Heat Transfer Equations

[wachunga]

With some help from this thread, I've empirically derived most of the formulas governing heat transfers. These formulas are for one tick on slowest speed (rapidly unpause/pause). You can plug in the various values and determine what the temperatures will be after one tick. Hopefully this will dispel much of the misinformation regarding these things. If you discover something that does not follow these equations please let me know.

q is the heat transferred, divide by mass and SHC of the material to get it's new temperature. dT is the difference in temperature. k1 is the conductivity of the first material. k2 is the conductivity of the second material. klow is the lower conductivity of the two materials. kave is the average conductivity ((k1 + k2)/2). Conductivity of insulated tiles is not that which is display in the tile property box. It is the conductivity of the base material divided by 16,256 (ask Klei, not me). HC is the heat capacity of the hotter material (mass * SHC). Buildings have 1/5 the HC they "should" have, relevant when they are the hotter material or in determining new temperatures. Buildings include pipes, wires, generators, etc. but not built tiles.

 

Debris in a Tile: q = klow * dT * 200

Debris on a Tile: q = klow * dT * 12.5

Building to Tile: q = k1 * k2 * dT * HC / 10

Insulated Pipe to Contents: q = klow * dT * 10

Normal/Radiant Pipe to Contents: q = kave * dT * 10

Tile to Tile: q = klow * dT * 200. Further multiplied by 25 if gas with solid or by 625 if liquid with liquid. Another multiplier of 2 for thermium, 4 if thermium with thermium. There is clamping that can cause odd results, but this is the general rule. The change in temperature maxes at dT / 4 sometimes and dT / 8 other times for example. It's basically black magic.

Again, if you discover any edge cases do say so!

 

 

[Angpaur]

13 minutes ago, wachunga said:

Tile to Tile: q = klow * dT * 200. Further multiplied by 25 if gas with solid

Well I guess this explains my observations I described in this topic: 

Just one question - what is formula for liquids and insulated tiles? Those seem to not transfer heat at all, no matter of insulated tile material it is made of.

[wachunga]

Yes I was going to comment in your thread but decided to put as much as I know altogether. Abyssalite's conductivity is 0.00001 btw.

The thing with liquid to insulated tiles is an oddity due to clamping in the Tile to Tile formula. Basically the game figures out how much heat to transfer (very small because of the very low conductivity of insulated tiles), figures out how much the tile changes temperature (usually very small due to the large mass of insulated tiles and the small heat transfer), then recalculates the heat transfer based off the new temperature. This often ends up rounding to nothing and no heat transfers. Ask Klei to explain why they implemented it that way.

If you use extremely hot liquid tungsten with insulated obsidian you can observe the very tiny heat transfer with the sample tool in debug. 5520C liquid tungsten interacting with 20C insulated obsidian. q = 2 / 16256 * 5500 * 200 = 135. Temperature change = 135 / 0.2 / 400000 = 0.00169. Sampling the insulated obsidian after 1 tick shows a change from 293.15K to 293.1516K. Rounding errors account for the missing 0.00009 I presume.

[Angpaur]

Still one thing is unexplained - I tested both gasous mercury and hydrogen. Both were at same mass and same temperature initially. Hydrogen haven't heated up any of abyssalite tiles. Even the one that was 1kg only.

[wachunga]

I suspect that may be because hydrogen's SHC of 2.4 is greater than mercury's of 0.14. If the amount of heat transferred is enough to change mercury's temperature but not hydrogen's (due to rounding to zero), there will be transfer with the mercury but not with the hydrogen. Can't say for sure, the Tile to Tile transfer is often difficult to decipher. Try reducing the mass of the hydrogen.

[qda]

My instinct tells me that the average thermal conductivity computed is k_ave = (k2-k1)/(ln(k2/k1)), rather than a pure geometric mean. For two thermal conductivities of the same order of magnitude, this results is very close to (k1+k2)/2. On the contrary, whenever (k2-k1) > 10, (k1+k2)/2 can roughly be estimated as max(k1,k2)/2, which doesn't seem to fit the actual behavior of thermal transfer, and feels inherently weird to me.  

Example, a granite tile next to an abyssalite tile :

 (k_granite+k_aby)/2 = k_granite/2 = 1.70 W/m/K
 (k_granite-k_aby)/ln(k_granite/k_aby) = 0.27 W/m/K, more than 6 times less, which seems to better describe what happens in ONI. However, I don't currently have access to ONI to verify any of this.

[Angpaur]

15 minutes ago, wachunga said:

I suspect that may be because hydrogen's SHC of 2.4 is greater than mercury's of 0.14. If the amount of heat transferred is enough to change mercury's temperature but not hydrogen's (due to rounding to zero), there will be transfer with the mercury but not with the hydrogen. Can't say for sure, the Tile to Tile transfer is often difficult to decipher. Try reducing the mass of the hydrogen.

I was rather trying to transfer heat from gases(both very hot like 3000 K, both were 1000kg) to tiles of abyssalite. Hydrogen haven't transfered any heat, which is strange.

[oosyrag]

I've been working on nailing down this mechanic lately too. I don't have a conclusion yet, but I am confident that "Insulated materials use the only the lowest thermal conductivity" is currently false, and that the geometric mean of two material's heat conductivity is not used anywhere.

[Nickerooni]

1 hour ago, oosyrag said:

I've been working on nailing down this mechanic lately too. I don't have a conclusion yet, but I am confident that "Insulated materials use the only the lowest thermal conductivity" is currently false, and that the geometric mean of two material's heat conductivity is not used anywhere.

If you’re looking for cases of geometric mean, you’ll want to look at radiant pipes and thermal shift plates. It’s definitely used there. I can’t think of any other places where it’s used, but I may just be missing an example.

[hpongledd]

On 6.12.2018 at 2:09 PM, wachunga said:

Debris in a Tile: q = klow * dT * 200

What is meant by debris "in" a tile? how can debris be "in" a tile?

[wachunga]

By tile I mean the solid/liquid/gas that fills every block of the map. So that applies to loose material sitting in liquid or gas. It is also possible to have a liquid freeze around loose material then you have debris in a solid tile. It also applies to the material on a conveyor traveling through solid/liquid/gas.

The contents of many buildings act as debris sitting in the tile that comprises the bottom middle or bottom left part of the building. For example, glass forges in a puddle of liquid often break the exit pipe. That's because the molten glass inside the forge acts as debris sitting in that puddle, it super cools before it's even in the pipe which breaks instantly.