Engineering Project Report
Cooling High Power Density Microprocessors: Employment of a Liquid
Gallium—Indium—Tin Eutectic Coolant Within a Magnetohydrodynamic
Heat Transfer Pump
William Martin
Saginaw Arts and Sciences Academy
Grade level 12
Acknowledgements
I would like to thank Mr. Gary Johnson and Paul Louks for their invaluable guidance during this
project. Additionally I would like to thank Dr. Gregory Schmidt, Ronald Sharp and Mr. Daniel
Sealey for their useful advice and answers about this project. I would also like to thank those
who supported me with their time and materials, Allan Badour of J.C. Tool Company and John
Hoffman of Hofmann Fluid Power, Inc. Thanks also goes to my parents for their help and
putting up with this project around the house for the last few months.
Abstract
The engineering goal of this project is to design an alternative high performance cooling
solution for the increasingly power dense microprocessors that are being used in today’s
computing platforms. In order to accomplish this, the design looks at using a non-toxic galliumindium-tin eutectic that is liquid at room temperature as a coolant circulated within a
magnetohydrodynamic heat transfer pump. The superior thermal and physical properties of a
gallium-indium-tin eutectic coolant lead to several advantages over traditional water cooling.
These include very high heat conductivity, a completely closed system, no moving parts, no
generated sound, and a very high boiling point that allows very hot sources to be cooled.
Since liquid metals are electrically conductive fluids, they offer an efficient pumping solution.
Magnetohydrodynamic pumps harness the Lorentz force, which is exhibited by a charge moving
through a magnetic field. This force depends upon an electrical field that is orthogonal to a
magnetic field, which together result in a force that is orthogonal to both of these fields. The
constructed pump utilized two permanent neodymium magnets positioned across from each
other and orthogonal to two pure tungsten electrodes also positioned across from each other.
Tests indicated that the liquid metal transferred heat very quickly throughout the pump.
Implementation of liquid metal cooling could allow microprocessor heat generated due to
transistor leakage and increasing power densities to be dissipated more efficiently. Greater
thermal dissipation leads to more advanced computing applications, such as protein structure
prediction, speech to text conversion, and natural language processing.
Table of Contents
Acknowledgements.......................................................................................................................... ii
Abstract ........................................................................................................................................... iii
Table of Contents ............................................................................................................................ iv
Table of Figures ............................................................................................................................... vi
1.0 Introduction .............................................................................................................................. 1
2.0 Background Information ........................................................................................................... 2
2.1 Transistor Leakage ........................................................................................................ 3
2.2 Current Methods of Cooling ..................................................................................................... 5
2.3 Turbulent vs. Laminar Flow Heat Transfer................................................................................ 7
2.4 The Prandtl Number and Nusselt Number in Turbulent Flow .................................................. 9
2.5 Physical Properties of Liquid Metals ....................................................................................... 10
2.6 Magnetohydrodynamics ............................................................................................. 11
3.0 Materials ................................................................................................................................. 16
3.1 Materials for Prototype .............................................................................................. 16
3.2 Materials for Final Pump............................................................................................. 17
3.3 Materials for Power Sources ....................................................................................... 18
3.4 Materials Used in Testing ........................................................................................... 18
4.0 Engineering Obstacles ............................................................................................................. 19
4.1 Corrosion ..................................................................................................................... 19
4.2 Safety and Toxicology ................................................................................................. 20
4.3 Tubing ......................................................................................................................... 20
4.4 Turbulent Flow in Liquid Metals ................................................................................. 21
4.5 Heat Exchangers.......................................................................................................... 22
4.6 Magnetohydrodynamic Pump .................................................................................... 23
4.7 Power Source .............................................................................................................. 25
4.8 Adhesive Sealant ......................................................................................................... 27
5.0 Procedure ................................................................................................................................ 28
6.0 Data and Results ..................................................................................................................... 29
7.0 Conclusion and Recommendations ........................................................................................ 37
References .................................................................................................................................... 39
Table of Figures
Table 1: Transistor count on Intel processors ................................................................................ 2
Figure 1: Cross sectional view of a metal oxide field-effect transistor .......................................... 2
Figure 2: Active and leakage microprocessor power since 1970 ................................................... 4
Figure 3: Passive cooling heat sink design with vertical fins .......................................................... 5
Figure 4: Laminar flow from a water faucet ................................................................................... 6
Figure 5: Turbulent flow of water around a post ........................................................................... 6
Figure 7: Magnetic field passing through a surface ...................................................................... 12
Figure 8: Magnetic field lines through a surface with the same edges ........................................ 13
Figure 9: The design of the heat exchanger pre and post drilling ................................................ 22
Figure 10: The direction of force due to a current in a magnetic field ........................................ 23
Figure 11: Electrical circuit diagram of the power source ............................................................ 24
Figure 12: Adhesion of West System Epoxy after various treatments ......................................... 27
Table 2: Temperatures from the first trial of the two heat exchangers after placing one onto a
250 watt heat plate.................................................................................................................. 28-29
Table 3: Temperature from the second trial of the two heat exchangers after placing one onto a
250 watt heat plate.................................................................................................................. 31-32
Table 4: Temperature from the control trial of the two heat exchangers after turning on the
power source ........................................................................................................................... 32-33
Table 5: Average of the heat transfer trials ............................................................................. 34-35
Figure 13: Graph representation of the average of the trials ...................................................... 36
1.0 Introduction
The engineering goal of this project is to design an alternative high performance cooling
solution for the increasingly power dense microprocessors that are being used in today’s
computing platforms. In order to accomplish this, the design looks at using a non-toxic galliumindium-tin eutectic metal that is liquid at room temperature as a coolant circulated within a
magnetohydrodynamic heat transfer pump.
