Thermal Conductivity
Thermal Conductivity is the property of a material that determines how quickly it heats or cools as it comes into contact with objects of different temperatures. Although the game states that between two objects, the lowest thermal conductivity is used, this is not true for all cases.
Equations
The calculation of Heat Transfer in is mainly a product of:
- the Temperature difference in °C
- the passing time, which is always one tick,
- the applicable thermal conductivity in
- is the lower of the two
- is the geometric mean of the two:
- the arithmetic average of the two:
- the two multiplied together:
For heat transfer with buildings, there is an additional factor:
- the thermal mass per area of the hotter object: where is mass, is specific heat capacity (SHC), is the area of the building/cell (1 for cells), and divide by 5 if the hotter object is a building.
Scenario | Formula |
---|---|
Cell ↔ adjacent Cell | |
Solid ↔ Solid | |
Solid ↔ Liquid | |
Gas ↔ Liquid | |
Gas ↔ Gas | |
Solid ↔ Gas | |
Liquid ↔ Liquid | |
Entity lying on a Solid | |
Building ↔ Solid tile below it | |
pipe ↔ adjacent pipe | |
Inside a Cell | |
Entity ↔ Cell | |
Building ↔ Cell | |
Building ↔ Building | |
Building ↔ Conduction Panel | Use Building ↔ Cell but treat panel as a 100 kg cell and divide result by 11 |
Building ↔ Entity | |
Building's Contents | |
pipe ↔ pipe contents | |
Insulated pipe ↔ contents | |
pipe contents ↔ conduction panel | (as the packet teleports across the panel) |
Cell ↔ pipe contents | : transfers through the pipe instead |
pipe bridge ↔ bridge contents | : bridges teleport elements, NO contents |
Building ↔ building contents | |
Building's Cell of Interest ↔ building contents | see Cell↔Entity |
Category | Examples |
---|---|
Cell | Gas, Liquid, Solid Block, Tiles, closed Doors, Joint Plate (middle), Tube Crossing (middle), etc |
Entity | Dupes, Creatures, Plants, Debris, Mesh Tile, Airflow Tile, etc |
Building | pipes, bridges, background buildings, geysers, generators, open Doors, Pneumatic doors (open/closed), etc |
Pipe | Liquid Pipe, Gas Pipe, Conveyor Rail, Wires (all kinds), Automation Wire, and Automation Ribbons |
Bridge | Liquid, Gas, Conveyor Wire, Automation, and Automation Ribbons |
Contents | Building Production Storage (Input/Output), Reservoirs, Fridges, Compactors, etc |
Special | Tempshift Plate, Conduction panel, Refrigerator, Compost |
Certain buildings apply a modifier to their material thermal conductivity:
- Insulated Tiles: divide by (not correctly reflected under Properties)
- Insulated Liquid Pipe and Insulated Gas Pipe: divide by 32
- Wires of any kind: divide by 20 (this may be a legacy of a ditched feature making wires truly overheat)
- Radiant Pipes, Radiant Gas Pipes and Conduction Panel: multiply by 2
a Tempshift Plate conducts as a building, and also conducts to all Cells in a 3x3 (centered on it)
a Conduction Panel is a (long) pipe
- conducts as a building in its cells
- specially conducts building ↔ building in its MIDDLE tile
- conducts any elements passing through it via pipe ↔ pipe contents
Entities act as if they only take up one tile of space, even if they appear to take up more than that. For example, Duplicants and upwards growing Plants exchange heat only at their bottom tile.
A building's contents act like they are in the building's Cell of Interest, and exchange heat through the Cell↔Entity Equation.
- Powered Refrigerator, or Compost act as a normal building. BUT the contents will only interact with an imagined 277.15K (fridge) or 348.15K (compost) source at a locked conductivity of 1000 regardless of their material.
Bridges act as a long building, conducting along its length.
- You can stack multiple bridges to increase heat transfer along the cells
- You can use bridges to help stabilize a Guide/Liquid Airlock from evaporation or sublimation.
Heavi-Watt Joint Plates, Heavi-Watt Conductive Joint Plates, & Transit Tube Crossings act as a cell, the connection points on the sides are cosmetic (for thermal conductivity). Radbolt Joint Plates acts as both a cell and a building, but the building does not conduct heat. Fish Feeders and Fish Releases conduct heat properly both as a cell and as a building.
Manual Airlocks and Mechanized Airlocks behave exactly like two equal mass tiles adding up to the weight of the door (so, for example, a Steel Mechanized Airlock behaves exactly like two tiles of 200 kg Steel). The displayed temperature is that of the Tile Of Interest but the other tile can and will likely have a different temperature. There is no heat transfer between the two tiles as a Building ↔ Cell, only heat transfer as a Cell ↔ Cell. Opening the door equalizes the temperature instantly. Closing the door causes temperature duplication.[2]
Insulated Tiles reduce the thermal conductivity of their building material by (2/255)² (or 16 256) instead of 100 as stated in the game. It also uses instead of for the purpose of cell to cell conductivity, which is mostly going to be the insulated tile conductivity. Solid to gas multiplier still applies.
Gas | Liquid | Solid | ||||
---|---|---|---|---|---|---|
Gas | 1 | 1 | 25 | |||
Liquid | 1 | 625 | 1 | |||
Solid | 25 | 1 | 1 |
Because of the Gas to Solid x25 multiplier, it's recommended to add a double tiles layer or a thin liquid layer when trying to insulate two rooms, to instead get a x1 multiplier.
