Heat sink
A fan-cooled heat sink on the processor of a personal computer. To the right is a smaller heat sink cooling
another integrated circuit of the motherboard.
In electronic systems, a
heat sink is a passive component that
cools a device by dissipating heat into the surrounding air. Heat sinks
are used to cool electronic components such as high-power semiconductor
devices, and optoelectronic devices such as higher-power lasers and
light emitting diodes (LEDs). Heat sinks are
heat exchangers such as those used in
refrigeration and air conditioning systems, or the
radiator in an automobile.
A heat sink is an essential component for cooling high-power integrated
circuits. This heat sink is a combination of aluminum fins and copper
heat pipes for cooling high-heat-dissipation processors (As shown is Freezer Xtreme from
Arctic).
[1]
A heat sink is designed to increase the surface area in contact with
the cooling medium surrounding it, such as the air. Approach air
velocity, choice of material, fin (or other protrusion) design and
surface treatment are some of the factors which affect the thermal
performance of a heat sink. Heat sinks are used to cool computer
central processing units or
graphics processors. Heat sink attachment methods and thermal interface materials also affect the eventual
die temperature of the integrated circuit.
Thermal adhesive or
thermal grease
fills the air gap between the heat sink and device to improve its
thermal performance. Theoretical, experimental and numerical methods can
be used to determine a heat sink's thermal performance.
Heat transfer principle
A heat sink is an object that transfers thermal energy from a higher temperature to a lower temperature
fluid
medium. The fluid medium is frequently air, but can also be water or in
the case of heat exchangers, refrigerants and oil. If the fluid medium
is water, the 'heat sink' is frequently called a cold plate. In
thermodynamics a heat sink is a
heat reservoir
that can absorb an arbitrary amount of heat without significantly
changing temperature. Practical heat sinks for electronic devices must
have a temperature higher than the surroundings to transfer heat by
convection, radiation, and conduction.
To understand the principle of a heat sink, consider
Fourier's law of heat conduction.
Joseph Fourier was a French mathematician who made important contributions to the analytical treatment of heat conduction.
[2] Fourier's law of heat conduction, simplified to a one-dimensional form in the
x-direction,
shows that when there is a temperature gradient in a body, heat will be
transferred from the higher temperature region to the lower temperature
region. The rate at which heat is transferred by conduction,
, is proportional to the product of the temperature gradient and the cross-sectional area through which heat is transferred.
Figure 2: Sketch of a heat sink in a duct used to calculate the
governing equations from conservation of energy and Newton’s law of
cooling.
Consider a heat sink in a duct, where air flows through the duct, as
shown in Figure 2. It is assumed that the heat sink base is higher in
temperature than the air. Applying the conservation of energy, for
steady-state conditions, and
Newton’s law of cooling to the temperature nodes shown in Figure 2 gives the following set of equations.
(1)
(2)
where
(3)
Using the mean air temperature is an assumption that is valid for
relatively short heat sinks. When compact heat exchangers are
calculated, the logarithmic mean air temperature is used.
is the air mass flow rate in kg/s.
The above equations show that
- When the air flow through the heat sink decreases, this results in
an increase in the average air temperature. This in turn increases the
heat sink base temperature. And additionally, the thermal resistance of
the heat sink will also increase. The net result is a higher heat sink
base temperature.
- The increase in heat sink thermal resistance with decrease in flow rate will be shown in later in this article.
- The inlet air temperature relates strongly with the heat sink base
temperature. For example, if there is recirculation of air in a product,
the inlet air temperature is not the ambient air temperature. The inlet
air temperature of the heat sink is therefore higher, which also
results in a higher heat sink base temperature.
- If there is no air flow around the heat sink, energy cannot be transferred.
- A heat sink is not a device with the "magical ability to absorb heat like a sponge and send it off to a parallel universe".[3]
Natural convection requires free flow of air over the heat sink. If
fins are not aligned vertically, or if pins are too close together to
allow sufficient air flow between them, the efficiency of the heat sink
will decline.
Design factors
Thermal resistance
For semiconductor devices used in a variety of consumer and industrial electronics, the idea of
thermal resistance
simplifies the selection of heat sinks. The heat flow between the
semiconductor die and ambient air is modeled as a series of resistances
to heat flow; there is a resistance from the die to the device case,
from the case to the heat sink, and from the heat sink to the ambient.
