Ts to the surrounding air at temperature Ta, the heat transferred is given by:
Q = heat transferred (W)
A = the surface area of the heat sink (m2)
h = the convective heat transfer coefficient
The associated thermal resistance, ΘFA, can be derived from the amount of heat transferred and the temperature difference that this creates:
The higher the value of h, and the higher the value of surface area, the higher will be the heat flow to the surrounding fluid, and the lower the effective thermal resistance.
The most difficult part in determining the behaviour of the heat sink is to obtain an accurate value for h, as this depends on the interaction of the surrounding fluid with the heat sink and the physical properties of the fluid, such as density, thermal conductivity, specific heat capacity and viscosity.
Whilst there are obvious major differences between liquids and gases, in most cases air is the coolant, so the properties are relatively fixed. However, there will still be minor changes in properties, for example when the surrounding air heats up and becomes less dense, or reduces in pressure and density at high altitudes. This matters because the degree of cooling is governed by the mass flow of the fluid and not simply its volume.
However, the major parameters affecting the heat transfer coefficient are the fluid velocity through the heat sink and the type of flow.
Source: Sergent & Krum Thermal Management Handbook
Of these, the more important is the type of flow, and whether this is natural convection, forced convection, or an intermediate ‘mixed flow’ situation. Figure 3 shows the thermal resistance of an aluminium fin as a function of air velocity and length. Notice that the thermal resistance increases rapidly with airflow velocity less than about 1m/s, this knee in the curve marking the transition between laminar and turbulent flow.
Unfortunately, there is no consensus as to what flow velocity distinguishes mixed flow from a forced flow regime, although it is generally accepted that the effect of natural convection diminishes to less than 5% of the overall heat transfer once the airflow velocity has exceeded 1.5–2m/s.
“Despite the multitude of materials and interfaces within an electronic package, the largest thermal resistance, and consequently the controlling resistance in the path between the source and the sink, is generally the boundary layer or film resistance at the solid/fluid interface. Given the inverse relationship between the film resistance and the product of the heat transfer coefficient and the surface area, an increase in either the heat transfer coefficient or the surface area results in increased heat transfer and lower operating temperatures.”
Culham, Teertstra and Yovanovich, Natural convection modeling of heat sinks using web-based tools
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The flow velocity and type of flow are parameters that depend considerably on the physical makeup of the heat sink, and on the arrangements made for cooling it. As an example of this dependence, Figure 4 shows the typical variation of the fin air velocity with fin height, and the resultant thermal resistance of the heat sink.
As one might expect intuitively, the air velocity through the heat sink decreases as the fin height is increased. This would tend to increase the thermal resistance, were it not more than compensated for by the extra surface area created.
But notice that the rate of improvement in thermal resistance diminishes as the fin height increases further; the point could potentially be reached where the air flow became restricted to such an extent that the performance gain obtained from the increase in fin height was outweighed by the performance loss caused by the reduction in air velocity.
Other factors that can affect the fin air flow velocity include:
In consequence, whilst having more fins is generally thought of as improving performance, this can be a dangerous generalisation – in most cases, having too many fins will induce a higher pressure drop across the heat sink, resulting in a reduction in flow velocity and/or a significant increase in flow bypass over the heat sink.
Source: Seri Lee, Optimum design and selection of heat sinks
Figure 5 compares flow bypass for different numbers of fins, in different conditions of turbulence, as indicated by the Reynolds number in the X-axis. Note how an increased number of fins leads to a greater percentage of the flow bypassing the heat sink, and that this percentage can be over 50% in the case of the non-turbulent flow indicated by a low value of Reynolds number.
“. . . due to the viscosity of air, the spacing between fins in natural convection must be a given distance to avoid ‘choking’ of the resulting boundary layers. This fin spacing results in heat sink volumes three to four times larger than equivalent forced convection heat sinks. . . .
“Closely-spaced fins require a higher pressure to move heated air away from the fins than natural convection can provide. If fins are closely placed, especially in natural convection, the heat sink will have as much usable surface area as a brick.”
Christopher Soule, Optimize fin spacing: how close is too close?
