Maximizing Heat Dissipation for a Stainless Steel Block in Contact with Air

[Glenn Alexander]

I am having trouble finding a general answer for this - search engine throws up lots of specific cases that don't quite match my needs. It is probably pretty basic but IANAE!

I have a polished bare metal stainless steel block with 100 square cm surface in contact with air at a maintained temperature of 25 degrees C. No forced-air-flow, but pleney of convection space.

How many watts of energy can I continuously pump into it to not have the block go above 50 degrees C?

 

[billy_joule]

This is a typical homework question for heat transfer courses, see the forum rules for homework.

https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

 

[Glenn Alexander]

This is a typical homework question for heat transfer courses, see the forum rules for homework.

https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

Fine. But I am not doing homework. I am wanting to embedd a CPU in a solid block of SS and want to know what TDP CPU I can get away with.

(If it sounds like a homework question, blame it on my former life as a primary school teacher!)

 

[berkeman]

Can you post a sketch of the setup, and list the differential equations you are wanting to solve? Do you have a numerical solver avaliable? (ANSYS, etc.)

 

[Glenn Alexander]

I am basically machining a cavity into a 168mm diameter, 21mm height stainless steel cylinder to hold a small board (possibly an intel NUC, or if that is too hot, an O-droid-UX, or an upcoming 300W AMD APU in dreamland :-) ). The top and the bottom of the disk will not be in contact with air (sandwitched between insulators from metal disks above and below with their own heat disapation needs), so only the edge (Pi x 16.8 x 2.1 = 110.7 sq cm -> round to 100 sq cm good enough for my purposes). The board and all components will be enclosed in this disk and the edge surface is the only one intended to disapate heat.

The outline for my project is at http://glenalec.net/ice/

I have no idea about things such as differential equations or numerical solvers, hence me annoying the board :-)

 

[Chestermiller]

This is a natural convection problem. What is the shape of your block, and what is its orientation relative to the vertical? There is certainly correlation in the literature for natural convection from a sphere. There may be correlations for other shapes as well. As long as there is lots of free space around your object (both above and below) with not much disruption of the natural convection air flow, you may be able to use these. Please tell us more.

Chet

 

[Glenn Alexander]

This is a natural convection problem. What is the shape of your block, and what is its orientation relative to the vertical? There is certainly correlation in the literature for natural convection from a sphere. There may be correlations for other shapes as well. As long as there is lots of free space around your object (both above and below) with not much disruption of the natural convection air flow, you may be able to use these. Please tell us more.

Chet

The air-facing surface is vertical. No obstructions above, below or before the surface for at least a few decimetres. (It is a silce from the middle a larger cylinder - the other parts of the cylinder can be considered thermally isolated (they won't be, but I want to treat this as if they were - those slices will have their own heat to disapate, though this slice will likely be the most intense)). Top diagram at http://glenalec.net/ice/

 

[Glenn Alexander]

I am happy to assume that the ambient air is able to refresh itself adequately to remain at 25degC. I am leaving myself quite a bit of leeway setting my target block temp at 50degC anyway. No reason to be overly precise - I just don't want to melt the CPU after an hour of flat-out operation (or burn myself on the enclosure!). Thanx!

 

[Chestermiller]

Would you be comfortable assuming that the rate of heat generation takes place uniformly inside the cylinder? Is the material within the cylinder pretty conductive, and is it pretty much packed, without much void (air) space? If you had to model the cylinder as a solid material, what material would you feel would best represent it? You don't have very much of a surface to volume ratio to cool the system.

What I'm envisioning is modeling the cylinder is a conductive solid with heat generation within. This is about the best you can possibly do, so it is a best bounding case. For a typical heat generation rate, we can see what the temperature of this would be. If it comes out higher than 50 C, your setup is not going to work. Does such an approach work for you?

