With the increase in heat dissipation from microelectronics devices and thereduction in overall form factors, thermal management becomes a more a moreimportant element of electronic product design.
Both the performance reliability and life expectancy of electronic equipmentare inversely related to the component temperature of the equipment. Therelationship between the reliability and the operating temperature of a typicalsilicon semi-conductor device shows that a reduction in the temperaturecorresponds to an exponential increase in the reliability and life expectancy ofthe device. Therefore, long life and reliable performance of a component may beachieved by effectively controlling the device operating temperature within thelimits set by the device design engineers.
Heat sinks are devices that enhance heat dissipation from a hot surface,usually the case of a heat generating component, to a cooler ambient, usuallyair. For the following discussions, air is assumed to be the cooling fluid. Inmost situations, heat transfer across the interface between the solid surfaceand the coolant air is the least efficient within the system, and the solid-airinterface represents the greatest barrier for heat dissipation. A heat sinklowers this barrier mainly by increasing the surface area that is in directcontact with the coolant. This allows more heat to be dissipated and/or lowersthe device operating temperature. The primary purpose of a heat sink is tomaintain the device temperature below the maximum allowable temperaturespecified by the device manufacturers.
Thermal Circuit
Before discussing the heat sink selection process, it is necessary to definecommon terms and establish the concept of a thermal circuit. The objective isto provide basic fundamentals of heat transfer for those readers who are notfamiliar with the subject. Notations and definitions of the terms are asfollows:
Q: total power or rate of heat dissipation in W, represent the rateof heat dissipated by the electronic component during operation. For thepurpose of selecting a heat sink, the maximum operating power dissipation isused.
Tj: maximum junction temperature of the device in °C.Allowable Tj values range from 115°C in typicalmicroelectronics applications to as high as 180°C for some electroniccontrol devices. In special and military applications, 65°C to 80°Care not uncommon.
Tc: case temperature of the device in °C. Sincethe case temperature of a device depends on the location of measurement, itusually represent the maximum local temperature of the case.
Ts: sink temperature in °C. Again, this representsthe maximum temperature of a heat sink at the location closest to the device.
Ta: ambient air temperature in °C.
Using temperatures and the rate of heat dissipation, a quantitative measureof heat transfer efficiency across two locations of a thermal component can beexpressed in terms of thermal resistance R, defined as
R = 
T/Q
Were 
T is thetemperature difference between the two locations. The unit of thermalresistance is in °C/W, indicating the temperature rise per unit rate ofheat dissipation. This thermal resistance is analogous to the electricalresistance Re, given by Ohm’s law:
Re =V/I
With V beingthe voltage difference and I the current.
Figure 1: Thermal resistance circuit
Consider a simple case where a heat sink is mounted on a device package asshown in Fig 1. Using the concept of thermal resistance, a simplified thermalcircuit of this system can be drawn, as also shown in the figure. In thissimplified model, heat flows serially from the junction to the case then acrossthe interface into the heat sink and is finally dissipated from the heat sink tothe air stream.
The thermal resistance between the junction and the case of a device isdefined as
Rjc = (Tjc)/Q = (Tj- Tc)/Q
This resistance is specified by the device manufacturer. Although the Rjcvalue of a give device depends on how and where the cooling mechanism isemployed over the package, it is usually given as a constant value. It is alsoaccepted that Rjc is beyond the user’s ability to alter or control.
Similarly, case-to-sink and sink-to-ambient resistance are defined as
Rcs = (Tcs)/Q = (Tc- Ts)/Q
Rsa = (Tsa)/Q = (Ts- Ta)/Q
respectively. Here, Rcs represents the thermalresistance across the interface between the case and the heat sink and is oftencalled the interface resistance. This value can be improved substantiallydepending on the quality of mating surface finish and/or the choice of interfacematerial. Rsa is heat sink thermal resistance.
Obviously, the total junction-to-ambient resistance is the sum of all threeresistances:
Rja = Rjc + Rcs + Rsa= (Tj – Ta)/Q
Required Heat-Sink Thermal Resistance
To begin the heat sink selection, the first step is to determine the heatsink thermal resistance required to satisfy the thermal criteria of thecomponent. By rearranging the previous equation, the heat sink resistance canbe easily obtained as
Rsa = ((Ts – Ta)/Q) – Rjc- Rcs
In this expression, Tj, Q and Rjcare provided by the device manufacturer, and Ta and Rcsare the user defined parameters.