The sum of these resistances is the total thermal resistance from the
die to the ambient. Thermal resistance is defined as temperature rise
per unit of power, analogous to electrical resistance, and is expressed
in units of degrees Celsius per watt (°C/W). If the device dissipation
in watts is known, and the total thermal resistance is calculated, the
temperature rise of the die over ambient can be calculated.
The idea of thermal resistance of a semiconductor heat sink is an
approximation. It does not take into account non-uniform distribution of
heat over a device or heat sink. It only models a system in thermal
equilibrium, and does not take into account the change in temperatures
with time. Nor does it reflect the non-linearity of radiation and
convection with respect to temperature rise. However, manufacturers
tabulate typical values of thermal resistance for heat sinks and
semiconductor devices, which allows selection of commercially
manufactured heat sinks to be simplified.
[4]
Commercial extruded aluminium heat sinks have a thermal resistance (heat sink to ambient air) ranging from
0.4 °C/W for a large sink meant for
TO3 devices, up to as high as
85 °C/W for a clip-on heat sink for a
TO92 small plastic case.
[4] The famous, popular, historic and notable
2N3055 power transistor in a TO3 case has an internal thermal resistance from junction to case of
1.52 °C/W.
[5] The contact between the device case and heat sink may have a thermal resistance of between
0.5 up to 1.7 °C/W, depending on the case size, and use of grease or insulating mica washer.
[4]
Material
The most common heat sink materials are
aluminium alloys.
[6] Aluminium alloy 1050A has one of the higher thermal conductivity values at 229 W/m•K
[7]
but is mechanically soft. Aluminium alloys 6061 and 6063 are commonly
used, with thermal conductivity values of 166 and 201 W/m•K,
respectively. The values depend on the
temper of the alloy.
Copper has around twice the conductivity of aluminium and faster thermal absorption, but is three times as dense
[6] and, depending on the market, around four to six times more expensive than aluminium.
[6] Aluminium can be extruded, but copper can not. Copper heat sinks are machined and
skived. Another method of manufacture is to solder the fins into the heat sink base.
Diamond is another heat sink material, and its thermal conductivity of 2000 W/m•K exceeds copper five-fold.
[8][unreliable source?]
In contrast to metals, where heat is conducted by delocalized
electrons, lattice vibrations are responsible for diamond's very high
thermal conductivity. For thermal management applications, the
outstanding thermal conductivity and diffusivity of diamond is an
essential. Nowadays
synthetic diamond is used as submounts for high-power integrated circuits and laser diodes.
Composite materials can be used. Examples are a
copper-tungsten pseudoalloy,
AlSiC (
silicon carbide in aluminium matrix),
Dymalloy (diamond in copper-silver alloy matrix), and
E-Material (
beryllium oxide in
beryllium
matrix). Such materials are often used as substrates for chips, as
their thermal expansion coefficient can be matched to ceramics and
semiconductors.
Fin efficiency
Fin efficiency is one of the parameters which makes a higher thermal
conductivity material important. A fin of a heat sink may be considered
to be a flat plate with heat flowing in one end and being dissipated
into the surrounding fluid as it travels to the other.
[9]
As heat flows through the fin, the combination of the thermal
resistance of the heat sink impeding the flow and the heat lost due to
convection, the temperature of the fin and, therefore, the heat transfer
to the fluid, will decrease from the base to the end of the fin. Fin
efficiency is defined as the actual heat transferred by the fin, divided
by the heat transfer were the fin to be isothermal (hypothetically the
fin having infinite thermal conductivity). Equations 6 and 7 are
applicable for straight fins.
[10] (6)
[10] (7)
Where:
- hf is the convection coefficient of the fin
- Air: 10 to 100 W/(m2K)
- Water: 500 to 10,000 W/(m2K)
- k is the thermal conductivity of the fin material
- Aluminium: 120 to 240 W/(m·K)
- Lf is the fin height (m)
- tf is the fin thickness (m)
Fin efficiency is increased by decreasing the fin
aspect ratio (making them thicker or shorter), or by using more conductive material (copper instead of aluminium, for example).