The solid-state-circuits industry is one of the largest in the world and has been the foundation
of the trillion-dollar electronics industry that has incorporated itself into almost all consumer
products. This growing industry of transistor manufacturing has followed an observation made
by Gordon E. Moore, co-founder of Intel, known as Moore’s Law; it states that that the number
of transistors on an integrated circuit for minimum component cost doubles every 24 months
[1]. As table 1 (pp. 2) displays, this law has led to a steady increase in the number of transistors
per microprocessor chip. The transistor count on Intel’s latest computer microprocessors has
exceeded half a billion and will break 1.7 billion upon the release of Intel’s next microprocessor
line [2], [3]. This continued exponential increase of transistors leads to greater power
consumption and heat dissipation due to transistor current leakage, increasing clock
frequencies and the shrinking size of chip features. To keep up with the rate of increasing
transistor count due to Moore’s Law, new innovations for microprocessors must be constantly
made in order to pass physical barriers that arise from increasing the number of transistors per
chip. Amongst these innovations come those of new cooling solutions to combat the increased
power dissipation in the form of heat. By implementing liquid metal as a viable coolant for high
performance consumer and industrial computing, the semiconductor industry can overcome
another barrier and continue developing with Moore’s law.
Copyright © 2005 Intel Corporation.
Table 1: Transistor count on Intel microprocessors
The reason behind shrinking transistor size and increasing transistor number is to shorten the
distance that electrons must travel within the microprocessor, effectively increasing the speed
at which the microprocessor can calculate [4]. What must be challenged next is just how this
dramatic increase in computing performance can be used. Despite many computer users only
utilizing email and word processing, there is a seemingly endless amount of high performance
computing applications that will require more computing power than is currently available.
This list includes but is certainly not limited to protein structure prediction, speech to text
conversion, natural language processing, and feature recognition. All of these draw closer to
becoming fully functional processes as microprocessor speed increases.
2.0 Background Information
In this section of the report background information concerning the project will be provided.
2.1 Transistor Leakage and Power Dissipation
Transistors are tiny electrical switches that are always in one of two states: “on” or “off”. The
transistor that today’s electronics are based on is known as the metal oxide semiconductor
field-effect transistor (MOSFET) (figure 1), which is made up of source and drain electrodes,
through which current flows, and a gate electrode, which controls the current [5]. In order for
Moore’s law to hold true, the distance between the source and drain of these transistors must
shrink by a factor of
every 24 months, reducing the area these take up by a factor of 2 and
therefore doubling the number of transistors per chip. Just as Moore’s law has increased
transistor number exponentially, the size of transistors has decreased exponentially with time
[6]. The most current generation of Intel chips utilizes transistors measuring only 35 nm in gate
length [3].
Figure 1: Cross sectional view of a metal oxide field-effect transistor
The gate electrode in a MOSFET is electrically insulated by a metal oxide and regulates the “on”
and “off” states with an energy barrier that is bypassed with a high “on” current but not
overcome with a low “off” current [5]. The gate voltage that determines whether a transistor
is in the “on” or “off” state is known as the threshold voltage. When the applied voltage meets
the threshold voltage a depletion region forms in the body of the transistor. The depletion
region is an insulating region with a semiconductor material where charges are eliminated due
to recombination of electrons and electron holes. This is important because until the threshold
voltage is met or exceeded, the electron holes in the depletion region outnumber the electrons
so the charges cannot carry over the gate without being recombined with electron holes. In
order to continue designing smaller gate lengths, the voltages applied along with the threshold
voltage must be reduced. Drain induced electrostatic effects from decreasing gate lengths
create a current in the off state making it impossible for the transistor to be completely turned
off, so it operates in a weak-inversion mode. The problem here is that as the size of features on
a chip shrinks, the insulation between transistors must also shrink. As this occurs, current
begins to “leak” more and more from the transistors. What adds to the problem is that
transistor leakage doesn’t just increase linearly with transistor number, but also increases with
temperature; this brings the dynamic current, the “on” current, closer to the leakage current
[7]. As this occurs, the “off” current becomes almost identical to the “on” current and less
parts of the chip are not under load.
In addition to this leakage, increasing clock frequencies in new microprocessor generations has
lead to a linear increase in thermal dissipation. This is because the clock frequency of a
microprocessor is the number of cycles it performs per second or in other words, the number of
times the transistors switch states. Since field-effect transistors consume most of their power
when they are switching states, demanding them to switch more frequently creates a linear
increase in power consumption and thermal dissipation. With this in mind, microprocessor chip
makers have stopped the race for increasing clock speeds and have begun implementing
multiple microprocessor cores on one chip and other designs to increase performance.
While the transistor leakage and clock frequency increase, the power density of the chip, the
amount of power dissipated per unit of area, also rises. Since this is mostly dissipated in the
form of heat, it increases the transistor leakage in a vicious cycle. This is because the electrical
resistance within the transistors increases with temperature and an increased resistance
creates more heat. As figure 2 (pp. 5) demonstrates, the difference between active power
dissipation and leakage power dissipation has been shrinking since the mid-nineties. The
synergistic effect of both active and leakage power dissipation has created the need for a new,
high performance cooling solution, which in the case of this project is liquid metal cooling.
Source: Gordon. E. Moore, “No Exponential is Forever: But “Forever” Can be Delayed,” 2003 IEEE International
Solid-State Circuits Conference Digest of Technical Papers, pp. 20-23, February 2003.
Figure 2: Active and leakage microprocessor power since 1970
2.2 Current Methods of Cooling
There are several diverse methods of cooling that are employed in computer systems today and
all of them rely on one or more of the fundamental methods of heat transfer: conduction,
convection and radiation. Conduction relies on the transfer of internal energy of atoms that are
in contact with each other and can occur in any substance or phase without the movement of
matter. Convection, on the other hand, can only occur in fluids and implies that the substance
is in motion, mixing the medium. The last method, radiation, does not require a medium and
can travel through a vacuum; it relies on the oscillation of charge within the atom and the
transfer of this energy between bodies of unequal temperature [8].
