PC Physics: How does cooling even work

[ChalkChalkson]

What is this thread about?

I am attempting to write up a little post here that conveys the physics of how the most common (ok, and maybe not so common) methods of PC cooling. If you are only interested in the stuff you need to pick the right coolers, you can skip to the respective paragraph. I am going to start basically from 0 with the physics, since I am specifically writing this for people holding common misconceptions like adding more coolers could get you below ambient or get the room temperature down.

 

What is heat?

Ok, first up, we need an idea of what heat is, and how heat travels. Heat is really nothing more than some type of energy (in equations I will write E) held in a material, so we use the unit J (Joules) for the amount of heat stored in an object. "But what about °C/°F/K ?" I hear you ask. Well, this is of course also quite important, the temperature (T) gives us a measure in which direction energy likes to flow. If you have a glass of water at 50°C there is a lot more energy in it than in the same volume of aluminium foil, even at 60°C. However energy will flow from the foil into the glass of water when you bring them together.

For convenience sake I also want to add, that energy divided by time is power (P) with the unit W.

TLDR; Energy travels, not temperature.

 

How does energy travel?

There are 3 main ways how heat energy travels from one place to another:

• Conduction
  Is the easiest to describe. It describes how heat travels through a solid object like a steel rod. Using this you can describe how the heat gets out of the CPU die, into the thermal paste, through the IHS, though the thermal paste and into the CPU cooler. How good heat travels depends on the difference in temperature, the area through which the heat travels and the material. Let us know think a slice of material with thickness d, where the two large faces have the temperatures T1 and T2 and have area A. Then the amount of energy dE that moves from one face of the slice to the other in time dt is:
  dE=C*A/d * dt * (T1-T2)    
  where C is a constant describing how well heat travels through a material. This constant is called thermal conductivity and has the units W/mK (Watts per meter Kelvin) and is the same as W/m°C
  we can also rewrite the equation slightly and get
  P=C*A/d
• Radiation
  Is pretty hard to describe with equations, luckily it is so super weak, that unless none of the other ways can happen, one can pretty much ignore the contribution of radiation
• Convection
  This is the most tricky one. The idea is the following, if you have a bag of marbles and the bottom few are 100°C, then you can make heat travel through the bag by just picking these marbles up and putting them somewhere else. The equations regarding this depend greatly on the specifics of the situation, I will go into more detail regarding air/water cooling in the respective paragraphs.

 

 

Ok, but what temperature is my CPU actually at?

 

Lets think for a moment about a heater plate with a power output P that is connected via a sheet of copper of area A and thickness d to some solid chunk of magic fairy dust of temperature T2 that doesn't ever change its temperature. What temperature will the heater plate have?

Well, the same temperature the underside of the copper plate will have, what is that temperature?

In general we can't answer that, I mean imagine you cooled the plate down to -10°C, turned on the heater and immediately measured the temperature -  of course your will find -10°C again, no matter what the power is. However, some amount of power will move into the copper and heat it up until, eventually, the temperature evens out. By that point all of the power from the heater needs to flow through the copper (otherwise the energy of the copper would increase and thus its temperature).

This state is called the (thermal) equilibrium.

 

We can use our equations for the 3 modes of heat transportation to figure out what the temperature difference between the top of the plate (T2) and the bottom (T1) is:

The copper is solid, so all we need to worry about is conduction, so we open up our physics textbook and look up the thermal conductivity C. We plug it into P=C*A/d * (T1 - T2) and find T1 = P*d/(C*A) + T2.

Notice that +T2 there? This means, when your room, uuuhm, I mean your magic fairy dust, increases its temperature by 5°C, so will your CPU, uhm, heater plate.

 

 

Cooling systems are like ogres

 

So what happens when there are multiple layers? Well, each layer needs to have a temperature difference between the two ends, and you just have to add them up, it's really that simple. So if you have a complex cooling system, say an air cooler,

1. You identify the layers involved (TIM, IHS, TIM, heatpipes, cooling fins->air)
2. figure out which layer can be modeled with which equations (conduction, conduction, conduction, conduction*, convection)
3. look up all the constants
4. calculate the temperature differences for each layer
5. add them up

Oh, and don't feel afraid to simplify things. Don't the like ~50 coupled 2D partial differential equations that come from looking at each cooling fin as a thing with a temperature gradient? Just assume each fin is the same temperature everywhere. Don't want to solve some complex thing including capillary action for the heatpipes? Just use the W/K for some random heatpipes of roughly the same diameter you find in a spec-sheet and use that instead (maybe divide by the cross-section and multiply by the length to get the a conductivity). Don't want to deal with complicated flow equations? Just assume the water is the same temperature everywhere in the loop.

And just like this you have all you need to solve pretty much all cooling systems that stay in an equilibrium (like water or air cooling, not LN2).