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Whilst it would be convenient if manufacturers gave independent values for ΘSF and ΘFA, these will vary with conditions, and it is usual to specify a heat sink in terms of a nominal thermal resistance between the surface of the package/assembly being cooled and the environment, expressed in K/W. Unfortunately, there are no standard conditions for such measurements, as there were with the thermal characteristics of packages, so a typical specification will take the form of a table, showing the heat rise for a given power level, under varying conditions of forced convection. As with all such characteristics, this makes certain assumptions about the environment of the heat sink (temperature and airflow) and its orientation, and about there being a zero interface resistance between the heat sink and source of heat.
The efficiency of a heat sink under natural convection reduces as the temperature differential between sink and ambient decreases, so a correction factor must be applied. As one example of industry practice, Aavid Thermalloy publish correction factors for values of temperature rise less than 75°C. Although significant, the correction factors are relatively small (Table 1).
|temperature rise||correction factor|
Source: Aavid Thermalloy
If we consider the case of a point heat source on a heat sink, the performance will depend on the length of heat sink; short heat sinks will have a comparatively high thermal resistance, whilst long heat sinks will have a lower value. Provided that space is available and the cost of additional material is acceptable, a simple way of reducing thermal resistance of a heat sink is merely to choose a longer section of the same profile. However, as Table 2 shows, unduly extending the length brings diminishing returns; a more effective way of reducing the thermal resistance will almost certainly be to move from natural to forced convection.
|heat sink length||correction factor|
Source: Aavid Thermalloy
As well as the primary characteristic of thermal resistance, a heat sink will be specified in terms of its dimensions and the number and arrangement of fins. By combining the overall dimensions with information on the thermal impedance and on the maximum thermal flux for the heat sink, it is possible to compute some measure of volumetric efficiency, though there are no standards for this.
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Provided that assumptions are made about the rate of heat loss from the heat sink surface (related to the convective heat transfer coefficient), it is possible to derive the thermal resistance of a heat sink by analytical analysis. From this, it is possible to compare the benefits of different designs.
Simple analysis for a flat plate is straightforward, as you will find from this example:
A component of dimensions 10×5×4mm has an average thermal conductivity of 5W/m·K. Air is blown over the component, providing an average heat transfer coefficient of 25Wm−2K−1. Assuming that all the heat is generated in the junction which lies in the centre plane of the component and escapes through its upper surface:
Review your results against ours at this link.
Of course real heat sinks have fins! Heat flows in at one end and is dissipated into the surrounding environment as it travels towards the other end. The flow of heat is impeded by the thermal resistance of the fin material, and heat is also lost by convection, so the temperature of the fin will vary from one end to another. This difference in temperature also affects the amount of heat lost from the fin surface.
Fins come in many shapes and sizes, but can be broadly classified into fins of constant cross-section (such as rectangular or pin fins) and fins of varying cross-section (such as tapered fins). For all fin types, by making simplified assumptions (such as ignoring the heat transfer through the tip, and assuming a constant heat transfer coefficient along the length) it is possible to calculate the heat transfer rate, show how fin efficiency varies as a function of geometry and dimensions, and estimate the heat transfer enhancement achieved by using a particular type of fin.
Considerable simplification can be made to the calculations by incorporating a correction factor to allow for the tip of the fin being cooler than the base, because it is further away from the source of the heat than the root of the fin. We define the fin efficiency as the ratio of the actual heat dissipation of a fin to its ideal heat dissipation if the entire fin surface were to be at the same temperature as its base:
where Ts is the temperature of the surface at the base of the fin and Ta is the temperature of the surrounding fluid.
Another way of looking at fin efficiency is as a correction factor for the amount of fin surface area that is actually “useful”, compared with the unfinned surface. From this equation, we can also derive the thermal resistance of a fin in terms of its efficiency:
where A is the area of the fin, and the factor 2 allows for the fact that both sides of the fin are exposed to the cooling gas.
Whether it is worth calculating fin efficiency depends on the accuracy required, but Biber suggests that this will generally be necessary for thin fins in a forced convection environment.
Whilst in this module we have made available a tool that will deal with the most complex styles of heat sink and flow conditions, in the outside world you may not have this level of sophistication available. A number of tools can be used to supplement hand calculation, of which two examples are:
Rules of thumb, analytical techniques, and spreadsheets can combine to give useful information for scoping the thermal challenge of a circuit, especially where there is reasonable margin. However, high performance heat sinks may require more complex simulations. This case study by Dr Monem Alyaser, the developer of Qfin, is interesting in that it shows the comparative results of a standard CFD simulation and an ‘intermediate’ level (our description) of software.
