The document discusses heat sink design for cooling electronic systems. It compares different design parameters for heat sinks such as fin material, shape, layout, working fluid, and forcing mechanism. Two solutions are proposed to achieve heat fluxes of 2 kW/m^2 and 200 kW/m^2. Sample calculations are shown for a solution using aluminum fins cooled by forced air to achieve a heat flux of 209.377 kW/m^2.

1. Alec Gauthier
4-20-2015
ME320
Heat Sink Design
Review and Proposal

2. Contents
Abstract.........................................................................................................................................................2
Nomenclature ...............................................................................................................................................3
Introduction ..................................................................................................................................................4
Comparisons .................................................................................................................................................5
Fin material ...............................................................................................................................................5
Fin Design..................................................................................................................................................6
Fin Shape...............................................................................................................................................6
Fin Layout..............................................................................................................................................7
Working Fluid............................................................................................................................................8
Forcing Mechanism...................................................................................................................................9
Solutions .....................................................................................................................................................10
Solution 1................................................................................................................................................10
Solution 2................................................................................................................................................11
Sample Calculations............................................................................................................................12
Conclusion...................................................................................................................................................14
References ..................................................................................................................................................15
Appendix 1 ..................................................................................................................................................16
Efficiency of common fin shapes ............................................................................................................16
Appendix 2 ..................................................................................................................................................17

3. Abstract

4. Nomenclature
H Heat Transfer Coefficient [
𝑊
𝑚2−𝐾
]
q” Heat Flux [
𝐾𝑊
𝑚2 ]
Cp Specific Heat Capacity [
𝐽
𝐾𝑔−𝐾
]
k Thermal conductivity [
𝑊
𝑚−𝐾
]
Kf Thermal conductivity of fluid [
𝑊
𝑚−𝐾
]
Nu Nusselt Number [
ℎ−𝐷
𝑘
]
Pr Pandtl Number [
𝜐
𝛼
]
𝛼 Thermal diffusivity [
𝑚2
𝑠
]
μ Dynamic Viscosity [
𝑁−𝑆
𝑚2 ]
ρ Density [
𝐾𝑔
𝑚3]
ν Kinematic Viscosity [
𝑚2
𝑠
]
Tb Temperature at base of fin [𝐾]
T∞ Temperature of surrounding fluid [𝐾]
V Velocity of fluid [
𝑚
𝑠
]
P Perimeter [𝑚]
t Thickness [𝑚]
Ac Cross Section area [𝑚2]
As Surface Area [𝑚2]

5. Introduction
This project is based around heat sinks used to cool electronic systems such as a CPU. A heat
sink is a heat exchanger that cools devices by dissipating heat into the surrounding medium.
Heat sinks are designed to maximize the surface area in contact with a cooling fluid, whether it
be air or another fluid. There are many different designs and systems of heat sinks that work for
different purposes. Common parameters that go into designing these heat sinks are the
material of the fins, the layout and design of the fins, what fluid will be pulling heat from the
fins and the mechanism that drives this fluid. (2)
The purpose of this study is to research current designs and solutions for common heat sinks
used to cool CPU’s as well as propose independent solutions to forced convection cooling using
heat sinks. Two separate solutions are needed, one must achieve a cooling heat flux of 2
KW/m2 and the other must achieve 200 KW/m2. The goal is to create a design that combines a
high heat transfer coefficient, a low pressure drop and reasonable cost along with specifying
the parameters discussed above.

6. Comparisons
Fin material
The material used to produce the fins in a heat sink is crucial to its overall effectiveness. Most
heat sinks found in computers today use alloys of metals such as aluminum or copper. These
different materials along with variations of each material allow for different thermal
conductivities.
Aluminum alloys such as 6061 or 6063 are very common because they have a low cost, whereas
aluminum 1050A has a higher thermal conductivity but is a relatively soft metal and is more
expensive. Copper alloys used have up to double the thermal conductivity but are much denser
and are more expensive. The copper alloys are also unnecessary for smaller electronics such as
the CPU of household computers. There are several other materials that can be used for heat
sinks such as silver, brass or even gold. Thermal conductivity values for these materials can be
seen in Table 1.
Table 1. Thermal conductivity of common metals. (8)
Metal Thermal Conductivity [
𝑊
𝑚−𝐾
]
Aluminum 6061 166
6063 201
1050A 229
Copper 400
Silver 429
Gold 316
Brass 120
Diamond 2000