The ambient air temperature Ta for cooling electronicequipment depends on the operating environment in which the component isexpected to be used. Typically, it ranges from 35 to 45°C, if the externalair is used, and from 50 to 60°C, if the component is enclosed or is placedin a wake of another heat generating equipment.
The interface resistance Rcs depends on the surfacefinish, flatness, applied mounting pressure, contact area and, of course, thetype interface material and its thickness. Precise value of this resistance,even for a give type of material and thickness, is difficult to obtain, since itmay vary widely with the mounting pressure and other case dependent parameters. However, more reliable data can be obtained directly from material manufacturersor from heat sink manufacturers. Typical values for common interface materialsare tabulated in Table 1.
| Material | Conductivity W/in °C |
Thickness inches |
Resistance in2 °C/W |
| There-O-Link Thermal Compound |
0.010 | 0.002 | 0.19 |
| High Performance Thermal Compound |
0.030 | 0.002 | 0.07 |
| Kon-Dux | 0.030 | 0.005 | 0.17 |
| A-Dux | 0.008 | 0.004 | 0.48 |
| 1070 Ther-A-Grip | 0.014 | 0.006 | 0.43 |
| 1050 Ther-A-Grip | 0.009 | 0.005 | 0.57 |
| 1080 Ther-A-Grip | 0.010 | 0.002 | 0.21 |
| 1081 Ther-A-Grip | 0.019 | 0.005 | 0.26 |
| A-Phi 220 @ 20psi | 0.074 | 0.020 | 0.27 |
| 1897 in Sil-8 | 0.010 | 0.008 | 0.81 |
| 1898 in Sil-8 | 0.008 | 0.006 | 0.78 |
| Table 1: Thermal properties ofinterface materials1 | |||
With all the parameters on the right side of the Rsaexpression identified, it becomes the required maximum thermal resistance of aheat sink for the application. In other words, the thermal resistance value ofa chosen heat sink for the application has to be equal to or less than Rsavalue for the junction temperature to be maintained at or below the specifiedTj.
Heat-Sink Selection
In selecting an appropriate heat sink that meets the required thermalcriteria, one needs to examine various parameters that affect not only the heatsink performance itself, but also the overall performance of the system. Thechoice of a particular type of heat sink depends largely to the thermal budgetallowed for the heat sink and external conditions surrounding the heat sink. Itis to be emphasized that there can never be a single value of thermal resistanceassigned to a given heat sink, since the thermal resistance varies with externalcooling conditions.
When selecting a heat sink, it is necessary to classify the air flow asnatural, low flow mixed, or high flow forced convection. Natural convectionoccurs when there is no externally induced flow and heat transfer relies solelyon the free buoyant flow of air surrounding the heat sink. Forced convectionoccurs when the flow of air is induced by mechanical means, usually a fan orblower. There is no clear distinction on the flow velocity that separates themixed and forced flow regimes. It is generally accepted in applications thatthe effect of buoyant force on the overall heat transfer diminishes tonegligible level (under 5%) when the induced air flow velocity excess 1 2 m/s(200 to 400 lfm).
The next step is to determine the required volume of a heat sink.. Table 2shows approximate ranges of volumetric thermal resistance of a typical heat sinkunder different flow conditions.
| Flow condition m/s (lfm) |
Volumetric Resistance cm3 °C/W (in3 °C/W) |
|
| natural convection | 500-800 | (30-50) |
| 1.0 (200) | 150-250 | (10-15) |
| 2.5 (500) | 80-150 | (5-10) |
| 5.0 (1000) | 50-80 | (3-5) |
| Table 2: Range of volumetricthermal resistance | ||
The volume of a heat sink for a given low condition can be obtained bydividing the volumetric thermal resistance by the required thermal resistance. Table 2 is to be used only as a guide for estimation purposes in the beginningof the selection process. The actual resistance values may vary outside theabove range depending on many additional parameters, such as actual dimensionsof the heat sink, type of the heat sink, flow configuration, orientation,surface finish, altitude, etc. The smaller values shown above correspond to aheat sink volume of approximately 100 to 200 cm3 (5 to 10 in3)and the larger ones to roughly 1000 cm3 (60in3).