On the modelling of heat sink performance: Azar and Tavassoli, How Much Heat can be Extracted from a Heat Sink?
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When selecting a heat sink for a fairly basic application, the sequence for design will probably mirror Luxeon’s suggested approach, which has three steps:
Step 1: Determine the reliable ΘJA, using the equation
with the absolute maximum value of TJ and the worst-case operating ambient condition TA.
Step 2: Subtract the ΘJB figure for the device, in order to obtain the target ΘBA.
Step 3: Determine the best heat sink configuration for the application from the target value of ΘBA.
The heat sink configuration will be based on tabular data from specifications, and rudimentary data on the cooling environment.
For those whose application will require more depth in the selection study, Dr Cathy Biber’s paper Designing an “optimum” heat sink fin has some excellent comments on the practicalities of heat sink design, sometimes as simple as “Does it work? Can I afford it?”! She suggests that the first step in heat sink design is to define how big the heat sink can be, how the heat sink can potentially be cooled, and how the heat sink and components are to be secured. But she has also addresses two rules of thumb for fin design:
#1 Fill the available space with as few fins as are required to do the cooling job
#2 Make the fins as thin as the manufacturing technique will allow.
The rationale behind the first of these is partly cost, and partly to allow more opportunity for airflow, both natural and forced convection. The rule on fin thickness is partly related to airflow, but also to a complex set of considerations relating to the way in which the fins are made. Reading her paper at the link above gives some useful insights.
For many purposes choosing a standard heat sink will be the most cost-effective solution, though some modifications to mounting arrangements may be needed. Less frequently, a standard design may be modified with local cut-outs and reduced height in order to fit the heat sink within the available space envelope. For heat sinks made by mass production methods such as extrusion, and where the quantities are not large, adapting an existing design will probably be more cost-effective than making a fully-customised product.
Generally the level of customisation increases as the thermal challenges grow, taking advantage of the greater flexibility of fabrication methods for assembling a heat sink, so that high-tech heat sinks are often custom parts. Typically the design will be developed in stages, in parallel with the electronic design and layout, and with the mechanical design of the overall enclosure.
When carrying out an assessment of the thermal performance of its elements, and estimating the maximum temperature rise of susceptible components, it is necessary to consider the whole equipment. Here a full simulation can save valuable time and the cost of “cutting metal”, allowing alternatives to be evaluated, and the effect of process variations, life changes, and anticipated risks to be assessed. But, however good the simulation, prudent engineers will validate the theoretical study by measurements of prototypes. Having a physical prototype available for assessment also allows a more accurate assessment of design for manufacturability, particularly in terms of the assembly difficulties and cost.
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An implicit assumption made in the discussion so far is that the airflow will be optimised with respect to the heat sink. For example, that the fins on the heat sink will be aligned with the normal direction of flow. It is for this reason that “intelligent” user-friendly programmes such as FLO/PCB automatically assume this alignment when adding heat sinks to a component.
Create a simple simulation of a component with a heat sink, and examine the effect of placing the fins at right-angles to the airflow. Then review our comments.
As we have indicated earlier, having airflow parallel to a fin is a condition under which a boundary layer may develop. The effective barrier that this creates adds to the thermal resistance, so some engineers prefer to blow air directly at the heat sink surface, in the same way as designers of reflow soldering ovens seek to break up the barrier layer by “impingement” designs, in which multiple jets create a turbulent flow at the surface being heated or cooled. Although more efficient from the heat transfer point of view, the disadvantage is that this requires a higher flow velocity.
Most of our discussions have concentrated on the situation where there is only a single heat sink on a board, but in many cases an assembly has multiple heat sinks. How should these be laid out? Wirtz and Colban in Comparison of the cooling performance of staggered and in-line arrays of electronic packages show that, at equal flow rates, staggered arrays have a higher heat transfer coefficient than in-line arrays. However, there is little to choose between the two configurations when they are compared on the basis of either equal coolant flow pressure drop or pumping power. So staggering the array may help, but this is a rule of thumb rather than a substitute for simulation.