Spreading resistance
Another parameter that concerns the thermal conductivity of the heat
sink material is spreading resistance. Spreading resistance occurs when
thermal energy is transferred from a small area to a larger area in a
substance with finite thermal conductivity. In a heat sink, this means
that heat does not distribute uniformly through the heat sink base. The
spreading resistance phenomenon is shown by how the heat travels from
the heat source location and causes a large temperature gradient between
the heat source and the edges of the heat sink. This means that some
fins are at a lower temperature than if the heat source were uniform
across the base of the heat sink. This nonuniformity increases the heat
sink's effective thermal resistance.
To decrease the spreading resistance in the base of a heat sink:
- Increase the base thickness
- Choose a different material with better thermal conductivity
- Use a vapor chamber or heat pipe in the heat sink base.
Fin arrangements
Figure 5: A pin-, straight- and flared fin heat sink types
A pin fin heat sink is a heat sink that has pins that extend from its
base. The pins can be cylindrical, elliptical or square. A pin is by
far one of the more common heat sink types available on the market. A
second type of heat sink fin arrangement is the straight fin. These run
the entire length of the heat sink. A variation on the straight fin heat
sink is a cross cut heat sink. A straight fin heat sink is cut at
regular intervals.
In general, the more surface area a heat sink has, the better it works.
[3]
However, this is not always true. The concept of a pin fin heat sink is
to try to pack as much surface area into a given volume as possible.
[3] As well, it works well in any orientation. Kordyban
[3] has compared the performance of a pin fin and a straight fin heat sink of similar dimensions. Although the pin fin has 194 cm
2 surface area while the straight fin has 58 cm
2, the temperature difference between the heat sink base and the ambient air for the pin fin is
50 °C.
For the straight fin it was 44 °C or 6 °C better than the pin fin. Pin
fin heat sink performance is significantly better than straight fins
when used in their intended application where the fluid flows axially
along the pins (see
figure 17) rather than only tangentially across the pins.
Comparison of a pin fin and straight fin heat sink of similar dimensions. Adapted from data of[3]
| Heat sink fin type |
Width [cm] |
Length [cm] |
Height [cm] |
Surface area [cm²] |
Volume [cm³] |
Temperature difference, Tcase−Tair [°C] |
| Straight |
2.5 |
2.5 |
3.2 |
58 |
20 |
44 |
| Pin |
3.8 |
3.8 |
1.7 |
194 |
24 |
51 |
Another configuration is the flared fin heat sink; its fins are not
parallel to each other, as shown in figure 5. Flaring the fins decreases
flow resistance and makes more air go through the heat sink fin
channel; otherwise, more air would bypass the fins. Slanting them keeps
the overall dimensions the same, but offers longer fins. Forghan, et al.
[11]
have published data on tests conducted on pin fin, straight fin and
flared fin heat sinks. They found that for low approach air velocity,
typically around 1 m/s, the thermal performance is at least 20% better
than straight fin heat sinks. Lasance and Eggink
[12]
also found that for the bypass configurations that they tested, the
flared heat sink performed better than the other heat sinks tested.
Surface color
The
heat transfer from the heatsink occurs by convection of the surrounding air, conduction through the air, and
radiation.
Heat transfer by radiation is a function of both the heat sink
temperature, and the temperature of the surroundings that the heat sink
is optically coupled with. When both of these temperatures are on the
order of 0 °C to 100 °C, the contribution of radiation compared to
convection is generally small, and this factor is often neglected. In
this case, finned heat sinks operating in either natural-convection or
forced-flow will not be effected significantly by surface
emissivity.
In situations where convection is low, such as a flat non-finned panel with low airflow,
radiative cooling
can be a significant factor. Here the surface properties may be an
important design factor. Matte-black surfaces will radiate much more
efficiently than shiny bare metal in the visible spectrum.
[13][unreliable source?]
A shiny metal surface has low effective emissivity due to its low
surface area. While the emissivity of a material is tremendously energy
(frequency) dependent, the noble metals demonstrate very low emissivity
in the Near-Infrared spectrum. The emissivity in the visible spectrum is
closely related to color. For most materials, the emissivity in the
visible spectrum is similar to the emissivity in the infrared spectrum;
however there are exceptions, notably certain metal oxides that are used
as "
selective surfaces".