While there are high performance cooling solutions that can be used for microprocessors, there
are several more simplistic methods that are used to dissipate heat from low power density
microprocessors. Some of these are natural radiative and conductive cooling heat sinks and
forced convection air cooling heat sinks.
Natural cooling heat sinks have the advantages of no moving parts, no required power input,
and quiet operation. They typically are made of a metal with high thermal conductivity and
consist of a thin finned structure attached to a thick base in order to dissipate the greatest
amount of heat with the smallest amount of weight and greatest surface area [8]. Despite the
stability and efficiency of natural cooling heat sinks, they are limited in the maximum power
they can dissipate over a set area, restricting them to low power density microprocessors.
Figure 3 gives an example of a typical heat sink design with passive cooling, no forced air flow.
Source: Toshio Aihara and Shigenao Maruyama, “Optimum Design of Natural Cooling Heat Sinks with Vertical Rectangular Fin Arrays,” in
Cooling Technology for Electronic Equipment, Win Aung, Ed. New York: Hemisphere Publishing Corporation, 1988, pp. 35-54
Figure 3: Passive cooling heat sink design with vertical fins
When passive cooling heat sinks will not dissipate heat fast enough, forced air convection can
be applied in the form of a fan. It is usually avoided where not necessary due to the high sound
pressure levels associated with air flow devices. Typical air velocity in these setups is 3-5 m/s,
which can dissipate power densities of 30-50 watts/cm2 [9]. However, for higher power density
microprocessors, such as the today's central processing units with power densities around 100
watts/cm2 (figure 2), high performance fans can be used with much higher air flow velocity.
The fluid flow that occurs with forced air convection is similar to the flow of liquids within liquid
cooling systems, which are also based on forced convection. Once only utilized by computer
enthusiasts, liquid cooling systems have begun to integrate into recent computer
manufacturer’s products, such as Apple’s G5 Power Mac [11]. These cooling setups typically
consist of a water based coolant circulated through a pump to take advantage of water’s high
specific heat. Also the low viscosity of water allows for easy transition to turbulent flow, an
important factor in water cooling systems. What limits water cooling systems is the poor
thermal conductivity of water, its low boiling point, and corrosion of many surfaces. The heart
of this project is utilizing a coolant with more ideal physical properties.
2.3 Turbulent vs. Laminar Flow Heat Transfer
When calculating the heat transfer rate in a liquid cooling system, it is important to look at
several variables. Aside from the coolant’s physical properties, the most important factor is
how the flow is described, laminar or turbulent. Smooth, undisturbed flows are characteristic
of laminar flow (figure 4), and rough, chaotic flows are characteristic of turbulent flow (figure
5). The transition from laminar flow to turbulent flow is an important obstacle to overcome
when designing a system that uses a liquid for heat transfer.
Figure 4: Laminar flow from a water faucet
Figure 5: Turbulent flow of water around a post
Perhaps the best classification of a flow is its unique Reynolds number, Re, which was named
after Osborne Reynolds who studied flows over a hundred years ago [12]. This dimensionless
number describes the ratio of inertial forces to viscous forces within a fluid and is defined by,
,
where V is the fluid velocity, d is the diameter of the orifice, and v is the kinematic viscosity of
the fluid. While the Reynolds number is below about 2,000, the flow will be laminar; above
2,000, the flow will usually become turbulent. However, for determining turbulence in a pipe
the Reynolds number is typically not considered turbulent until it has reached at least 2,300.
The different traits that laminar and turbulent flows possess alter the heat transfer of the flow
under study. When a fluid flows through a pipe, the velocity along the solid surface of the pipe
wall is zero, something known as the no-slip condition [8]. This occurs because, on a molecular
level, the pipe wall is rough and the molecules of the fluid are being absorbed for a moment.
Meanwhile, at the center of the fluid there is a higher velocity and momentum. Once again due
to molecular interactions, the high velocity molecules rub against their neighbors, diffusing the
momentum towards the wall. At some point towards the middle, the fluid is not impeded by
the wall; the part of the fluid that is still affected by the wall is known as the boundary layer. As
with any diffusion, greater difference between high and low concentrations leads to a quicker
rate of diffusion. From this description, it can be said that there is a change in momentum
along the width of the pipe. According to Newton’s second law,
,
where dp is the change in momentum and dt is the change in time. This force is called the
shear stress and is exerted along the wall. As the flow increases in velocity, the momentum in
the center also increases; this results in a higher diffusion rate of momentum and therefore a
higher force. Eventually the momentum cannot be transferred fast enough and the flow breaks
down into turbulent flow. A turbulent flow indicates greater mixing of the fluid and greater
transfer of things such as momentum, heat, and matter. For this reason, it is important to have
a turbulent flow when using a liquid for heat transfer.
2.4 The Prandtl Number and Nusselt Number in Turbulent Flow
In addition to the Reynolds number, there are two more dimensionless numbers that are very
important to heat transfer involving a fluid. The first of the two is the Nusselt number (Nu),
which measures the enhancement of heat transfer from a surface from convection compared
to the heat transfer with only conduction [13]. It is defined as,
,
where L is the characteristic length (diameter in a tube), kf is the thermal conductivity of the
fluid, and h is the convection heat transfer coefficient. The larger the Nusselt number, the
more efficient convective heat transfer is. A value of one would indicate heat transfer only by
conduction, while a Nusselt number in the order of 100 to 1000 is most commonly seen for
turbulent water flow in a pipe.
The second important number is also a ratio, the Prandtl number (Pr), named after Ludwig
Prandtl. It approximates the ratio of viscous or momentum diffusion to the thermal diffusion
in a fluid,
,
where v is the kinematic viscosity and α is the thermal diffusivity [13]. This is the ratio of the
velocity boundary layer, where the fluid is affected by the wall, to the thermal boundary layer,
where the fluid is affected by heat from the wall. A small Prandtl number indicates the thermal
boundary layer is much larger than the velocity boundary layer, such as with liquid metals. This
allows the heat to diffuse very quickly compared to the velocity of the fluid.