Many practical systems are probably over-cooled, being designed for worse case conditions. This provides an opportunity for power conservation by monitoring the effectiveness of the cooling, and feeding this information to a fan control circuit. As well as a saving in energy, this may have significant benefit in reducing the level of noise from the fan, a noticeable benefit in an office environment. At the same time, the measurement circuitry used for fan control can double up as a means of protecting the system against breakdown, or reduction in performance due to factors such as filters becoming clogged.
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The process by which a thermal management system involving a heat sink is developed can range from a simplistic calculation to a full-blown simulation, depending on the application and the extent of the thermal challenge. However, regardless of the scope of the problem or the analysis tool used, care should be taken to check that:
Always assume that both calculation and measurement are potentially incorrect. As a way of avoiding error, Cathy Biber recommends (in Heat Sink Performance Calculation) as part of any thermal design task trying some parametric variations in order to see general trends. She suggests that getting design guidance is actually the most powerful reason for making the effort of carrying out a calculation. She also recommends a degree of engineering scepticism, based on the many simplifying assumptions made, and the many possible sources of error in the experimental data used to validate a calculation.
“The biggest (possible source of error) is usually the fact that heat from the chip is going to take any possible escape route. The heat sink might be the most efficient one, but it isn’t the only one, so not all the heat will go that way. This has the effect of making experimental data look “better” than your calculation. In my experience, even if you go to quite a bit of effort to make all the heat go through the heat sink, about 10% of it still escapes by this route.
Cathy Biber, op. cit.
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If your planned heat sink doesn’t keep that high-dissipation device cool enough, what do you do? Even using materials with improved thermal conductivity, which we have already suggested, has its limitations. However, fortunately for those facing severe thermal challenges, there are other techniques for enhancing performance:
In some designs it is possible to immerse the assembly in coolant, or spray a suitable liquid directly onto the hot parts, but these are for specialist applications, and most engineers prefer to segregate liquid and electronics!
Indirect liquid cooling uses cold plates, typically made from copper, aluminium, or aluminium-clad copper, and attached directly to the object being cooled, or liquid-cooled heat sinks. Heat is absorbed by liquid pumped through channels in the plate, or through tubes attached to the plate or the heat sink fins:
Liquid-cooled heat sinks can be much more compact than air-cooled heat sinks of equivalent rating, but the potential for leakage is a concern. Regular maintenance can also be a requirement, since warm water can stimulate the growth of algae, leading to reduction in cooling efficiency and sometimes to complete blockage.
The thermal resistance of a water-cooled heat sink will vary with the coolant temperature and coolant flow rate, and the absence of measurement standards makes comparison difficult.
As with air-cooled heat sinks, we have to consider fluid flow; there is a trade-off between heat transfer performance and pressure drop, and this varies between different designs. The challenges become significant at very high power densities, and especially in thermal management within an automotive environment, where high power densities combine with high coolant temperatures.
For some applications, liquid-cooled devices are limited by the fact that they cannot cool below ambient (liquid) temperature and do not offer control of device temperature.
For many purposes, coolants other than water are appropriate. In An overview of liquid coolants for electronics cooling Mohapatra describes the wide range and stresses the need to understand a wide range of the fluid characteristics.
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Compressor-based cooling systems, similar to those found in commercial refrigerators and air conditioners, have three fundamental parts: an evaporator, a compressor, and a condenser:
Compressor-based refrigeration is effective for large heat loads (300W or more) and can cool components far below ambient temperature. The technique also allows users to control temperature. However, refrigerators must be used in their designed orientation, which limits installation flexibility. Compressor-based systems also tend to be bulky and noisy, and maintenance and reliability are compromised by their having moving parts.
Refrigerated systems are a useful way of keeping critical components cool, but run the risk that they may result in unwanted condensation if the temperature of the card being cooled falls below the dew-point. In their paper Design and analysis of a scheme to mitigate condensation on an assembly used to cool a process module, Ellsworth and his collaborators recommend finite element analysis to model the enclosure as a way of finding a optimal solution. They investigated both insulating the surfaces and providing strategically-placed heaters to maintain the card surface above the dew point. Unfortunately, their solution, though successful in eliminating condensation, was thermally inefficient because of the extra heaters, although using a liquid refrigerant, rather than water, had made it possible to have heat fluxes that were beyond the limits of conventional cooling methods.
