Heat-Sink SelectionIn 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 convection500-800(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

3.0150

6.0225

9.0300

12.0Natural convection6.5

0.257.5

0.3010

0.3813

0.501.0 (200)4.0

0.155.0

0.206.0

0.247.0

0.272.5 (500)2.5

0.103.3

0.134.0

0.165.0

0.205.0 (1000)2.0

0.082.5

0.103.0

0.123.5

0.14Table 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 TypesHeat 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 typen range,%Stamping & flat plates10-18Finned extrusions15-22Impingement flow

Fan heat sinks25-32Fully ducted extrusions45-58Ducted pin fin,

Bonded & folded fins78-90Table 4: Range of heattransfer efficiencies

The improved thermal performance is generally associated with additionalcosts in either material or manufacturing, or both.

Thermal Performance GraphPerformance 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,Tsaislinearly 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 Qtoyield 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/ftFactor0, sea level1.00100030000.951500 50000.90200070000.863000 100000.803500120000.75Table 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.

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