7. Fin Design
Fin Shape
Metallic fins used in heat sinks can be laid out into several geometries and patterns. These
different combinations generate several varying results in terms of heat transfer, cost and size.
Fin shapes range from rectangular plate fins to cylindrical or cone shaped fins. These common
fin shapes can be seen in Figure 1. More detail found in Appendix 1. These different shapes lead
to different heat flux values. The heat Transfer coefficient is related to the dimensionless
parameter for relative heat transfer, the Nusselt number, which is a direct correlation to the
Reynolds number. The Reynolds number, another dimensionless parameter, relates a fluids
velocity and its viscosity. Velocity of a working fluid is greatly influenced by the shape the fluid
is flowing over or around. Therefore, the higher the Nusselt number, the higher the heat
transfer coefficient and the higher the heat flux. Figure 2 compares some of these shapes and
their Reynolds numbers with a corresponding Nusselt number for various shapes and layouts.
Figure 1. Common Fin shapes in heat sinks. (8)
Figure 2. Nusselt number vs Reynolds number for
various geometries and layouts. (6)

8. Fin Layout
The layout of these fins is also important. These variations are involved when there are size
constraints and also when the fluid flow across the fins needs to be maximized so it passes over
as much area as possible. Common geometries can be seen in Figure 3 below.
The efficiency of these layouts and designs can be related to the heat transfer coefficients and
Nusselt number as well and can also be seen in Figure 2 above.
Figure 3. Common fin layouts in CPU heat sinks. (3)

9. Working Fluid
The fluid passing over the fins in a heat sink can vary over different industries and applications.
The most common fluid in a heat sink is air because it is so readily available and does not
damage electronics. Air also has an adequate heat transfer coefficient for cooling small
electronics found in computers. There are some designs that incorporate liquids such as water
or refrigerant flowing over the fins. These methods create a much larger heat flux but are also
more expensive and hard to self-contain. Liquids are also detrimental to electronic devices,
making them a hazardous working fluid and often unnecessary. In Table 2 below, ranges for
Thermal conductivity are compared.
Table 2. Thermal conductivities for common heat sink working fluids. (9)
Working Fluid Thermal conductivity Range [
𝑊
𝑚−𝐾
] ∗ 103
For temperatures between 100-600K
Air (10 – 48)
Glycerin (280 – 300)
R-134a (52 – 110)
Water (569 -700)
Water has an extremely high thermal conductivity and can be used when temperatures are very
high. Although air has a fairly low conductivity, it is often adequate because all that is needed is
a fan to force it over the heat sink. Room temperature air is also easy to use because it naturally
surrounds most electronic components.

10. Forcing Mechanism
In most heat sinks, the working fluid is forced over the heated area in order to increase the heat
transfer. A mechanism that is widely used for this process is a fan. Fans help move the air along
so the heated air passes and colder air enters and the cycle continues. For fluids that are liquid,
pumps or gravity fed systems are used. The viscosity of the fluid does not affect the heat
transfer as long as it is able to move at an adequate velocity (1). Some applications cannot
accommodate these forcing mechanisms and may be cooled using free convection. These
systems are immersed in either air or standing fluid. Figure 4 shows the correlation between
air velocity and the heat transfer coefficient. As seen, the heat transfer increases greatly by
increasing the speed of the air by only a small amount.

11. Solutions
The goal is to achieve a heat flux of 2 Kilowatts per square meter and 200 Kilowatts per square
meter. In order to do so, certain constraints must be known. Through research and other
methods, the following known values are derived (4).
Tb = 90° C = 363 K
T∞ = 20° C = 293 K
Solution 1
One solution that would allow for 2 Kilowatts per square meter of het flux is described below.
Figure 4. Heat transfer coefficient vs air velocity. (7)

12. Solution 2
A second proposed solution that would allow for a heat flux of 200 kilowatts per square meter is shown
below in Figure 5. This design incorporates 20 aluminum alloy (1050A) fins, each with a thickness of
2mm. Each fin is 25mm in width by 25mm in height. The fin is cooled with room temperature air and is
forced through the 2mm air gap between fins with a fan that creates air velocities of 5 m/s. Air
properties were taken at 293 K.
Fluid Properties
Kf = 26.3*10-3 [
𝑊
𝑚−𝐾
]
q” = 2[
𝐾𝑊
𝑚2
] or 200[
𝐾𝑊
𝑚2
]
Cp = 1.007 [
𝐾𝐽
𝐾𝑔−𝐾
]
α = 22.5 * 10-6 [
𝑚2
𝑠
]
ν = 15.9 * 10-6 [
𝑚2
𝑠
]
Pr = .707
Knowns
k = 229 [
𝑊
𝑚−𝐾
]
V = 5 [
𝑚
𝑠
]
Ac = .00005 [𝑚2]
As = .00125 [𝑚2]
P = .054 [𝑚]
t = .002 [𝑚]
25 mm
mm
Figure 5. Proposed design of heat sink. (4)