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In the same way that cooling liquid can be applied direct to an assembly, allowing coolant to boil on the hot surface, extracting the substantial latent heat needed to turn the liquid into vapour, can be used to provide very efficient heat transfer in a high-power situation. Such total immersion of the electronics requires a liquid with appropriate dielectric and heat transfer properties, and a container that can withstand both atmospheric pressure on the outside (when it is evacuated for filling) and the vapour pressure of the boiling liquid from the inside.
Detailed consideration of this “ebullient cooling” is beyond the scope of this module, although the method is often used in high-voltage applications because immersion in a dielectric is already a requirement for arc suppression. However, the same boiling coolant principle, but encapsulated as a ‘heat pipe’, is becoming a common solution for difficult thermal challenges.
“The rudiments of the modern day heat pipe can be traced to the Perkins Tube patented in the mid-1800s. The Perkins Tube, classified now as a thermosyphon heat pipe (no capillary wick structure), provided the initial building blocks for the heat pipe. In 1944, Gaugler, from General Motors, added a capillary wick structure on the inside of the heat pipe for liquid pumping. The heat pipe remained in fallow until 1964 when Grover from Los Alamos National laboratory wrote a report and coined the name “heat pipe.” Subsequently, heat pipes have been applied to numerous applications ranging from spacecraft thermal control to permafrost temperature regulation for the Alaskan pipeline. A heat pipe remained a relatively high cost/low volume device until the late 1980s, early 1990s when the thermal demands of the computer industry warranted high volume production.”
Thermacore, Inc., Heat Pipe Reliability Documentation (archived file)
Heat pipes use the high values of latent heat associated with evaporation and condensation processes, turning an internal working liquid into vapour at the point to be cooled, and converting the vapour back into liquid at another part of the device where heat can be transferred into the environment through a heat sink or heat exchanger.
As heat is absorbed at the evaporator and the working fluid is vaporised, this creates a pressure gradient that forces the vapour to flow to the cooler end of the pipe, where it condenses, giving up its latent heat to the environment. However, for the operation to be continuous, the condensed working fluid has to be returned to the hot zone. Whilst this can be carried out by gravity alone, it is usual to assist the movement of condensed fluid by capillary action within a ‘wick’ structure.
The simplest internal structure is a grooved tube. This kind of ‘coarse wick’ allows a large volume of liquid to be transported, but the lift produced is low, so the heat pipe is sensitive to the orientation of the heat pipe with respect to gravity. More commonly used, because of their better capillary action, are wicks made of multi-layered metal meshes and sintered finely-powdered metal. A powder wick produces a higher lift, and is thus less sensitive to orientation, although the performance of the heat pipe will still vary with position, and upside-down operation of a heat pipe is usually not possible.
Although not so much a means of removing heat as a way of transferring it from one place to another, a heat pipe has the advantage over a straight conduction process that it can support a heat flux many times greater. For example, John Graebner (Heat pipe fundamentals) gives a typical value of thermal resistance for a heat pipe as 60 times lower than for a copper cylinder of the same dimensions. Other sources indicate that this is a conservative figure, although the value is determined by the dimensions, the working fluid, the wick construction and the temperature of operation.
Although secondary heat sinking will still be required, heat pipes are particularly useful for removing heat from parts of the equipment where conventional heat sinks cannot be fitted directly, as they can be made very small. By appropriate design of heat pipe, it is possible to site the heat sink some distance away from the hot zone, although a longer pipe will transport less energy than a short one because the rate at which the working fluid is returned to the evaporator is reduced.
Heat pipes may be used as separate components, or integrated into other heat management products. For example, heat pipes are often found inserted in fabricated heat sinks, in order to reduce the thermal resistance between base and fins.
Whilst the heat pipe concept is 40 years old, it is only in recent years that it has become used more widely. Part of the reason for this is that the systems are very non-linear, and a heat pipe will thus have a preferred operating temperature range that is determined by the working fluid chosen and the pressure within the unit. Water is a good choice of fluid in many cases, because it has a high latent heat of evaporation, but ammonia, acetone, or methanol can also be used, and special fluids are used for cryogenic and high-temperature applications.