Extensive experimental and theoretical efforts have been done to find solutions for turbulent
forced convection heat transfer. Due to the chaotic nature of turbulence, solutions are very
hard to find at large Reynolds numbers. One of the correlations that is pertinent to this project
is the Sleicher-Rouse equation for low Prandtl numbers which takes into account high thermal
conductivity [14]. To find the average Nusselt number with a low Prandtl number fluid, the
equation is
.
2.5 Physical Properties of Liquid Metals
Many of the difficulties associated with using liquid metals as coolants lie in the extreme
physical properties they exhibit. Some of these thermophysical advantages make it worthwhile
to find ways to harness them as coolants. Despite there being no computer product on the
market that utilizes a liquid metal for cooling, some studies have looked into the feasibility of
such a device [15]. The largest obstacles are finding an efficient way to circulate the coolant
and developing a system that will not be corroded by the coolant, both problems that water
cooling systems continue to have today. In contrast, the cooling advantages that liquid metals
hold over water include a superior thermal conductivity, a high surface tension, and an
incredibly high boiling point.
Perhaps best known today for its toxic properties, pure mercury is found to be liquid at room
temperature. Like most metals, it exhibits a decent thermal conductivity around 8.3 Wm-1K-1.
Unfortunately, the health risks associated with this metal eliminate it as a candidate.
Another attractive metal is a eutectic solution of sodium and potassium, something that has
been used to cool nuclear reactors. What makes it so attractive is its extremely high thermal
conductivity near 35 Wm-1K-1, higher than that of most liquid metals. Unfortunately, this alloy
has two rather large draw backs; first, it reacts violently with water and air to the point where it
can cause explosions, and second, it is very corrosive. While it is possible to use this metal
under an inert gas, this is not feasible for use on most commercial computers.
As the list of possible metals thins out, it can be seen that alloys of bismuth and indium have
low melting points, reaching down to 47 degrees Celsius [16]. However, their melting points
are still not low enough to be used as a liquid metal coolant around room temperature.
Lastly, there is gallium, an element that melts at just under human body temperature at around
30 degrees Celsius and has a great thermal conductivity around 33 Wm-1K-1. It also shares with
water the unique property of having a less dense solid phase than liquid phase. Possessing the
largest liquid range of any metal, gallium can alloy with indium and tin to create eutectic
solutions with very low melting points, even reaching -20 degrees Celsius [17]. In addition, it
has an extremely low vapor pressure, essentially zero at room temperature, and the only
significant toxic property it has been associated with is possible skin defatting. The obstacle to
overcome with gallium alloys is their severe corrosiveness to other metals.
2.6 Magnetohydrodynamics
Since liquid metals are electrically conductive fluids, they offer a unique and efficient pumping
solution. Magnetohydrodynamic pumps, also known as magnetofluid dynamic pumps, harness
the Lorentz force, which is exhibited by a charge moving through a magnetic field [18]. This
force depends upon an electrical field that is orthogonal to a magnetic field, which together can
be used to calculate the resulting force, which is orthogonal to both of these fields.
One way to derive the Lorentz force law is from Maxwell’s equations, a set of equations
developed by James Maxwell to explain the relationships between electric fields, magnetic
fields, electric charge, and electric current. In order to understand this relationship, the electric
field strength at a given point must be defined as “the vector limit of the quotient of the force
that a small stationary charge at that point will experience, by virtue of this charge, to the
charge as the charge approaches zero.” [19] In mathematical notation it is written,
,
where
is the electric field and is the force that would be felt by the charge q. However,
because a charged particle in an electric field exerts a force on the charge distribution that is
producing the electric field, the charge distribution is modified so the charged particle is also
modified until the charge on the particle reaches zero. This allows for the removal of the limit,
simplifying the equation:
.
By solving for the force, an equation results:
.
The next equation that should be examined is Faraday’s Law, one of Maxwell’s equations. In
order to inspect this law one needs to look at a continuous surface and a path along it. To
make this easier to visualize, the 3D surface is presented in 2D in figure 6. By using the path,
the surface can be divided into two regions (gray and white in figure 6).
Figure 6: A continuous surface
By setting the direction of the path to be counterclockwise, the mathematical representation of
Faraday's law can be explained as,
,
Or put another way, the sum of the dot product, at every point along this path, of the electric
field vector, , and the differential vector in the direction of the path, d , is equal to the
negative of the speed with which the magnetic flux through the inner surface is changing [20].
This can be somewhat confusing though if flux is not defined. Put simply, it can be thought of
as the number of magnetic field lines passing through a surface (figure 7) and is a measure of
quantity of magnetism. Mathematically it is an integral of the magnetic field vector with
respect to the differential portion of the area vector, which is orthogonal to the surface,
.
Figure 7: Magnetic field passing through a surface
To further derive the Lorentz force we must look at a flux that is varying with time,
.
From the magnetic flux equation, we can see the flux can change if either the magnetic field or
the surface changes. Since the magnetic field will be constant in this project, this will be left
constant. In order to change the number of times a magnetic field line crosses the surface, the
edges of the surface must change because moving the inside up or down will cause any newly
intersecting field lines to intersect the surface twice in opposite directions, thus canceling their
effect, (figure 8).
Figure 8: Magnetic field lines through a surface with the same edges
So to generate a flux with varying time, only the path (edges) must change. This allows the
equation to be turned into a more simple line integral rather than a surface integral,
.
Now since the area vector is pertinent to the derivation, the next investigation is the rate of
change of the area with respect to time. One way to look at this is by looking at parallelograms
equal to the differential vector along the path,
, placed along the path. As smaller and
smaller segments of time are taken
will approach zero and the approximation in
parallelograms will be equal to the change in area. A good way to find the area of a
parallelogram is by taking the cross product of two vectors that make up the shape,
.