The above tabulated ranges assume that the design has been optimized for agiven flow condition. Although there are many parameters to be considered inoptimizing a heat sink, one of the most critical parameters is the fin density. In a planar fin heat sink, optimum fin spacing is strongly related to twoparameters: flow velocity and fin length in the direction of the flow. Table 3may be used as a guide for determining the optimum fin spacing of a planar finheat sink in a typical applications.
| Fin length, mm (in) | ||||
| Flow condition m/s (lfm) |
75 3.0 |
150 6.0 |
225 9.0 |
300 12.0 |
| Natural convection | 6.5 0.25 |
7.5 0.30 |
10 0.38 |
13 0.50 |
| 1.0 (200) | 4.0 0.15 |
5.0 0.20 |
6.0 0.24 |
7.0 0.27 |
| 2.5 (500) | 2.5 0.10 |
3.3 0.13 |
4.0 0.16 |
5.0 0.20 |
| 5.0 (1000) | 2.0 0.08 |
2.5 0.10 |
3.0 0.12 |
3.5 0.14 |
| Table 3: Fin spacing (in mm/inches) versus flow and fin length | ||||
The average performance of a typical heat sink is linearly proportional tothe width of a heat sink in the direction perpendicular to the flow, andapproximately proportional to the square root of the fin length in the directionparallel to the flow. For example, an increase in the width of a heat sink by afactor of two would increase the heat dissipation capability by a factor of two,whereas and increase the heat dissipation capability by a factor of 1.4. Therefore , if the choice is available, it is beneficial to increase the widthof a heat sink rather than the length of the heat sink. Also, the effect ofradiation heat transfer is very important in natural convection, as it can beresponsible of up to 25% of the total heat dissipation. Unless the component isfacing a hotter surface nearby, it is imperative to have the heat sink surfacespainted or anodized to enhance radiation.
Heat Sink Types
Heat sinks can be classified in terms of manufacturing methods and theirfinal form shapes. The most common types of air-cooled heat sinks include:
- Stampings: Copper or aluminum sheet metals are stamped intodesired shapes. they are used in traditional air cooling of electroniccomponents and offer a low cost solution to low density thermal problems. Theyare suitable for high volume production, because advanced tooling with highspeed stamping would lower costs. Additional labor-saving options, such astaps, clips, and interface materials, can be factory applied to help to reducethe board assembly costs.
- Extrusion: These allow the formation of elaboratetwo-dimensional shapes capable of dissipating large heat loads. They may becut, machined, and options added. A cross-cutting will produceomni-directional, rectangular pin fin heat sinks, and incorporating serratedfins improves the performance by approximately 10 to 20%, but with a slowerextrusion rate. Extrusion limits, such as the fin height-to-gap fin thickness,usually dictate the flexibility in design options. Typical fin height-to-gapaspect ratio of up to 6 and a minimum fin thickness of 1.3mm, are attainablewith a standard extrusion. A 10 to 1 aspect ratio and a fin thickness of 0.8″can be achieved with special die design features. However, as the aspect ratioincreases, the extrusion tolerance is compromised.
- Bonded/Fabricated Fins: Most air cooled heat sinks areconvection limited, and the overall thermal performance of an air cooled heatsink can often be improved significantly if more surface area can be exposed tothe air stream. These high performance heat sinks utilize thermally conductivealuminum-filled epoxy to bond planar fins onto a grooved extrusion base plate. This process allows for a much greater fin height-to-gap aspect ratio of 20 to40, greatly increasing the cooling capacity without increasing volumerequirements.
- Castings: Sand, lost core and die casting processes areavailable with or without vacuum assistance, in aluminum or copper/bronze. thistechnology is used in high density pin fin heat sinks which provide maximumperformance when using impingement cooling.
- Folded Fins: Corrugated sheet metal in either aluminum or copperincreases surface area and, hence, the volumetric performance. The heat sink isthen attached to either a base plate or directly to the heating surface viaepoxying or brazing. It is not suitable for high profile heat sinks on accountof the availability and fin efficiency. Hence, it allows high performance heatsinks to be fabricated for applications.
Figure 2 shows the typical range of cost functions for different types ofheat sinks in terms of required thermal resistance.
Figure 2: Cost versus required thermalresistance
The performance of different heat sink types varies dramatically with theair flow through the heat sink. To quantify the effectiveness of differenttypes of heat sinks, the volumetric heat transfer efficiency can be defined as
where, m is the mass flow rate through the heat sink, c isthe heat capacity of the fluid, andTsa isthe average temperature difference between the heat sink and the ambient air. The heat transfer efficiencies have been measured for a wide range of heat sinkconfigurations, and their ranges are listed in Table 4.
| Heat sink type | n range, % |
| Stamping & flat plates | 10-18 |
| Finned extrusions | 15-22 |
| Impingement flow Fan heat sinks |
25-32 |
| Fully ducted extrusions | 45-58 |
| Ducted pin fin, Bonded & folded fins |
78-90 |
| Table 4: Range of heattransfer efficiencies | |
The improved thermal performance is generally associated with additionalcosts in either material or manufacturing, or both.