When specifying a heat pipe, take care to consider the heat transfer demands as well as the operating temperature range. One limitation on power rating comes from the need to supply the evaporator with fluid; for many applications, the wick is the limiting factor in the amount of power that can be dissipated, as the transport of fluid back to the heat source governs the cycle time of the fluid. This is where the heat pipe dimensions become important, as does the type of wick, a grooved wick being able to transport a higher volume of liquid than a powder wick.
Another limitation is that heat pipes need to be kept within what is referred to as their “nucleate boiling range”. Under conditions of high heat flux, the heat sink surface may be higher than the boiling point of the fluid, which becomes superheated, small bubbles of vapour forming close to the hot surface and collapsing again in cooler fluid elsewhere. Whilst this increases the heat transfer coefficient enormously, the effect works only as long as the liquid wets the surface. Once a stable vapour jacket is formed around the hot surface, preventing liquid contact, the heat transfer coefficient reduces drastically.
Having no moving parts, heat pumps are typically highly reliable, with a 20-year MTBF, provided that they are properly made and remain undamaged. However, contamination sealed in during manufacture may degrade its performance, and any leakage, such as may be caused by bending and flattening of the pipe, will eventually result in pipe failure.
Because heat pipes exploit the latent heat effects of the working fluid, they can be designed to keep a component near ambient conditions, but they cannot cool objects below ambient temperature or allow the temperature to be controlled.
A “vapour chamber” is a flat plate variant of the heat pipe, with a thin rectangular enclosed volume and a porous medium close to the heated surface (Figure 7). The vapour chamber is positioned between a zone where heat can be absorbed from the source and a heat sink region on the opposite side.
The enclosure is partially filled with a fluid in equilibrium with its own vapour. The heat flux from the source causes the fluid to evaporate, increasing the vapour pressure, and in turn leading to increased condensation at the heat sink end over the entire area of the heat sink. As with the heat pipe, the condensed fluid is returned to the hot zone by gravity or capillary action.
Although appearing similar to a vapour chamber, with a flat extruded, aluminium plate that incorporates the working fluid, the oscillating/pulsating heat pipe, invented by Akachi in 1994, differs from the conventional heat pipe and vapour chamber in that it does not contain a wicking structure. Instead it relies on combined vaour and liquid transport within an undulating turned capillary tube (Figure 8).
Note: Only three of a larger number of serpentine flow paths is shown. Blue circles are vapour bubbles; blue oblongs are vapour slugs; the remaining white background region inside the serpentine-shaped ducting is liquid.
Source: Vogel and Xu, op. cit.
Polasek describes the operation of the oscillating heat pipe as follows: “When one end of the undulating capillary tube is subjected to high temperature, the working fluid inside evaporates and increases the vapour pressure, which causes the bubbles in the evaporator zone to grow. This pushes the liquid column toward the low temperature end (condenser). The condensation at the low temperature end will further increase the pressure difference between the two ends. Because of the interconnection of the tube, the motion of liquid slugs and vapour bubbles at one section of the tube toward the condenser also leads to the motion of slugs and bubbles in the next section toward the high temperature end (evaporator). This works as the restoring force”. As a result the force of gravity has a minimal effect on fluid flow direction.
A range of applications for heat pipes is given by Zaghdoudi, Tantolin and Godet in Use Of Heat Pipe Cooling Systems In The Electronics Industry.
Some recent developments in Vogel and Xu, Low Profile Heat Sink Cooling Technologies for Next Generation CPU Thermal Designs.
Christopher Soule, Heat Pipe Reliability in High-Power Applications.
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In 1821 Seebeck discovered that when two conductors of different materials were joined together in a loop, and there was a temperature difference between the two junctions, a current flowed through the loop. In 1833, Peltier demonstrated the reverse effect; by cutting one of the conductors, and forcing a current through the loop, a temperature differential between the two junctions was produced (Figure 9).
where Q = heat in or out (W)
πP = Peltier coefficient (W/A)
I = current (A)
This ‘Peltier effect’, creating a temperature difference between two junctions by passing a current between them, is the basis of thermoelectric cooling (TEC) systems. TECs are now made from semiconductor materials such as bismuth telluride, and a practical Peltier device in its simplest form (Figure 10) consists of a single semiconductor ‘pellet’ soldered at each end to an electrical conductor, usually of plated copper. In this configuration, the dissimilar material required for the Peltier effect is the copper connection path through the power supply. With a DC voltage source connected as shown, electrons will flow from bottom to top, heat being absorbed at the bottom junction and released at the top junction.