This produces a vector orthogonal to both vectors involved. Because the change in area must
be orthogonal to both the velocity vector and the differential vector along the path, the change
in area with respect to time is,
.
Now all that is left is to simplify and substitute with the other equations.
substitute
substitute
rule of a scalar triple product
rule of a cross product
substitute
solved for each point on the path
substitute
sum forces
Now the Lorentz force has been derived, but to solve for forces in the magnetohydrodynamic
pump, one must integrate the Lorentz force on an individual charged particle over a current of
charged particles, resulting in
,
where is the current in amperes, is the length the charges must travel, and
is the magnetic
field, or magnetic flux density.
3.0 Materials
This section will cover the materials that were necessary to construct this project.
3.1 Materials for Prototype
(1) 1520 cm length, 0.64 cm inside diameter, 0.16 cm wall, Tygon® beverage tubing
(1) 0.64 diameter hose "T"
(1) 60 mL bottle of blue ultraviolet dye
(1) 120 mL salt water
(1) 60 mL syringe
(2) 2.5 cm diameter x 1.3 cm length cylindrical grade N50 neodymium-iron-boron permanent
magnets
(1) 122 cm x 2.5 cm x 2.5 cm high density polyethylene rectangular block
(2) 5 cm length x 0.5 cm diameter brass screws
(1) roll Teflon® pipe thread tape
(1) West System G/5 epoxy resin and hardener kit
(1) drill press
(1) 0.8 cm drill bit
(1) 0.5 cm drill bit
(1) screwdriver
(1) jigsaw
(1) pair of scissors
(1) wooden dowel
3.2 Materials for Final Pump
(1) 762 cm length, 0.5 cm inside diameter, 0.25 cm wall, Tygon® laboratory and vacuum tubing
(1) 0.5 cm diameter hose "T"
(1) 200 grams gallium-indium-tin eutectic alloy
(1) 12 mL syring
(1) spinal needle
(2) 2.5 cm diameter x 1.3 cm length cylindrical grade N50 neodymium-iron-boron permanent
magnets
(1) 122 cm x 2.5 cm x 2.5 cm high density polyethylene rectangular block
(2) 0.5 cm diameter x 18 cm length cylindrical pure tungsten Radnor welding electrodes
(1) roll Teflon® pipe thread tape
(1) West System® epoxy resin and hardener kit
(2) 5 cm x 5 cm x cm electrolessly nickel plated copper blocks
(1) tube Arctic Silver® 5 high polysynthetic silver thermal compound
(4) 1 cm length hex machine screws
(4) 0.5 cm diameter hose barb to 0.6 cm diameter male national pipe thread pieces
(1) drill press
(1) 0.5 cm drill bit
(1) 0.8 cm drill bit
(1) 1 cm drill bit
(1) 0.8 cm pipe tap
(1) jigsaw
(1) handheld wood file
(1) wooden dowel
(1) pair of scissors
(1) vice
3.3 Materials for Power Sources
(1) 762 cm gauge 10 insulated copper wire
(1) 12 volt tractor battery with 200 cranking amps
(6) 30 ampere maximum battery clamps
(2) 50 ampere maximum battery clamps
(4) 3 ampere maximum, 44 ohm maximum rheostats
(2) 6.5 ampere maximum, 10 ohm maximum rheostats
(2) 30 ampere maximum electric scooter ammeters
(1) wire cutter
(1) kitchen knife
(8) alligator clips
(1) 6010 cm gauge 14 insulated copper wire
(1) 6 volt Energizer® battery
(1) screwdriver
(1) pair of pliers
3.4 Materials Used in Testing
(2) digital thermometers
(4) Styrofoam® cups
(1) Exacto® knife
(1) gallium-indium-tin eutectic catch basin
(1) 750 watt max variable hot plate
(2) wooden blocks
4.0 Engineering Obstacles
While the theory of the pump design is straightforward, the engineering design and
construction of the pump met some obstacles.
4.1 Corrosion
The most significant problem with utilizing a gallium based alloy as a coolant is the corrosive
nature of most liquid metals. Gallium reacts readily with many metals by diffusing into their
metal lattice. This makes it very hard to find an enclosure that is suitable for both a gallium
based alloy and heat transfer. Numerous studies have been done looking into which metals
can resist the attack by gallium [21], [22], [23], [24].
Unfortunately, most metals that provide high thermal conductivity, such as copper and
aluminum, corrode too fast to be used as an enclosure [17]. There are a few refractory metals
that can resist attacks up to high temperature near 800°C [16]. These may be useful but in the
case of heat transfer they are not economically feasible for a heat exchanger and offer meek
thermal conductivity when compared to copper. The next option that was investigated was
plating the heat exchanging surface with a resistant metal, which would allow the heat
exchanger to be constructed from copper. The corrosion studies found two resistant metals
that could feasibly be plated, nickel and chromium [21], [22]. Chromium appears to be a good
choice at first, but the plating process does not work very well on copper, leaving an uneven
distribution of chromium. Nickel, on the other hand, can undergo electroless plating, which
leaves an even deposit of nickel over the entire surface.
The last material to consider is the tubing the coolant must travel through. Luckily, a corrosion
resistant material is not hard to find due to gallium’s inertness to plastics. High density
polyethylene, polypropylene, general-purpose polystyrene and poly methyl methacrylate show
no corrosion in the presence of liquid gallium [24].
4.2 Safety and Toxicology
The toxicity of galinstan, the specific gallium alloy that was used, is of great importance to this
project. In order to predict and prevent any possible hazards associated with using the liquid
metal, the safety of galinstan was investigated. The galinstan reactions when exposed to air at
20°C produce extremely low levels of gallium, indium, or tin oxide [25]. This study found that
after rats were exposed to high concentrations of gallium oxide, Ga2O3, for a 4-week period,
progressive lung damage was observed. The hazard of gallium oxide provides no threat in the
case of a coolant, as the oxide does not become airborne but instead adheres to the surface of
liquid gallium. Additionally the system would be entirely sealed.