In a vacuum or in
outer space,
there is no convective heat transfer, thus in these environments,
radiation is the only factor governing heat flow between the heat sink
and the environment. For a satellite in space, a 100 °C (373 Kelvin)
surface facing the
sun
will absorb a lot of radiant heat, since the sun's surface temperature
is nearly 6000 Kelvin, whereas the same surface facing deep-space will
radiate a lot of heat, since deep-space has an effective temperature of
only a few Kelvin.
Engineering applications
Microprocessor cooling
Heat dissipation is an unavoidable by-product of electronic devices and circuits.
[9]
In general, the temperature of the device or component will depend on
the thermal resistance from the component to the environment, and the
heat dissipated by the component. To ensure that the component
temperature does not overheat, a thermal engineer seeks to find an
efficient heat transfer path from the device to the environment. The
heat transfer path may be from the component to a printed circuit board
(PCB), to a heat sink, to air flow provided by a fan, but in all
instances, eventually to the environment.
Two additional design factors also influence the thermal/mechanical performance of the thermal design:
- The method by which the heat sink is mounted on a component or processor. This will be discussed under the section attachment methods.
- For each interface between two objects in contact with each other,
there will be a temperature drop across the interface. For such
composite systems, the temperature drop across the interface may be
appreciable.[10] This temperature change may be attributed to what is known as the thermal contact resistance.[10] Thermal interface materials (TIM) decrease the thermal contact resistance.
Attachment methods
As power dissipation of components increases and component package
size decreases, thermal engineers must innovate to ensure components
won't overheat. Devices that run cooler last longer. A heat sink design
must fulfill both its thermal as well as its mechanical requirements.
Concerning the latter, the component must remain in thermal contact with
its heat sink with reasonable shock and vibration. The heat sink could
be the copper foil of a circuit board, or else a separate heat sink
mounted onto the component or circuit board. Attachment methods include
thermally conductive tape or epoxy, wire-form z clips, flat spring
clips, standoff spacers, and push pins with ends that expand after
installing.
- Thermally conductive tape
Figure 6: Roll of thermally conductive tape.
Thermally conductive tape is one of the most cost-effective heat sink attachment materials.
[14]
It is suitable for low-mass heat sinks and for components with low
power dissipation. It consists of a thermally conductive carrier
material with a pressure-sensitive adhesive on each side.
This tape is applied to the base of the heat sink, which is then
attached to the component. Following are factors that influence the
performance of thermal tape
[14]:
- Surfaces of both the component and heat sink must be clean, with no residue such as a film of silicone grease.
- Preload pressure is essential to ensure good contact. Insufficient
pressure results in areas of non-contact with trapped air, and results
in higher-than-expected interface thermal resistance.
- Thicker tapes tend to provide better "wettability" with uneven
component surfaces. "Wettability" is a term used to describe the
percentage area of contact of a tape on a component. Thicker tapes,
however, have a higher thermal resistance than thinner tapes. From a
design standpoint, it is best to strike a balance by selecting a tape
thickness that provides maximum "wettablilty" with minimum thermal
resistance.
- Epoxy
Epoxy
is more expensive than tape, but provides a greater mechanical bond
between the heat sink and component, as well as improved thermal
conductivity.
[14]
The epoxy chosen must be formulated for this purpose. Most epoxies are
two-part liquid formulations that must be thoroughly mixed before being
applied to the heat sink, and before the heat sink is placed on the
component. The epoxy is then cured for a specified time, which can vary
from 2 hours to 48 hours. Faster cure time can be achieved at higher
temperatures. The surfaces to which the epoxy is applied must be clean
and free of any residue.
The epoxy bond between the heat sink and component is semi-permanent/permanent.
[14]
This makes re-work very difficult and at times impossible. The most
typical damage caused by rework is the separation of the component die
heat spreader from its package.
Figure 7: A pin fin heat sink with a z-clip retainer.
- Wire form Z-clips
More expensive than tape and epoxy, wire form z-clips attach heat
sinks mechanically. To use the z-clips, the printed circuit board must
have anchors. Anchors can be either soldered onto the board, or pushed
through. Either type requires holes to be designed into the board. The
use of RoHS solder must be allowed for because such solder is
mechanically weaker than traditional Pb/Sn solder.