Chet

 

[Glenn Alexander]

Would you be comfortable assuming that the rate of heat generation takes place uniformly inside the cylinder? Is the material within the cylinder pretty conductive, and is it pretty much packed, without much void (air) space? If you had to model the cylinder as a solid material, what material would you feel would best represent it? You don't have very much of a surface to volume ratio to cool the system.

What I'm envisioning is modeling the cylinder is a conductive solid with heat generation within. This is about the best you can possibly do, so it is a best bounding case. For a typical heat generation rate, we can see what the temperature of this would be. If it comes out higher than 50 C, your setup is not going to work. Does such an approach work for you?

Chet

Thanks, that sounds exactly like what I am looking for - just a rough idea of if my idea is even feasable.

- An assumption of uniform heat generation in the cylinder is fine. I can install short center-to-edge heat-pipes to improve internal-to-external heat transfer too if needed.
- The Cylinder is 431-grade stainless steel so reasonable heat conduction (my eventual target is copper-tungsten alloy, but at $1000 per plate, machined, I won't be even thinking about that until I have everyithing just right in SS)
- Some far-too-rough experimental estimates based on power-vs-temperature-vs-surface-area of my soldering iron has me coming in at around 1.5degC per watt with a total power envelope per plate of around 16W. That is in tablet-class-cpu range, if correct, so barely possible. Once I have a real figure I can look at other options such as extra solid-metal plates above and below high-power plates too.

 

[Glenn Alexander]

I worked it out, I think. The problem was simply I didn't know the formal technical term for what I wanted to know. Once I learned it was 'Emissivity' a quick websearch for this value for common items (such as unpolished - or deliberately micro-roughened - SS) and a Stefan Boltzmann Law web-calculator did the rest.

The answer I have is about 8W per plate edge, which is, as I was warned to expect above, quite low. But it gives me something to start with and from here I can think about things like:

1. Accept the low power envelope and use a mobile-phone/tablet CPU (and greatly de-rate my power supply and gain a ludicrously huge runtime from the supercapacitor UPS - which was origionally intended to provide just enough power for a clean auto-hybernate in a power-fail situation).
2. Increase the surface area by making the plates larger (no tungsten-copper alloy later, then. I am already pushing my budget on that one).
3. Increase the surface area by cutting fins into the machined block that forms the chasis (ruining my desired look!).
4. Increase the surface area by adding 'blanks' extra plates with no heat source in them.
5. Add powered cooling plates (ie a plate with a fan and vents) and put up with the noise and having to clean dust out of them periodically.

I am looking at a combination of 1 and 4 for now. Maybe also a bit of #5 as long as the fans can run down at night when the thing is in server-only-mode - the thing will be in my bedroom and I like silence.

 

[billy_joule]

Emissivity applies only to radiative heat loss, I would bet most of your heat loss will be through convective heat transfer.
Hold your hand above and below your hot soldering iron, below is just radiation, above is radiation plus convection. You should notice convective heat transfer swamps radiative.
Surely the chip manufacturer has comprehensive guidelines on cooling requirements? Have you checked datasheets? Have you looked at cooling systems in laptops without fans?

 

[Glenn Alexander]

Emissivity applies only to radiative heat loss, I would bet most of your heat loss will be through convective heat transfer.
Hold your hand above and below your hot soldering iron, below is just radiation, above is radiation plus convection. You should notice convective heat transfer swamps radiative.
Surely the chip manufacturer has comprehensive guidelines on cooling requirements? Have you checked datasheets? Have you looked at cooling systems in laptops without fans?

I know exactly what heat output is generated by every potential chip. I am not building a system anything like what is commercially available (if it was commercially available I would go out and buy it!)

In the abscence of any other information, I have to cludge whatever data I can get together my-inexpert-self.

If someone wants to tell me the convective transfer in watts per cm2 of dull stainless steel to air (assuming abient temp 300degK, metal temp 350degK, a vertical interface surface and sea-level atmospheric density), I will more than happily factor that in.