The only other risk associated with liquid gallium, is a possible skin irritation or skin defatting
after long exposures to the metal [26]. Overall, the metal does not pose a significant threat.
Gallium compounds are even used today in nuclear medicine imaging and have been proposed
as a dental amalgam [27].
4.3 Tubing
One potential drawback of using galinstan is its cost. Gallium–indium –tin alloys from Sigma
Aldrich are about $4/g. Galinstan from RG Medical Products (for use in thermometers) is
quoted at about $1/g and some metal alloys firms have been able to sell galinstan for only
$0.25/g [25]. The galinstan for this project was purchased at about $1/g. Even at manageable
prices, the quantity of galinstan was important to conserve in the design of this pump. With
this in mind the selected tubing for the pump was Tygon® R-3603 laboratory and vacuum
tubing with a small inside diameter of 0.5 cm and thick walls of 0.25 cm. The thickness of the
walls aid in retaining the heat while it is being transported to the other heat exchanger; it also
ensures the coolant will not leak if the tubing is cut slightly. This tubing has a maximum
operating temperature of 74°C and is made of chemical resistant PVC materials with
plasticizers, allowing the tubing to transport heated gallium [28].
4.4 Turbulent Flow in Liquid Metals
Among the several advantages of using a liquid metal coolant over a water coolant is the
amount of turbulence necessary. Water’s poor thermal conductivity and high Prandtl number
require a lot of mixing so heat can diffuse into it; therefore water requires a high Reynolds
number. Liquid metals on the other hand have a low Prandtl, high thermal conductivity, and
high thermal diffusivity from free electrons that are not restrained by intermolecular forces
[12]. This allows for lower Reynolds numbers to be used while transferring heat. As would be
expected, liquid metals offer great heat transfer coefficient advantage over water for laminar
flows and low Reynolds number turbulent flows [29].
Since turbulence in a tube generally happens at Reynolds numbers over 2300 [14], the
minimum velocity must be found for the fluid.
,
,
plugging in values
solving for V
Now that a Reynolds number has been determined it is important to find the Prandtl number of
the gallium-indium-tin alloy.
,
,
plugging in values
solving for Pr
Its low value of 0.0208 indicates that for relatively low values of velocity, heat will diffuse
throughout the coolant. Because of this, low Reynolds number turbulent flow will be more
than adequate for complete thermal diffusivity.
Lastly, using the Reynolds number and the Prandtl number, the Nusselt number can be found
for high thermal conductivity fluid in turbulent flow with the Sleicher-Rouse equation.
, Re > 2300, Pr = 0.0208
plugging in values
Solving for Nu
This relatively low value of 6.6281 agrees with the previous prediction of requiring only low
turbulent flow for convective heat transfer and mixing. It also indicates that increasing the
velocity greatly is not necessary to increase heat transfer. This is due to galinstan’s large
thermal boundary layer, allowing heat to diffuse quickly. Water on the other hand requires
much turbulence and mixing to distribute the heat.
4.5 Heat Exchangers
The design of the heat exchangers in this heat transfer pump utilized copper that was plated by
electroless nickel plating. The use of copper made it easier to drill than other metals and easier
to conduct thermal power dissipation. It is an ideal metal for use in heat transfer due to its
reasonable price and high thermal conductivity around 401 Wm-1K-1. Nickel plating did not
impede the thermal conductivity much due its decent thermal conductivity around 90.9
Wm-1K-1 and thin layer.
The position and size of the channels that were drilled into the block (figure 9 pp. 23) were
decided based upon the gallium-indium-tin eutectic coolant. Since not much turbulence was
needed for the coolant, larger channels could be drilled and less severe turns were needed.
The surface area of the channels was increased with several smaller channels placed in the
middle, but due to the high thermal diffusivity of the coolant, it was not necessary to make
abundant microchannels to increase the surface area further. Microchannels would have
added greatly to the cost of the pump. Nevertheless, a few swift turns were incorporated into
the design to improve turbulence slightly.
In order to seal the channels, high polysynthetic silver thermal compound was applied between
channels and a small slate of electrolessly nickel plated copper was screwed to the top. This
improved the contact between pieces of metal and prevented leaks.
Figure 9: The design of the heat exchanger pre and post drilling
4.6 Magnetohydrodynamic Pump
The low resistance that liquid metals show to electricity allow them to be pumped more
efficiently than a peristaltic pump and with no moving parts. As mentioned earlier,
magnetohydrodynamic (MHD) pumps work by conducting a current over a fluid that is within a
magnetic field. Some of the major obstacles with MHD pumps are the high currents and
magnetic fields that must be generated in order to produce a significant force. For the purpose
of this pump, the version of the Lorentz force equation that will be used is,
,
Where is the current, is the length the charges must travel and
is the magnetic field. In
order for the force to be in the desired direction, the magnetic field must be placed orthogonal
to the electric field (figure 10).
Figure 10: The direction of force due to a current in a magnetic field
The magnets used on this pump are two neodymium-iron-boron rare earth magnets of grade
N50. They are cylindrical, measuring 2.5 cm in diameter and 1.25 cm tall and are plated in black
nickel (nickel-copper plating). Their magnetic field at the surface is .6450 tesla ; they are
separated by 1.5 cm so the magnetic field is .5980 tesla. The value of is the diameter of the
tube the pump was contained in, 1 cm or 10-2 m. The component that was easiest to modify
was the current, which operated between 15 and 25 amperes depending on the trial. The
electrodes that supplied this are pure tungsten rods, measuring 0.5 cm in diameter and 18 cm
long. Tungsten was necessary to resist the corrosive properties of gallium while providing low
resistance. With these values, the Lorentz force varied between 0.0897 and 0.1495 newtons.
This force was applied to move 0.174 kg of the gallium-indium-tin coolant in the pump.
