Heat sink tutorial
Thermal conductivity
Usually a heat sink is used to spread the heat away from a
thermal source in order to reduce the temperature of the source. Typical
sources in my world are power semiconductors and power resistors.
This means that thermal conductivity is the most important
property of the heat sink. Thermal conductivity of a heat sink is a function of
cross section and the material property (thermal conductivity) of the
metal.
In metals heat is transferred though conduction electrons
and phonons. The phonon (lattice vibration) contribution is similar to that of
an insulator with the same weight atoms, so the phonons are not insignificant.
For example the thermal conductivity of aluminum oxide is 30, versus aluminum
metal at 220, so about 10-15% of the thermal conductivity is due to the
phonons. But for most of the thermal conductivity the electrons are doing most
of the heavy lifting.
Thermal conductivity of a metal depends on how far
conduction electrons, can travel without scattering. Conduction electrons can
be scattered by phonons, which is why thermal conductivity gets worse as the
temperature goes up. The more phonons traveling through the metal, the higher
the probability of having them run into a conduction electron.
Conduction electrons and phonons are also scattered by
impurities. An electron traveling through an aluminum crystal will be scattered
if it runs into an impurity atom in the lattice, such as zinc or copper. They
can also be scattered by defects in the aluminum crystal. So if an aluminum
atom is missing, or is displaced from the crystal lattice it will scatter
electrons.
Conduction electrons and phonons are also scattered by
interfaces. Interfaces include the edges of the metal, but also crystal domain
edges.
Here I should point out that the same thing that makes a
metal strong also lowers its thermal conductivity. A pure crystal is soft
because it is easy to slide the crystal layers over one another. Impurities
will "pin" the crystal layers to keep them from sliding. Crystal defects
introduced by deforming the metal (work-hardening) strengthen the metal by
using crystal defects to keep the atomic layers from sliding. And will also
create scattering centers to lower the thermal (and electrical) conductivity.
So the highest thermal conductivity metals will be pure
and annealed with large crystal domains. Table 1. Aluminum wrought
alloys arranged by thermal conductivity. In annealed state except 4032-T6. The
strength of tempered versions can be considerably higher than listed here. For
flat stamped heat sinks I usually specify 1100, it is one of the best,
inexpensive and easily remembered. For heat sinks that will need extensive
machining 2024 or 6101.
Aluminum Alloys |
Thermal Conductivity W/(°C-meter) |
Tensile Strength MPa |
Extrudability |
Forming |
Main alloying element |
1350 |
234 |
83 |
100 |
+ |
99.5% Aluminum |
1060 |
231 |
69 |
100 |
+ |
99.6% Aluminum |
1050 |
222 |
105-145 |
100 |
+ |
99.5% |
1100 |
222 |
90 |
100 |
+ |
99.0% |
6101 |
220 |
97 |
50 |
+ |
1% Si+Mg+B |
3003 |
193 |
110 |
60 |
++ |
1% Manganese |
2024 |
193 |
186 |
10 |
+ |
4% Copper |
2017 |
193 |
179 |
10 |
+ |
4% Copper |
6061 |
180 |
124 |
50 |
+ |
2% Mg+Si+Cu |
7075 |
173 |
228 |
5 |
- |
9.7% Cu+Mg+Zn |
2219 |
171 |
172 |
10 |
+ |
6% Copper |
3105 |
171 |
117 |
60 |
+ |
1% Mn+Mg |
4043 |
163 |
145 |
|
|
5% Silicon |
4032-T6 |
154 |
379 |
|
|
12% Silicon |
2011 |
151 |
379 |
10 |
+ |
5% Copper |
5052 |
138 |
180 |
30 |
+ |
2% Magnesium |
5456 |
117 |
310 |
30 |
+ |
5% Magnesium |
8090 |
95 |
340 |
|
|
2% Li 2% Cu |
Table 2. Copper has great thermal conductivity,
but add any alloying elements to it and the thermal conductivity drops fast, as
you can expect.
Copper Alloys |
Thermal Conductivity W/(°C-meter) |
Tensile Strength MPa |
|
|
Type |
C10100 |
394 |
221 |
|
|
Oxygen free high conductivity |
C15000 |
367 |
255 |
|
|
0.15% Zirconium |
C18200 |
324 |
234 |
|
|
1% Chromium |
C17000 |
107 |
483 |
|
|
1.7% Beryllium |
C26000 |
121 |
338 |
|
|
Cartridge brass |
C35000 |
116 |
324 |
|
|
Leaded brass |
C46400 |
116 |
400 |
|
|
Naval brass |
C51000 |
46 |
485 |
|
|
Tin bronze |
C75200 |
33 |
414-1000 MPa |
|
|
Nickel silver |
Table 3. Sometimes sheet steel is already in
your product, and if you can get away with using it as a heat sink it saves
money and complexity.
Steel |
Thermal Conductivity W/(°C-meter) |
Tensile Strength MPA |
|
|
Fabrication |
1006 |
65 |
295 |
|
|
Hot rolled |
1010 |
52 |
325 |
|
|
Hot rolled |
1018 |
52 |
325 |
|
|
Hot rolled |
1020 |
52 |
380 |
|
|
Hot rolled |
1070 |
51 |
640 |
|
|
Cold drawn |
2205 Stainless |
19 |
750 |
|
|
Annealed |
410 Stainless |
25 |
520 |
|
|
Annealed |
316 Stainless |
16 |
586 |
|
|
Annealed |
304 Stainless |
16 |
586 |
|
|
Annealed |
Table 4. Zinc can be die cast to make complicated
shapes at low cost. Injection molding machines are made specifically to mold
zinc just like plastic. The thermal conductivity of zinc is moderate because it
has large percentages of five different isotopes that cause electron
scattering. Because of this the thermal conductivity doesn't change much when
small percentages of alloying metals are added.
Zinc |
Thermal Conductivity W/(°C-meter) |
Ultimate Tensile Strength MPA |
|
|
|
Pure Zinc |
125 |
145 |
|
|
|
Zamak 3 |
113 |
268 |
|
|
4% Aluminum |
Zamak 5 |
108 |
331 |
|
|
4%Al 1%Ci |
KS |
105 |
200 |
|
|
4%Al 3%Cu |
|