Plans A1/A2, Plan B, & Plan C Details

A project log for Mac mini 2018 Hexa Core Cooling Analysis

Aiding the stock cooling of the CPU in a 2018 Mac mini

Michael O'BrienMichael O'Brien 01/19/2019 at 09:200 Comments

As I've been working on the project, I've been able to figure out what needs to be done and what I can do in order to try and achieve it. As such, I've been developing backup plans concurrently to each other. What I'll be discussing here is the figurative fleshing out of the said ideas and bringing up the rationalization of that has cause me to pump over to the "next level" of cooling, thus the next plan. Most of what I've already written thus far is regarding Plan A. What I'd like to achieve is a solution that fits inside the mini if at all possible.

Note: I'm not providing many links in this log right now due to the WIP-state a lot of the research I'm conducting. With whichever plan(s) I execute, I will have full documentation.

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Plan A1/A2

Shush, it's in the title... Recap though. There are 2 heat pipes in the current solution provided by Apple. I'm betting on them being the limiting factor in cooling this SFF (small form factor) computer. There are a variety of combinations of aftermarket heat pipes that can move greater power away from the CPU. Similarly, the cold plate would need to redesigned, a little, to accommodate for this change. A common method of increasing surface area if that of creating louvers. Now why do I want more surface area?

There are 2 problems when dealing with the heat coming from the i7-8700B. The first is removing it from the die in totality and then dissipating it by the fins. The other is spreading it away from the die reducing the effective heat flux so that the cold plate can do its job better. In conjunction with a sandwich plate, placing a piece of PGS film between the die and cold plate can achieve this. The current power density (heat flux) for the ~120 W peak, ~81 W sustained, over the 149.6 mm^2 die area is ~54-80 W/cm^2. With that PGS film, that can go down to ~10.2% of what it currently is. The 2 versions of this plan deal with figuring out if I want a louvered or sandwich plate.

Plan B

The problem with heat pipes is that the long they get, the less power they can transmit. Currently, My best case scenario gets my Qmax up from an estimated 60 W to ~107 W. I mean, when on burst workloads, the solution already helps and does a kinda okay job with thermals not spiking after you pt on better paste, but a 78% increase in capacity might not get me as far as I need. I'm looking for a max operating temperature of 85 °C in a 35 °C environment, which means I need to drop the overall absolute thermal resistance of the cooling solution to a little less than half of what is currently is. The math isn't quite there.

If though, I use 2 shorter heat pipes, like a particular 8 mm pair I'm spying, then I have the capacity of removing ~150 W right off the bat, but they are only 100 mm long. I'd make a junction piece of copper to terminate them with and then use 2-3 other heat pipes coming off the fin stack and mating with that pair in the block. The junction block would allow for direct contact, but also greater contact area and thus lower resistance to transfer the heat to the fin stack.

However, there is a clearance problem, or more specifically, 3 of them that make this a daunting task.

Larger heat pipes means larger bend radii. It's a SFF computer so something has to give and though the speaker is crappy, I don't intend on removing anything just yet.

Anyhow, deciding which Plan A to use and if I'll double down and produce an extra set of parts doubling my cost on Plan B is dependant upon one factor I mentioned before: thermal resistance.

Now I won't talk about it much here because I have a log file that is forthcoming that deals with this topic explicitly but to reiterate, I'm attempting to double the performance of Apple's cooling solution. Granted, 85 °C is definitely not ideal, but it certainly is acceptable. If I cannot find sufficient information to support that modifications to the air cooling setup will net at least a 2x increase, I will have to ditch them. If the math is supportive enough but practical human implementation without specialized manufacturing equipment doesn't produced acceptable results, I will ditch them.

Plan C

Exotic cooling. A category that hardly a soul touches. The simple end is water cooling, which is no longer niche. Next up you might chill your water. Then maybe dry ice. To top it off, liquid nitrogen. All of these have inherent drawbacks aside from some of them not being practical for a daily driver computer. One such item that very few people have toyed with but might actually be perfect for this application is liquid cooling, but at 0.6 W / (m * K), water isn't high on my list as a coolant.

Even still, I'm confident that there if I go with liquid cooling, this is still a feasible task. I don't possess the time to establish low count contacts to have special parts machined, but I'm away that metal foams exist. Instead of dealing with having micro-fins, micro-channels, or micro-posts machined into a low-profile, direct die water block, I can solder copper foam to a plate with an o-ring and bolt it all together. Restrictive, yes, but I have only one thing in the loop! Looking around at radiators, it is apparent that a good, all copper, single 120 mm radiator can dissipate more than 100 W of heat with a 10 °C delta in water temps.

Why am I considering this? Well, this mini will be paired next to a 2012 quad core and both will be mounted underneath a shelf. This shelf is being modified to have 2, 120 mm fans circulate air and their RPM will be directly controlled by its neighboring mini. The internal fan connectors are Molex's Pico-EZMate and you can pickup pre-crimped wire from Mouser along with SMD board connectors and female wire housings. I digress. On to of the shelf will be a collection of 2.5" and 3.5" drives in HDD and SSD flavors. Behind them will be enough room to squeeze in a small pump. The only fabrication problem I have as a result of this Plan is that I need to physically modify the fin stack to allow tubing to enter and exit the case. Now about that coolant...