Applying Newton’s second law in the form
, the acceleration is
found to be between 0.516 m/s2 and 0.859 m/s2.
The pump is housed in a high density polyethylene block that measures 7.5 cm x 2.5 cm x 2.5
cm and has been drilled and sawed to accommodate the electrodes, tubing and magnets.
4.7 Power Source
The production of large current that is needed to generate force in a magnetohydrodynamic
pump was a large obstacle to overcome. The resistance over the tungsten electrodes and
gallium-indium-tin eutectic is negligible, so the majority of the resistance has to come from
external resistors. Since this project was constructed from obtainable parts in a home
environment, it was easier to use a tractor battery than to find or construct a DC voltage
converter that could provide low enough voltages. The circuit was planned out around this
battery (figure 11).
12 volt DC battery
Rheostat 1
Rheostat 2
Rheostat 3
Tungsten electrode
Rheostat 4
Tungsten electrode
Rheostat 5
Rheostat 6
DC Ammeter
A
Ammeter
Figure 11: Electrical circuit diagram of the power source
With these facts in mind, the appropriate resistance can be determined by Ohm’s law,
,
Where I is the current, V is the voltage, and R is the resistance in the circuit. Using a 12 volt car
battery, 15 amperes of current can be reached with 0.8 ohms of resistance and 25 amperes of
current can be reached with 0.48 ohms of resistance. In order to achieve the necessary
resistance, 6 variable resistors, rheostats, were set up in parallel and a 30 ampere DC ammeter
was added to the circuit to measure current. All wiring for the circuit was done with gauge 10
insulated copper wire.
With the rheostats in parallel, their resistances add such that,
.
The rheostats that were available for use in the project included 4 rheostats with a maximum of
3 amperes current and 44 ohms and 2 rheostats with a maximum of 6.5 amperes current and
10 ohms. In order to find the appropriate settings for the desired resistance, it was assumed
that rheostats with identical properties would be set the same. With this, the equation
becomes,
or
,
Where R1 is the 3 ampere rheostat and R2 is the 6.5 ampere rheostat. The choice of equation
depends on whether the resistance desired is 0.8 ohms or .48 ohms.
The maximum current the rheostat can carry also has to be taken into account and can be
represented with inequalities based on Ohm’s law and each resistors maximum resistance.
and
This allows for a range of acceptable values that will produce 0.8 ohms of resistance with the
appropriate currents across the rheostats. It also reveals the settings for the highest available
current that can safely be used.
15 amperes : 0.8 ohms :
25 amperes : 0.48 ohms :
and
and
With this information the distance the slide on the rheostat must move can be found by
determining how much each setting is of the total resistance available.
4.8 Adhesive Sealant
To ensure that all joints were completely sealed, an adhesive sealant was necessary that could
bond to the high density polyethylene the pump enclosure was made of, the tungsten
electrodes, and the PVC material of the tubing. The sealant used was an epoxy from the West
System, and readily adhered to the electrodes and the tubing. The high density polyethylene
had to be heat treated with a propane torch in order to oxidize the surface [30]. Heat treating
is required in order for a successful bond (figure 12 pp. 28). This allowed the epoxy to adhere
to the polyethylene, completing the seals.
Source: West System® Inc.
Figure 12: Adhesion of West System Epoxy after various treatments
5.0 Procedure
In order test how well the design transferred heat from one exchanger to the other, a test of
the design was conducted. This test measured how quickly the heat was transferred from a
heat exchanger in contact with a heat source to an insulated heat exchanger.
First, a wooden block was positioned next to a hot plate so there would be a level surface
throughout the pump, preventing one point from being higher than any other. The pump was
laid onto this surface so that one of the heat exchangers was completely in contact with the hot
plate. The other heat exchanger was insulated with two Styrofoam® cups that were modified
to seal off the exchanger as greatly as possible. A contact pad from a digital thermometer was
applied to the top surface of each of the heat exchangers. Beneath the entire pump was a
plastic catch basin in the event of a leak.
At this point, the pump’s circuit was completed, the hot plate was turned on to the 250 watt
marking, and a timer was started simultaneously. At the very start and exactly every 20
seconds thereafter, a reading was taken from the two digital thermometers and recorded.
After 20 minutes had passed the test was stopped.
6.0 Data and Results
Tests showed that heat was conducted very rapidly, as the design predicted.