Because a single pellet will draw of the order of 5A with only 60mV applied, resistive losses will be lower (and power supplies easier to provide) if multiple junctions can be arranged in series. In order to give the required series electrical connection, but allow the elements to operate thermally in parallel, we make use of the facts that the heat ‘pump’ action operates in the direction of charge carrier movement, and that the carriers (‘holes’) in p-type semiconductors flow in the opposite direction to electrons in n-type semiconductor material. This allows us to configure elements in ‘couples’ as shown in Figure 11.
To make a TEC module, a series of p-type and n-type elements is sandwiched between thin ceramic plates (Figure 12), whose outer faces become the thermal interface between the Peltier assembly and the environment. Ceramics are generally used as they represent the best compromise between mechanical strength, electrical resistivity, and thermal conductivity.
TEC systems come in many different sizes, some as small as 2mm across. A typical large module (Tellurex CZ1-1.4-127-1.14) measures 40mm×44mm×3.3mm, contains 254 elements, draws up to 8A from a 16V supply, and will pump as much as 80W of heat.
Being solid-state, Peltier modules have no moving parts or working fluid, are light, noiseless, inherently reliable and easy to control, can be used in any orientation and are compatible with heat sinks, cold plates and heat pipes.
Other than refrigeration-cooled heat sinks, Peltier devices offer the only heat management method able to produce temperatures below ambient, and this has been used for special applications where system performance improved as the device temperature was lowered.
And TECs are the only available solution when bidirectional temperature control is needed, as they are able to pump heat into the controlled area as well as out, by reversing the current. Because the amount of heat pumped is proportional to the current flowing, it becomes possible, by using a feedback system, to hold a sensitive device at an accurately known temperature (within <0.01°C is claimed). TECs are therefore often used in measurement head applications; see Kevin Moody, Chips on Fire, New Approach to Thermal Management (PDF PowerPoint print, 353Kb).
There is of course a downside:
Peltier devices are therefore mostly suitable for localised cooling for temperature control of a single component, rather than a main cooling method for an entire system.
More information from Tellurex in An Introduction to Thermoelectrics (PDF, 397Kb)
Bismuth telluride is not the only material used in commercial thermoelectric cooler modules, and there have been a number of developments over the past ten years. In Effect of improved thermoelectric ZTs on electronic module coolability, Robert Simons discusses the potential improvements that might be made.
TECs based on bismuth telluride are relatively large in size, and have poor compatibility with integrated circuits, since the cooling device must be placed on the back of the chip. This is not ideal for the common situation where there are significant temperature differences over the die surface. In Solid-state microrefrigerator on a chip, Fukatami and his colleagues discuss an alternative approach, fabricating a “microrefrigerator” direct on the chip surface.
In Latest developments in thermoelectrically enhanced heat sinks, Bierschenk and Johnston discuss the integration of TEC and heat sink, and introduce the interesting idea of the TEC being a “variable negative thermal resistance” in the thermal path.
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In these last sections we have looked briefly at a range of techniques that are mostly appropriate for high-energy larger systems. But in many cases the thermal challenge is more acute at the device level. For an insight into this, read Ellsworth and Simon’s High powered chip cooling – air and beyond, which scopes the challenge and indicates some solutions.
The idea of the increasing challenge produced by hot spots localised within the die is discussed further by Daxi Xiong in Packaging for improved thermal management: reducing thermal resistance at die level. One innovative solution proposed combines different sizes of channel through which circulating fluid is used to spread heat. The technique allows heat fluxes of up to 1200W·cm−2, merely by conducting the heat to a heat sink, and without the need for external liquid cooling.
In Indirect thermosyphons for cooling electronic devices, Tuma and Mortazavi discuss the way in which a relative of the heat pump can be used for cooling individual devices of extremely high dissipation.
It is always a temptation to think primarily of integrated circuits as requiring cooling. Yet other components can present just as much as a thermal challenge. An example of this is the LED array, which is increasingly used as a high-intensity source of light, and not just as a low-luminosity indicator. More information in Thermal challenges in LED cooling by James Petroski.
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Each of these lists is in the order in which the material is referenced in the Unit text. However, note that links to SAQ answers are not included!
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