13. Sample Calculations
Solving for the Reynolds number
Laminar flow was established,
Using relation for laminar flow and a constant heat flux over a flat plate
The Nusselt number was gathered
𝑁𝑢 = .68 ∗ 𝑅𝑒
1
2 ∗ 𝑃𝑟
1
3 = .68 ∗ (7.87 ∗ 103)
1
2 ∗ (. 707)
1
3 = 53.729 (2)
Using this calculated Nusselt number, a heat transfer coefficient was derived
ℎ =
𝑁𝑢 ∗ 𝑘
𝐿
=
53.729 ∗ 26.3 ∗ 10−3 𝑊
𝑚 − 𝐾
. 025 𝑚
= 56.5
𝑊
𝑚2 − 𝐾
(3)
Having this coefficient, it’s now possible to find the heat transfer from the fin to the air
After the constants are found
𝑅𝑒 =
𝑉 ∗ 𝐿
ν
=
(5
𝑚
𝑠
∗ .025 𝑚)
15.9 ∗ 10−6 𝑚2
𝑠
= 7.87 ∗ 103
(1)
𝑀 = √ℎ ∗ 𝑃 ∗ 𝑘 ∗ 𝐴 𝑐 ∗ 𝜃 𝑏 = √56.52
𝑊
𝑚2 − 𝐾
∗ .054 𝑚 ∗ 229
𝑊
𝑚 − 𝐾
∗ .00005 𝑚2 ∗ 70 𝐾
𝑀 = 13.086
(4)
𝑚 = √
(ℎ ∗ 𝑝)
(𝑘 ∗ 𝐴𝑐)
= √
(56.52
𝑊
𝑚2 − 𝐾
∗ .054 𝑚 )
(229
𝑊
𝑚 − 𝐾
∗ .00005 𝑚2)
𝑚 = 16.327 𝑚−1
(5)

14. The heat transfer can now be calculated
𝑞 = 𝑀 ∗ 𝑇𝑎𝑛ℎ( 𝑚 ∗ 𝐿 ) = 13.086 ∗ 𝑇𝑎𝑛ℎ(16.327 ∗ .025𝑚) = 13.086 𝑊 (6)
By dividing this value by the surface area the heat flux is found for each fin
𝑞" =
𝑞
𝐴 𝑠
=
13.086 𝑊
. 00125 𝑚2
= 10468.9
𝑊
𝑚2
𝑝𝑒𝑟 𝑓𝑖𝑛
(7)
This provides a total heat flux for the heat sink
𝑞" total = q" ∗ 𝑁 = 10468.9
𝑊
𝑚2
∗ 20 𝑓𝑖𝑛𝑠
(8)
𝑞" 𝑡𝑜𝑡𝑎𝑙 = 209.377
𝐾𝑊
𝑚2

15. Conclusion

16. References
(1) Heat Transfer and Pressure Drop in Mini Channel Heat Sinks." Taylor & Francis. Web. 26
Apr. 2015.
http://www.tandfonline.com/doi/full/10.1080/01457632.2015.965097#f0011
(2) "Thermal Cooling Enhancement Techniques for Electronic Components ☆." Thermal
Cooling Enhancement Techniques for Electronic Components. Web. 26 Apr. 2015.
http://www.sciencedirect.com/science/article/pii/S0735193314002929#
(3) "What Temperature Should My Processor Be Running At?" What Temperature Should
My Processor Be Running At? Web. 26 Apr. 2015.
http://www.computerhope.com/issues/ch000687.htm
(4) "Cpu Heatsink Fan Socket -Web. 26 Apr. 2015.
http://www.wpclipart.com/computer/hardware/CPU/cpu_heatsink_fan_socket.png.ht
ml
(5) "Heat Sink." Wikipedia. Wikimedia Foundation. Web. 26 Apr. 2015.
http://en.wikipedia.org/wiki/Heat_sink
(6) http://www.imaps.org/journal/2001/q1/soodphakdee-1.pdf
(7) Engineering Tool Box. Web. 26 Apr. 2015.
http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html
(8) Ber, Heinrich, and Sigmund Erk. Fundamentals of Heat Transfer. 3d ed. New York: McGraw-Hill,
1961. Print.

17. Appendix 1
Efficiency of common fin shapes

18. Appendix 2