To assemble with a z-clip, attach one side of it to one of the
anchors. Deflect the spring until the other side of the clip can be
placed in the other anchor. The deflection develops a spring load on the
component, which maintains very good contact. In addition to the
mechanical attachment that the z-clip provides, it also permits using
higher-performance thermal interface materials, such as phase change
types.
[14]
Figure 8: Two heat sink attachment methods, namely the maxiGRIP (left) and Talon Clip
- Clips
Available for processors and
ball grid array
(BGA) components, clips allow the attachment of a BGA heat sink
directly to the component. The clips make use of the gap created by the
ball grid array (BGA) between the component underside and PCB top
surface. The clips therefore require no holes in the PCB. They also
allow for easy rework of components. Examples of commercially available
clips are the maxiGRIP
TM and superGRIP
TM range from Advanced Thermal Solutions (ATS) and the Talon Clip
TM
from Malico. The three aforementioned clipping methods use plastic
frames for the clips, but the ATS designs uses metal spring clips to
provide the compression force. The Malico design uses the plastic "arm"
to provide a mechanical load on the component. Depending on the product
requirement, the clipping methods will have to meet shock and vibration
standards, such as Telecordia GR-63-CORE, ETSI 300 019 and MIL-STD-810.
- Push pins with compression springs
For larger heat sinks and higher preloads, push pins with compression springs are very effective.
[14]
The push pins, typically made of brass or plastic, have a flexible barb
at the end that engages with a hole in the PCB; once installed, the
barb retains the pin. The compression spring holds the assembly together
and maintains contact between the heat sink and component. Care is
needed in selection of push pin size. Too great an insertion force can
result in the die cracking and consequent component failure.
- Threaded standoffs with compression springs
For very large heat sinks, there is no substitute for the threaded standoff and compression spring attachment method.
[14]
A threaded standoff is essentially a hollow metal tube with internal
threads. One end is secured with a screw through a hole in the PCB. The
other end accepts a screw which compresses the spring, completing the
assembly. A typical heat sink assembly uses two to four standoffs, which
tends to make this the most costly heat sink attachment design. Another
disadvantage is the need for holes in the PCB.
Summary of heat sink attachment methods
[14]
| Method |
Pros |
Cons |
Cost |
| Thermal tape |
Easy to attach. Inexpensive. |
Cannot provide mechanical attachment for heavier heat sinks or for
high vibration environments. Surface must be cleaned for optimal
adhesion. Moderate to low thermal conductivity. |
Very low |
| Epoxy |
Strong mechanical adhesion. Relatively inexpensive. |
Makes board rework difficult since it can damage component. Surface must be cleaned for optimal adhesion. |
Very low |
| Wire form Z-clips |
Strong mechanical attachment. Easy removal/rework. Applies a preload
to the thermal interface material, improving thermal performance. |
Requires holes in the board or solder anchors. More expensive than tape or epoxy. Custom designs. |
Low |
| Clip-on |
Applies a preload to the thermal interface material, improving
thermal performance. Requires no holes or anchors. Easy removal/rework. |
Must have "keep out" zone around the BGA for the clip. Extra assembly steps. |
Low |
| Push pin with compression springs |
Strong mechanical attachment. Highest thermal interface material preload. Easy removal and installation. |
Requires holes in the board which increases complexity of traces in PCB. |
Moderate |
| Stand-offs with compression springs |
Strongest mechanical attachment. Highest preload for the thermal interface material. Ideal for large heat sinks. |
Requires holes in the board which increases complexity of trace layout. Complicated assembly. |
High |
Thermal interface materials
Figure 10: Thermal conductivity and the interface resistance form part
of the thermal interface resistance of a thermal interface material.
Thermal contact resistance occurs due to the voids created by surface
roughness effects, defects and misalignment of the interface. The voids
present in the interface are filled with air. Heat transfer is
therefore due to conduction across the actual contact area and to
conduction (or natural convection) and radiation across the gaps.
[10] If the contact area is small, as it is for rough surfaces, the major contribution to the resistance is made by the gaps.