I don't need (or want) someone to work the whole project out for me. I just need a few rough-but-realistic numbers to use to work out things for myself. If I am out by 5 or 10 watts, no matter - I can adjust the clocking on the CPU. If I am out by 50W, however I will have used entirely the wrong class of CPU.

 

[Glenn Alexander]

Overall Heat Transfer Coefficient seems to be the next bit of the puzzle. I'm only getting an extra 3W for that, which is nice, but not that significant.

Total is now about 11W per plate accounting for OHTC and Radiation. I'll call it 10W for my purposes.

 

[billy_joule]

I know exactly what heat output is generated by every potential chip. I am not building a system anything like what is commercially available (if it was commercially available I would go out and buy it!)

Power output is only half the story, heat transfer is driven by temperature difference, you need to know that difference. You need temperatures - From the data sheets.

There are a huge range of commercially available heat sinks, they are widely used in many industries. 'CPU heatsink' nets 1.6 million google results. They may not look like your design (probably for good reason...) but they are doing the same job - transfer energy from a chip to the atmosphere.

Have you thought about thermosyphon or heat pipe systems? They are available commercially or could be made relatively easily. They are silent.

 

[Glenn Alexander]

No no and NO. This does not even try to answer the question I am posing. I origonally phrased my question in generalised textbook terms (which got me shouted at) to avoid just this sort of tangent-shooting faffing about. I want an answer to a particular question: how many watts can I put into my metal block without the temparature at the edge exceeding 350degK in ambient air at 300degK. (All of these numbers are mentioned before in the thread).

That is all I want to know. Everything else is out of scope. How I move heat around within the metal block is an entirely different problem, one I am far more able to work out for myself. It is the metal-air interface that has me stumped and hence what I am asking about.

All further responses that don't address the actual question asked will be ignored. Sorry, I am getting really frustrated here! I realize as a non-engineer I am not asking the question in the most optimal way, but this seems just a little too much! It is like if an engineer came to me asking what shell command to use to achieve a particular OS function and I insisted on teaching him to program in PERL. End rant.

 

[billy_joule]

Here is an intro to convective heat transfer:
http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html

Note that:

Typical convective heat transfer coefficient for some common fluids:

• Free Convection - air, gases and dry vapors : 0.5 - 1000 (W/(m2K))

A rather large range, to find the value for your problem, you'll need some of these:

http://en.wikipedia.org/wiki/Rayleigh_number
http://en.wikipedia.org/wiki/Grashof_number
http://en.wikipedia.org/wiki/Prandtl_number

I thoroughly recommend this book for learning heat transfer for engineering.
https://www.amazon.com/dp/0077366646/?tag=pfamazon01-20

It is like if an engineer came to me asking what shell command to use to achieve a particular OS function and I insisted on teaching him to program in PERL. End rant.

The problem is that from an engineering design perspective what you're doing doesn't make much sense. You're designing a computer around a heat sink. It's like designing a car around a radiator (Or a hub cap...) - it raises a big flag to an engineer which is hard to move past.

 

[Chestermiller]

Bird, Stewart, and Lightfoot, Transport Phenomena give some typical values for heat transfer coefficients in various situations for gases:

Free convection: 3 - 20 w/m²-hr-C
Force convection: 10 - 100 w/m²-hr-C

Assume as a best case that the resistance to heat transfer within your cylinder is zero, so that all the heat transfer resistance resides in the air boundary layer. For the heat generation rate you anticipate, see what surface temperature would be required. This should get you into the ballpark.

Chet

 

[Glenn Alexander]

Thanks Billy. Designing to the heatsink was not my original intent but as I have set particular physical constraints and forms on my design, heat management has turned out to be the dominant factor, so I am having to limit everything else to that factor.

I will look into the resources suggested with gratitude. Despite my (I'm sure, self-inflicted) frustration, I have learned a lot from what has been mentoned here.