Plan C's Coolant

Stop. I know all about Aluminum and Gallium, and it's alloys. Just read the rest will ya? Anyhow, gallium-based liquid metal alloys have been explored for their potential for cooling. The trademarked Galinstan isn't specifically on the table for use and when you drop that capitalization, "galinstan" references nearly all alloys that come from the ternary mix of gallium, indium, and tin.

Most who have dealt with higher end cooling are familiar with 3 common liquid metal products, Conductonaut being the most recognizable to some, that are all in this family. The thing is, not even their datasheets give much information as to the specific ratios used for the mix. Additional reading indicates doping with antimony as an antioxidant, bismuth to reduce viscosity, and zinc reduces the melting point. Despite the common "16.5 W / (m * K)" claim to Galinstan, it actually ranges from ~22-35 W / (m * K) on the usable temperatures for computer CPU cooling. What has always bugged me is that Thermal Grizzly claims a melting point near 8 °C and a thermal conductivity of ~73 W / (m * K) or more than double that of any public data I can find on galinstan. Additionally, to make your own, you need gallium, which can be a tad expensive for how much you get, to which ~60% of your traditional liquid metal would consist of this.

But, I found 2 research documents that claim a 30-10-60 (% by weight), Gallium-Indium-Tin mix is still eutectic and has a melting point of 12 °C. That's half the Gallium or less of every other mix I've seen. Optimizing for buying the metals for the least dollar-per-gram cost, I can reportedly pick up all of the needed metals for ~$170 and will be able to produce ~98 ml of liquid metal. Compare that to Conductonaut at $15/gram, this works out to $0.27/gram.

Now, anyone who is more familiar with chemistry than me, I'm aware of a big caveat that I need to test. According to the ternary phase diagram for GaInSn alloys, nearly any reduction in Gallium increases the melting point well beyond 30 °C. The problem though is that eGaIn, which is a 75-25-0 mix, has a melting point of 16 °C, but in fact shouldn't be a liquid at that temp according to the binary phase plot. GaInSn in a 62-25-13 mix has a melting point of 5 °C. GaInSnZn in a 71-15-13-1 mix has a melting point of 3 °C. and just 4% by weight of 67-29-4 of GaInZn melts at 13 °C. There are others too, but it appears that that 1-5% of zinc by weight can alter the crystalline structures heavily. Moreover, with more tin in the 30-10-60 mix, the thermal conductivity has got to be higher, or so I assume. Add up to 3-5% by weight of a couple other metals and if the alloy behaves, I couldn't be happier.

But Pumps! Flow Rates!

Water  vs galinstan alloys:

WaterGalinstan-like alloysUnits
Density1.0~6.4gram / ml
Thermal Conductivity~0.6~24-35 (73 tops?)W / (m * K)
Specific Heat4183~296J / (kg * K)
Absolute Viscosity1.02.4cP

Yeah, so??? Even if you pick a middle ground thermal conductivity of 30 W / (m * K), these alloys have about 5x the thermal conductivity of water and they are 6 times denser. If you account for the specific heat and take in account density, 1 ml of water will accept 41.83 J / ml for a 10 °C temperature increase and galinstan alloys will be about 18.94 J / ml. Heat transfer happens better when there is a greater temperature delta and this is achieved. Thermal conductivity is 30x better which means that you need 1/30th the fluid to conduct the same amount of heat from the system. It also means you don't need a massive flow rate to achieve the same cooling performance. It also means you don't need complicated geometry and flow patterns to maximize the surface area to achieve the same cooling performance. You just need a lot less of it and it doesn't need any maintenance except for the occasional hose swap in the pump. Pump?

There are a few options that can be had. If there were enough room, I'd try for a magnetohydrodynamic pump, of MHP. Using a TEC, apparently these can be pretty low on power consumption. I don't have enough space for a 200 W TEC though. I could go for a water lubricated D5 of DDC pump, but I don't know what the life of that ceramic bearing would be, nor do I have an lubricity data on galistan. There is some friction research out there, but I doubt the properties are comparable. Next up, peristaltic pumps. If you've used a mix-you-own drink from a specific soft drink company, you've used a peristaltic pump. They are non-contact with the fluid involved and the pump heads can be separate from the motors. Even better still is that the motors are commonly stepper motors, which can be practically silent.

Heat Pickup & Radiation

Just one, $50 copper tube, brass & steel in the end caps, 1x 120 mm fan, 30 mm thick, radiator is all that I'll need. A single one can easily dissipate the heat I need when dealing with a water setup so I expect it to perform even better with a better coolant on board.

The pump I'm currently eying claims up to 240 ml/min whereas a detailed research document got a 61 °C heating element temperature with a 73 W load at 14 ml/min with a simple 'U' copper tube between about 6 mm in diameter (not stated). Copper foam soldered to a plate, with a variable fan and pump speeds based on the fan speed signal given off by the mini should net a pleasing result.

Yeah, I put a lot of thought into Plan C. Last thing I need is an electrically conductive coolant spraying everywhere inside the computer. Thankfully, in the normal orientation, gravity is away from the motherboard. I really want the elegance of Plan A1/A2 to work. Initial math tells me that I need to beef it up a lot which is where Plan B came to mind. I definitely need to model more obstructions in the case to have Plan B work, which is more technically complex than Plan C.

Stay tuned on my Thermal Resistance log. I won't be going into CFD analysis and getting 2D & 3D dispersion graphics, but I have been able to work the math and make sense of 1D data for a variety of TIMs, not thermal greases, but even how metals behave in order to explain very clearly why very specific things happen.