[10]
To decrease the thermal contact resistance, the surface roughness can
be decreased while the interface pressure is increased. However, these
improving methods are not always practical or possible for electronic
equipment. Thermal interface materials (TIM) are a common way to
overcome these limitations,
Properly applied thermal interface materials displace the air that is
present in the gaps between the two objects with a material that has a
much-higher thermal conductivity. Air has a thermal conductivity of
0.022 W/m•K
[15] while TIMs have conductivities of 0.3 W/m•K
[16] and higher.
When selecting a TIM, care must be taken with the values supplied by
the manufacturer. Most manufacturers give a value for the thermal
conductivity of a material. However, the thermal conductivity does not
take into account the interface resistances. Therefore, if a TIM has a
high thermal conductivity, it does not necessarily mean that the
interface resistance will be low.
Selection of a TIM is based on three parameters: the interface gap
which the TIM must fill, the contact pressure, and the electrical
resistivity of the TIM. The contact pressure is the pressure applied to
the interface between the two materials. The selection does not include
the cost of the material. Electrical resistivity may, or may not, be
important, depending upon electrical design details.
Selection Based on Interface Gap
[16]
| Interface gap values |
Products types available |
| < 0.05 mm |
< 2 mil |
Thermal grease, epoxy, phase change materials |
| 0.05 - 0.1 mm |
2 – 5 mil |
Phase change materials, polyimide, graphite or aluminium tapes |
| 0.1 - 0,5 mm |
5 – 18 mil |
Silicone coated fabrics |
| > 0.5 mm |
> 18 mil |
Gap fillers |
Selection Based on Contact Pressure
[16]
| Contact pressure scale |
Typical pressure ranges |
Product types available |
| Very low |
< 70 kPa |
Gap fillers |
| Low |
< 140 kPa |
Thermal grease, epoxy, polyimide, graphite or aluminium tapes |
| High |
2 MPa |
Silicone coated fabrics |
TIM Application Notes Based on Product Type
| Product type |
Application notes |
Thermal performance |
| Thermal paste |
Messy. Labor intensive. Relatively long assembly time. |
++++ |
| Epoxy |
Creates ‘permanent’ interface bond. |
++++ |
| Phase change |
Allows for pre-attachment. Softens and conforms to interface defects at operational temperatures. Can be repositioned in field. |
++++ |
| Thermal tapes, including graphite, polyimide, and aluminium tapes |
Easy to apply. Some mechanical strength. |
+++ |
| Silicone coated fabrics |
Provide cushioning and sealing while still allowing heat transfer. |
+ |
| Gap filler |
Can be used to thermally couple differing-height components to a heat spreader or heat sink. Naturally tacky. |
++ |
Figure 11: High power LEDs from Philips Lumileds Lighting Company mounted on 21 mm star shaped metal-core
PCBs
Light emitting diode lamps
Light emitting diode (LED) performance and lifetime are strong functions of their temperature.
[17]
Effective cooling is therefore essential. A case study of a LED based
downlighter shows an example of the calculations done in order to
calculate the required heat sink necessary for the effective cooling of
lighting system.
[18]
The article also shows that in order to get confidence in the results,
multiple independent solutions are required that give similar results.
Specifically, results of the experimental, numerical and theoretical
methods should all be within 10% of each other to give high confidence
in the results.
In soldering
Temporary heat sinks were sometimes used while soldering circuit
boards, preventing excessive heat from damaging sensitive nearby
electronics. In the simplest case, this means partially gripping a
component using a heavy metal crocodile clip, hemostat or similar clamp.
Modern semiconductor devices, which are designed to be assembled by
reflow soldering, can usually tolerate soldering temperatures without
damage. On the other hand, electrical components such as magnetic reed
switches can malfunction if exposed to hotter soldering irons, so this
practice is still very much in use.
[19]
Methods to determine performance
In general, a heat sink performance is a function of material thermal conductivity, dimensions, fin type,
heat transfer coefficient,
air flow rate, and duct size. To determine the thermal performance of a
heat sink, a theoretical model can be made. Alternatively, the thermal
performance can be measured experimentally. Due to the complex nature of
the highly 3D flow in present in applications, numerical methods or
computational fluid dynamics
(CFD) can also be used. This section will discuss the aforementioned
methods for the determination of the heat sink thermal performance.