 

 

Things I still like to add include solving these problems for specific methods of cooling. Especially the more common ones. However if I want to actually make it understandable, each of these will be quite a few words with illustrations and probably code examples. So I think it will be a bit much for this thread. Tell me if you are interested and I will write them up in a separate post. Otherwise I might end up doing other physics topics first like "How does a transistor actually work?" or "What are the physical limits of computers?". Please tell me which of these you'd be interested in. And don't hold your breath  

[ChalkChalkson]

21 hours ago, Pangea2017 said:

what? Diethylether for electric systems sounds like a good idea...

^^It is a thing I saw exactly once, that guy filled a pot (like for LN2) with ether, get the temperature down below 0, has trhe big disadvantage of filling the room with intoxicating, flammable fumes

[ChalkChalkson]

11 hours ago, Pangea2017 said:

smoking is deadly.

Do you have run the mathe on this if sub zero is realistic?

The  Δ_fH^°_m values does look like it work for normal cooling (-252.1 kJ/mol).  

 

With aceton and a decend airflow you can freeze DMSO without a problem even if it is not totally submerged 

Aceton has a way higher boiling point and lower evaporation pressure. When you but a glass of Diethylether out it will actually collect ice on the outside. So at idle/pre start-up, I totally believe the guy, under load I am rather unsure

[ChalkChalkson]

On 4/25/2018 at 12:57 PM, Pangea2017 said:

Yeh, dietyhlether is nice but a pain if the water bath is still at 60°C.

There is also a nice demonstration where you freeze water at the outside of the test tube.

 

With over from the cpu 200w things get more complicated also the amount of vapor have to be impressive. More then 2 L/s gas from the small heatspreader condensing.

If you are interested I could write that up in a separate thing, maybe with some numerical analysis for different liquids.

[ChalkChalkson]

On 5/2/2018 at 6:14 PM, Pangea2017 said:

I have tought about building a phase changed pc for my self to get it silent. The problem was i did not came up with a suitable liquide: cheap, easy to buy, no health risk  (small leaks will happen), no risk for the parts.

Temperatures will be pretty bad, but Acetone and Ethanol spring to mind as relatively safe options. Diethylether and pentane would be better

[Jtalk4456]

Like the shrek reference

[ChalkChalkson]

2 hours ago, Pangea2017 said:

Acetone: disolve to much inside your pc, flammable

ethanol: flammable

Acetone isn't really a problem for your PC, especially in low quantities. Kinda emptied a bottle of it over a fully built and running PC once by accident... Got amazing thermals for a short period of time

2 hours ago, Pangea2017 said:

diethylether: extremly flammable, can build explosive atmospheres, Peroxide build up over time  -->> worst option

Yeah, terrible option, kinda fucked up when I put it there, wanted to include DCM, but that one might (well is probably) illegal where you live.

2 hours ago, Pangea2017 said:

pentane. flammable, might dislove some prats

Also not particularly good for you and your environment...

[ChalkChalkson]

1 hour ago, Pangea2017 said:

H315  

 

do you think using nitril gloves would make the idea even worse?

Honestly not a clue

[ChalkChalkson]

1 hour ago, Pangea2017 said:

@ChalkChalkson ifixit would know it:

https://www.ifixit.com/Store/Tools/iFixit-Adhesive-Remover-for-Battery-Screen-and-Glass-Adhesive/IF145-400-4

Aceton + safty glasses + nitrile gloves + average user = invulnerable = brilliant idea

But aren't nitrile gloves notorious for making your hands sweat so much the acetone might be better?

 

DCM is another thing though. As usual its listed that your skin/eyes/organs might not like long exposure, but it is also listed as a potential carcinogen... Its a pretty dope coolant otherwise though. And hey, its not BCF, so it doesn't even kill the ozone layer that much.... If you can get it, it might actually be perfect. Especially if you can mix it with some simple chloromethane.

Its also used as an organic solvent to get rid of grease or paint, so availability should be decent. Vapor pressures also look good, heat capacity is at ~100J/kgK... This should keep the CPU below 50°C silently, if you manage to get a radiator set up as a passive condenser that is.

One annoyance would be, that you should probably use copper or glass tubing and full metal blocks with that one since it is a really good solvent for most organic compounds (I think PE and PTFE should be fine though).

 

There are some liquids specialized for this very purpose, but they tend to be expensive.

 

Thinking about it some more, Acetaldehyde might be a decent alternative, much less safe and probably harder to get though

[ChalkChalkson]

1 minute ago, Pangea2017 said:

Let's buy some bromine. The vapor color is amazing. Also color matching is not a problem. All the parts will have a nice red touch. 

^^pretty sure your CPU would throttle before you could even start to cough from the vapors, but hey, yellow goes well with red, why not go cryogenic?