Thermal Performance Graph
| Performance graph typical of those published by heat sink vendors are shownin Fig. 3. The graphs are a composite of two separate curves which have beencombined into a single figure. It is assumed that the device to be cooled isproperly mounted, and the heat sink is in its normally used mounting orientationwith respect to the direction of air flow. The first plot traveling from thelower left to the upper right is the natural convection curve of heat sinktemperature rise, Tsa,versus Q. The natural convection curves also assume that the heat sinkis painted or anodized black. The curve from the upper left to lower right isthe forced convection curve of thermal resistance versus air velocity. Inforced convection,Tsa islinearly proportional toQ, hence Rsa is independent of Q and becomesa function only of the flow velocity. However, the natural convectionphenomenon is non-linear, making it necessary to presentTsa asa function of Q. |
 Figure 3: Typical performance graphs |
One can use the performance graphs to identify the heat sink and, for forcedconvection applications, to determine the minimum flow velocity that satisfy thethermal requirements. If the required thermal resistance in a force convectionapplication is 8 °C/W, for example, the above sample thermal resistanceversus flow velocity curve indicates that the velocity needs to be at or greaterthan 2.4 m/s (470 lfm). For natural convection applications, the requiredthermal resistance Rsa can be multiplied by Q toyield the maximum allowableTsa. The temperature rise of a chosen heat sink must be equal to or less than themaximum allowableTsa atthe same Q.
The readers are reminded that the natural convection curves assume anoptional orientation of the heat sink with respect to the gravity. Also, theflow velocity in the forced convection graph represent the approach flowvelocity without accounting for the effect of flow bypass. There have been alimited number of investigations2,3 on the subject of flow bypass. These studies show that flow bypass may reduce the performance of a heat sink byas much as 50% for the same upstream flow velocity. For further consultation onthis subject, readers are referred to the cited references.
When a device is substantially smaller than the base plate of a heat sink,there is an additional thermal resistance, called the spreading resistance, thatneeds to be considered I the selection process. Performance graphs generallyassume that the heat is evenly distributed over the entire base area of the heatsink, and therefore, do not account for the additional temperature rise causedby a smaller heat source. This spreading resistance could typically be 5 to 30%of the total heat sink resistance, and can be estimated by using the simpleanalytical expression developed in Reference 4.
Another design criterion that needs to be considered in the selection of aheat sink, is the altitude effect. While the air temperature of an indoorenvironment is normally controlled and is not affected by the altitude change,the indoor air pressure does change with the altitude. Since many electronicsystems are installed at an elevated altitude, it is necessary to derate theheat sink performance mainly due to the lower air density caused by the lowerair pressure at higher altitude. Table 5 shows the performance derating factorsfor typical heat sinks at high altitudes. For example, in order to determinethe actual thermal performance of a heat sink at altitudes other than the seallevel, the thermal resistance values read off from the performance graphs shouldbe divided by the derating factor before the values are compared with therequired thermal resistance.
| Altitude m/ft |
Factor |
| 0, sea level | 1.00 |
| 1000 3000 | 0.95 |
| 1500 5000 | 0.90 |
| 2000 7000 | 0.86 |
| 3000 10000 | 0.80 |
| 3500 12000 | 0.75 |
| Table 5: Altitude deratingfactors | |
References
- Aavid Engineering, Inc., EDS #117, InterfaceMaterials, January 1992.
- R.A. Wirtz, W. Chen, and R. Zhou, Effect of FlowBypass on the Performance of Longitudinal Fin Heat Sinks, ASME Journal ofElectronic Packaging”,Vol.~116,pp.~206-211,1994.
- S. Lee, Optimum Design and Selection of Heat Sinks,Proceedings of 11th IEEE Semi-Therm Symposium, pp. 48-54, 1995.
- S. Song, S. Lee, and V. Au, Closed Form Equation forThermal Constriction/Spreading Resistances with Variable Resistance BoundaryCondition, Proceedings of the 1994 IEPS Technical Conference, pp. 111-121,1994.