A heat transfer theoretical model
Figure 13: Sketch of a heat sink with equivalent thermal resistances.
Figure 14: Thermal resistance and heat transfer coefficient plotted against flow rate for the specific heat sink design used in.
[20]
The data was generated using the equations provided in the article. The
data shows that for an increasing air flow rate, the thermal resistance
of the heat sink decreases.
One of the methods to determine the performance of a heat sink is to
use heat transfer and fluid dynamics theory. One such method has been
published by Jeggels, et al.,
[20]
though this work is limited to ducted flow. Ducted flow is where the
air is forced to flow through a channel which fits tightly over the heat
sink. This makes sure that all the air goes through the channels formed
by the fins of the heat sink. When the air flow is not ducted, a
certain percentage of air flow will bypass the heat sink. Flow bypass
was found to increase with increasing fin density and clearance, while
remaining relatively insensitive to inlet duct velocity.
[21]
The heat sink thermal resistance model consists of two resistances, namely the resistance in the heat sink base,
, and the resistance in the fins,
. The heat sink base thermal resistance,
,
can be written as follows if the source is a uniformly applied the heat
sink base. If it is not, then the base resistance is primarily
spreading resistance:
(4)
where
is the heat sink base thickness,
is the heat sink material thermal conductivity and
is the area of the heat sink base.
The thermal resistance from the base of the fins to the air,
, can be calculated by the following formulas.
(5)
[10] (6)
- [10] (7)
(8)
(9)
[22] (10)
[22] (11)
(12)
(13)
The flow rate can be determined by the intersection of the heat sink
system curve and the fan curve. The heat sink system curve can be
calculated by the flow resistance of the channels and inlet and outlet
losses as done in standard fluid mechanics text books, such as Potter,
et al.
[23] and White.
[24]
Once the heat sink base and fin resistances are known, then the heat sink thermal resistance,
can be calculated as:
(14)
Using the equations 5 to 13 and the dimensional data in,
[20]
the thermal resistance for the fins was calculated for various air flow
rates. The data for the thermal resistance and heat transfer
coefficient are shown in Figure 14. It shows that shows that for an
increasing air flow rate, the thermal resistance of the heat sink
decreases.
Experimental methods
Experimental tests are one of the more popular ways to determine the
heat sink thermal performance. In order to determine the heat sink
thermal resistance, the flow rate, input power, inlet air temperature
and heat sink base temperature need to be known. Figure 2 shows a test
setup for a ducted flow heat sink application. Vendor-supplied data is
commonly provided for ducted test results.
[25]
However, the results are optimistic and can give misleading data when
heat sinks are used in an unducted application. More details on heat
sink testing methods and common oversights can be found in Azar, et al.
[25]
Numerical methods
In industry, thermal analyses are often ignored in the design process
or performed too late — when design changes are limited and become too
costly.
[9]
Of the three methods mentioned in this article, theoretical and
numerical methods can be used to determine an estimate of the heat sink
or component temperatures of products before a physical model has been
made. A theoretical model is normally used as a first order estimate.
Numerical methods or computational fluid dynamics (CFD) provide a
qualitative (and sometimes even quantitative) prediction of fluid flows.
[26] [27]
What this means is that it will give a visual or post-processed result
of a simulation, like the images in figures 16 and 17, but the
quantitative or absolute accuracy of the result is not guaranteed.
CFD can give an insight into flow patterns that are difficult, expensive or impossible to study using experimental methods.
[26]
Experiments can give a quantitative description of flow phenomena using
measurements for one quantity at a time, at a limited number of points
and time instances. If a full scale model is not available or not
practical, scale models or dummy models can be used. The experiments can
have a limited range of problems and operating conditions. Simulations
can give a prediction of flow phenomena using CFD software for all
desired quantities, with high resolution in space and time and virtually
any problem and realistic operating conditions. However, the results
still need to be validated. Another problem with CFD is that the inputs
need to be correct. It is the classic case of "Garbage in, garbage out."
[3]
Figure 16: Radial heat sink with thermal profile and swirling forced convection flow trajectories predicted using a CFD analysis package
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Figure 17: Pin fin heat sink with thermal profile and free convection flow trajectories predicted using a CFD analysis package
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