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Liquid Metal Cooling |
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| Home page......: | Frigus Primore |
| Learn more......: | Thermal Design for Electronics |
Introduction
High heat flux cooling is currently attracting an intense interest. Several methods have been suggested. They all perform well from a pure thermal point of view but there are also many other aspects to consider. All methods have advantages and disadvantages. The problem is that some of the latter does not appear until a method actually has been implemented. It is therefore difficult to predict which methods that will be used tomorrow.
This article is about one particular method that rarely has been addressed, liquid metal cooling. It is certainly a powerful cooling method but the list of associated problems can be made long. There are nevertheless also some attractive advantages: the ability to cool high heat fluxes and the possibility to use pumps without moving parts. The ambition here is not to present a ready to use solution but rather to surface some basic properties.
| Metal |
Melting point [C] |
Density [kg/m3] |
Spec heat [J/kgK] |
Cond [W/mK] |
Viscosity [kg/ms] |
| Bi-alloys | 47--271 | 9800 | 142 | 8.4 | ? |
| Ga | 30 | 5900 | 334 | 33 | 2.04e-3 |
| Hg | -39 | 13546 | 140 | 8.4 | 0.15e-3 |
| H2O | 0 | 1000 | 4184 | 0.6 | 0.86e-3 |
| NaK (22/78 %) | -12 | 892 | 1058 | 35 | 0.94e-3 |
Approximate thermal properties for liquid metals. Water is included for comparison.
Candidates
Table 1 shows approximate properties for some liquid metal candidates. The viscosity is given at room temperature. Water is included for comparisons.
Pure Bismuth, (Bi), melts at 271 C but some of it alloys have considerable lower melting points. Woods metal is probably the most well known, (melts at 70 C). By alloying with metals such as led, tin, cadmium and indium it is possible to get even lower, 47 C seems to be the limit. Such alloys could potentially be advantageous but they do have the disadvantage of high melting points.
Pure gallium, (Ga), melts at 30 C but several of its alloys have much lower melting points. The main drawback is its aggressiveness towards almost all other metals. All gallium alloys must therefore be enclosed within ceramic walls, which seems difficult to realise.
Mercury, (Hg), has very attractive thermal properties. It has even been suggested as working fluid for power generating purposes. It can unfortunately not be used for environmental reasons.
The best candidate seems to be an eutectic solution of sodium and potassium, (NaK). The melting point is as low as -12 C. Its density and viscosity are similar to water but it has a lower specific heat and a much higher thermal conductivity. NaK can be used with nickel, chrome and steel but it is aggressive to cadmium, antimony, bismuth, copper, lead, silicon, tin, and magnesium. It also reacts violently with air and water. It is apparent that this alloy is associated with several material and handling problems. Liquid sodium has nevertheless been used as a coolant for nuclear reactors, which shows that these drawbacks can be managed.
Figure 1
Principle difference between water and liquid metal heat transfer.
Thermal performance
The heat transfer properties for liquid metals are relatively well known. The correlations found in the literature have the same non-dimensional structure as for any other fluid. The only difference is the formulation, (constant values etc).
Liquid metals conduct heat much better than water. The temperature difference needed to push heat from the walls into more central parts of a flow channel is therefore small. Compared with water they do however have smaller specific heats. The temperature increase in a liquid metal flow is therefore, for comparable conditions, larger than for water. Figure 1 shows this fundamental difference.
Figure 2
Assumed arrangement.
There are numerous ways to compare cooling properties for liquids. None is fully exhaustive. The particular arrangement used here is flow in a gap between two small plates, (10x10 mm), of which one is heated, figure 2. It has a reasonable resemblance with a real word hot spot problem. The results should therefore be a good indicator of what is possible to achieve. In this context it should also be underlined that the purpose of this article not is to present accurate numbers but to indicate levels of performance.
The comparisons that follow show the how various parameters of interest vary with the heat load. Fully developed flow was assumed. It is a conservative assumption. The actual heat transfer coefficients could be 10% - 50% higher. Since the temperature difference mainly is caused by the temperature increase of the fluid and not by the heat transfer coefficient, this will in no case change the general conclusions.
Figure 3
Pumping power as function of the heat load for a temperature difference of 10 K.
Figure 3 shows the pumping power as function of the heat load for a temperature difference of 10 K. Water flowing in a 1 mm gap is included for comparison. It is interesting to note that NaK performs several magnitudes better than water. Another interesting result is that heat fluxes as high as 200 W/cm2 are possible even for a very small input of pumping power, 0.02 %! It is evident that NaK cooling in this aspect competes very well with other high performance methods.
Figure 4
Pressure losses as function of the heat load.
Figure 4 shows the pressure loss as function of the heat load. 1000 Pa equals 100 mm H2O, (4 inc). It is a modest value for liquid flow. Even simple pumps can do a factor 10 better.
Figure 5
Velocity as function of the heat load.
Figure 5 shows the velocity as function of the heat load. For 200 W/cm2 heat flux NaK flowing in a 1 mm gap would require 3.5 m/s. It is slightly higher than typical velocities for water in a radiator heating system but by no means alarming.
Figure 6
Liquid temperature increase as function of the heat load.
Figure 6 shows the liquid temperature increase. It can be noted that the temperature increase for the smallest gap, 0.5 mm, is almost the same as the inlet temperature difference, (10 K). For 200 W/cm2 and 2 mm gap it is 3 K. The outlet temperature difference is in that case 7C, which could indicate that it could be advantageous to use fins. They would however need to be so thick that it is improbable that any radical gains can be made.
Figure 7
Principle function of a MHD pump.
MHD pumps
Metal liquids of the Nak type oxidise very fast in contact with air. The oxide created can in addition initiate crystal growth on the heat transfer surfaces. Any pump in a NaK cooling system must therefore be absolutely hermetic. Rotating pumps, sealed with inert gas, have been used for nuclear reactor cooling but they are hardly realistic in this context. There are also hermetic pumps with magnetically driven rotors and they could very well be used. Another and more exiting possibility is to use MHD, (magneto-hydro-dynamic), pumps.
MHD pumps function much as electrical motors. The physical principle exploited is that an electrical current placed in a magnetic field results in a force, figure 7. A pump that works in this way is very simple. All that is needed are a couple of electrodes and a magnet. MHD pumps have been used for all kinds of purposes including liquid metal cooling. The scale has in most cases been much larger than what is needed for 200 W cooling but smaller pumps have also been designed.
Figure 3 indicates that 200 W can be cooled from a 10x10 mm surface for an input of 35 mW pumping power. The pumping power for an entire system is of coarse higher. A factor 5 could be realistic. The efficiency of small MHD pumps is of the order 10%. This coarse estimation therefore indicates that the electrical power feed to a MHD pump in a 200 W cooling system would be on the 2 W level. It is 1 % of the heat absorbed, which indeed is a favourable value.