Time
(seconds)
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
520
540
560
580
600
Primary Heat Exchanger
Temperature (°C)
16.9
16.9
16.9
17.0
17.3
18.0
18.5
19.0
19.6
20.0
20.8
21.3
24.1
25.2
25.8
26.3
27.7
29.0
30.1
33.2
33.8
34.3
35.1
35.4
38.1
38.3
39.1
40.0
40.3
41.1
42.2
Secondary Heat Exchanger
Temperature (°C)
16.9
16.9
16.9
16.9
17.0
17.3
17.5
17.9
18.5
18.7
19.6
20.0
21.3
23.5
24.1
24.9
25.6
26.9
28.5
31.3
32.0
32.6
33.4
34.1
36.2
37.1
38.0
39.1
39.3
39.7
40.2
620
640
660
680
700
720
740
760
780
800
820
840
860
880
900
920
940
960
980
1000
1020
1040
1060
1080
1100
1120
1140
1160
1180
1200
42.5
43.1
43.6
44.1
44.3
44.5
44.7
44.8
44.9
44.9
45.0
45.1
45.2
45.4
45.6
45.8
46.0
46.0
46.1
46.1
46.2
46.3
46.4
46.5
46.7
46.7
46.8
46.9
47.0
47.0
40.8
41.3
41.6
42.1
42.3
43.4
43.5
43.7
43.9
44.3
44.5
44.6
44.7
44.9
45.0
45.1
45.3
45.5
45.8
45.9
46.0
46.0
46.1
46.2
46.2
46.3
46.4
46.6
46.8
46.9
Table 2: Temperatures from the first trial of the two heat exchangers after placing one onto a
250 watt heat plate
Time
(seconds)
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
520
540
560
580
600
620
640
660
680
700
720
Primary Heat Exchanger
Temperature (°C)
16.7
16.7
16.7
16.9
17.0
17.3
17.6
17.8
18.1
18.5
18.9
19.1
19.4
21.5
22.3
24.5
26.8
27.8
29.3
31.4
32.8
33.9
34.5
36.8
37.4
37.7
38.2
39.2
40.1
40.6
41.2
41.5
42.1
43.8
44.0
44.1
44.2
Secondary Heat Exchanger
Temperature (°C)
16.7
16.7
16.7
16.7
16.7
16.7
16.9
17.1
17.5
17.7
17.9
18.1
18.4
18.9
19.1
19.5
20.1
21.5
23.1
25.9
27.6
29.4
30.2
31.6
33.0
33.5
34.0
34.6
36.2
38.0
38.9
39.2
39.5
39.9
40.4
41.3
42.1
740
760
780
800
820
840
860
880
900
920
940
960
980
1000
1020
1040
1060
1080
1100
1120
1140
1160
1180
1200
44.4
44.6
44.7
44.8
44.9
44.9
45.1
45.1
45.3
45.4
45.6
45.8
46.0
46.1
46.1
46.1
46.2
46.2
46.3
46.5
46.7
46.8
46.8
46.9
43.3
44.2
44.3
44.4
44.5
44.7
44.8
45.1
45.2
45.3
45.4
45.6
45.8
46.0
46.1
46.1
46.1
46.2
46.2
46.3
46.4
46.6
46.7
46.8
Table 3: Temperatures from the second trial of the two heat exchangers after placing one onto
a 250 watt heat plate
Time
(seconds)
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
520
540
560
580
600
620
640
660
680
700
720
740
Primary Heat Exchanger
Temperature (°C)
16.9
16.9
16.9
16.9
16.9
16.9
16.9
16.9
16.9
16.9
16.9
17.0
17.0
17.0
17.0
17.0
16.9
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.1
17.1
17.1
17.1
17.1
17.1
Secondary Heat Exchanger
Temperature (°C)
16.9
16.9
16.9
16.9
16.9
16.9
16.9
17.0
17.0
16.9
16.9
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.1
17.0
17.0
17.0
17.0
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
760
780
800
820
840
860
880
900
920
940
960
980
1000
1020
1040
1060
1080
1100
1120
1140
1160
1180
1200
17.1
17.0
17.0
17.0
17.0
17.0
17.1
17.1
17.1
17.1
17.1
17.1
17.0
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.0
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.1
17.0
17.1
17.1
17.1
Table 4: Temperatures from the control trial of the two heat exchangers after turning on the
power source
Time
(seconds)
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
520
540
560
580
600
620
640
660
680
700
720
740
Primary Heat Exchanger
Temperature (°C)
16.8
16.8
16.8
16.9
17.0
17.3
17.8
18.2
18.6
19.1
19.5
20.0
20.4
22.8
23.8
25.2
26.6
27.8
29.2
30.8
33.0
33.9
34.4
36.0
36.4
37.9
38.3
39.2
40.1
40.5
41.2
41.9
42.3
43.5
43.8
44.1
44.3
44.5
Secondary Heat Exchanger
Temperature (°C)
16.8
16.8
16.8
16.8
16.8
16.9
17.1
17.3
17.7
18.1
18.3
18.9
19.2
20.1
21.3
21.8
22.5
23.6
25.0
27.2
29.5
30.7
31.4
32.5
33.6
34.9
35.6
36.3
37.7
38.7
39.3
39.7
40.2
40.6
41.0
41.7
42.2
43.4
760
780
800
820
840
860
880
900
920
940
960
980
1000
1020
1040
1060
1080
1100
1120
1140
1160
1180
1200
44.7
44.8
44.9
44.9
45.0
45.1
45.2
45.4
45.5
45.7
45.9
46.0
46.1
46.1
46.2
46.3
46.3
46.4
46.6
46.7
46.8
46.9
47.0
Table 5: Average of the heat transfer trials
43.9
44.0
44.2
44.4
44.6
44.7
44.9
45.1
45.2
45.3
45.5
45.7
45.9
46.0
46.1
46.1
46.2
46.2
46.3
46.4
46.5
46.7
46.8
Figure 13: Graph representation of the average of the trials
7.0 Conclusion and Recommendations
After analyzing the collected data, it is apparent that the designed system is capable of
transferring heat at a very quick rate. As figure 13 displays, the secondary heat exchanger’s
temperature was less than a minute behind the primary heat exchanger’s temperature in the
worst cases. This excellent conductivity of heat throughout the pump further demonstrates the
power that liquid metal cooling can offer.
Liquid metal cooling is the ideal cooling innovation for high performance computing. The
superior thermal and physical properties of a gallium-indium-tin eutectic coolant lead to an
extreme increase in heat transfer within a cooling pump. Among the several advantages are
very high heat transfer rates, a completely closed system, no moving parts, no generated
sound, and a very high boiling point that allows very hot sources to be cooled. One of the
obstacles that needs to be addressed is the economic feasibility of using a gallium based
coolant. The good news is that by using a liquid metal as a coolant, the need to manufacture
expensive microchannels and powerful peristaltic pumps is avoided. In addition, the
employment of a large scale production of this alloy would lower the cost of this substance.
Future advancement that could be made on this project includes the implementation of
thermoelectric cooling. This type of cooling takes advantage of the Peltier effect, which is
characterized by the creation of a heat difference from an electric voltage. From a project point
of view, further study should be done to test a liquid metal cooling system on various
microprocessors. This test would require an additional passive cooling heat sink, shrinking the
size of the pump, and a yoke to shield the magnets.
The engineering goal of this project was successfully met with the thermally efficient design of
the pump. The gallium-indium-tin eutectic coolant displayed outstanding heat transfer
capabilities when tested.
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