Limits of Heat Transfer
Lower Limits
Heat Transfer will not occur if:
- the temperature difference is less than 1 °C
- the calculated thermal flow is less than 0.1 DTU
- either of the masses is less than 1g
Upper limits
Heat Transfer between cells has the following cap:
- If the calculated heat transfer would result in a temperature jump of more than a fourth of their temperature difference in either material.
Simply said: if the temperature difference is 40 °C, a materials temperature can change at most 10 °C per tick
Building Limits
Heat transfer between a building and a cell has different limits, the lower limits which are applied to cells do not apply to buildings, but the upper limit is conceptually similar.
A building exchanges heat with all cells it covers simultaneously. In order to ensure that thermodynamics will not be violated the game limits heat transfer per cell such that at most the final temperature of the building would be the equilibrium temperature, assuming that the building completely covers such cells:
The maximum permitted heat transfer per cell is the difference between the building's temperature and the equilibrium temperature divided by the Area of the building.
If the thermal mass of the cell is very large relative to the building, then the maximum temperature change can be approximated as simply
Floating Point Calculation Limits
While the above limits are deliberately implemented, it is also possible for heat exchange to fail to happen due to limitations of the floating point calculations used to calculate temperature changes.
Internally ONI uses 32 bit floating point numbers to represent temperatures, and due to the limited precision of floating point numbers it is possible for the result of a floating point calculation to be the same number. For example with 32 bit floats, the calculation: 300.0 + 0.00001 = 300.0
The game has a rule that if either tile fails to change temperature, then no heat exchange is allowed to take place. This prevents an exploit where a large tile, especially an unnaturally large tile, infinitely dumps heat/cooling into a smaller tile without itself changing temperature.
Floating Point Calculation Limits In Insulated Tiles
In real games, the floating point limit comes up all the time when the temperature difference between an Insulated Tile and a solid or liquid tile is relatively small. For example an Igneous Rock Insulated Tile which is itself at 20°C, will not exchange heat with a solid or liquid tile unless the temperature delta is at least 248.05°C, and won't exchange heat with a gas tile unless the temperature delta is at least 9.92°C. This makes it quite easy to achieve actually zero heat transfer without resorting to the Insulite material or Vacuum. The exact formulas governing this are: and , where , , and are for the cell holding everything constant, and is the heat-exchange formula relevant between the two cells, which can be reversed to find .
It is also readily observed with liquid tiles, Magma and Water can have immense thermal mass which means relatively large DTU inputs are required to cause a temperature change. This results in the paradoxical outcome where full magma tiles don't exchange heat with insulated tiles, but partial magma tiles can exchange heat if they are sufficiently low mass. Using the above formula but applied to the Magma tile instead of the insulated tile, we can see that a cell with 715.6 kg or more magma will be unable to exchange temperature with an Igneous Rock Insulated Tile at 0°C or higher, regardless of the magma temperature. For Mafic Rock, which has half the conductivity, only 357.8 kg of magma are needed.
Suffice to say that while floating point imprecision sometimes causes heat exchange to not happen at all, when temperature changes are small it also causes the actual temperature change to deviate quite significantly from what higher precision calculations would suggest.
Thermal descriptors
There are 4 thermal descriptors in the game, and they get attached to elements when their thermal characteristic reach a certain threshold. These descriptor does not affect the element any further.
- Thermally Reactive: Elements have a specific Heat Capacity of less than or equal to 0.2
- Slow heating: Elements have a specific Heat Capacity of greater than or equal to 1.0
- Insulator: Elements have a thermal conductivity of less than or equal to 1.0
- High Thermal Conductivity: Elements have a thermal conductivity of greater than or equal to 10.0
Pipes list
Liquid Pipes
Gas Pipes
Pipe | Material | Thermal Conductivity |
---|---|---|
Insulated Gas Pipe | Insulite | 0.0000003125 |
Gas Pipe | Insulite | 0.00001 |
Insulated Gas Pipe | Ceramic | 0.019375 |
Insulated Gas Pipe | Mafic Rock | 0.03125 |
Insulated Gas Pipe | Obsidian | 0.0625 |
Insulated Gas Pipe | Igneous Rock | 0.0625 |
Insulated Gas Pipe | Sedimentary Rock | 0.0625 |
Insulated Gas Pipe | Sandstone | 0.090625 |
Insulated Gas Pipe | Granite | 0.1059375 |
Gas Pipe | Ceramic | 0.62 |
Gas Pipe | Mafic Rock | 1 |
Gas Pipe | Obsidian | 2 |
Gas Pipe | Igneous Rock | 2 |
Gas Pipe | Sedimentary Rock | 2 |
Gas Pipe | Sandstone | 2.9 |
Gas Pipe | Granite | 3.39 |
Radiant Gas Pipe | Gold Amalgam | 4 |
Radiant Gas Pipe | Iron Ore | 8 |
Radiant Gas Pipe | Cobalt Ore | 8 |
Radiant Gas Pipe | Copper Ore | 9 |
Radiant Gas Pipe | Pyrite | 9 |
Radiant Gas Pipe | Wolframite | 30 |
Radiant Gas Pipe | Aluminum Ore | 41 |
Radiant Gas Pipe | Niobium | 108 |
Radiant Gas Pipe | Steel | 108 |
Radiant Gas Pipe | Thermium | 440 |
Solid Tiles list
Important: For Insulated Tiles, these numbers will not match what is seen in-game. This is because the value displayed in-game is , but the actual value used by calculations (and shown here) is .
Tips
- When cooling or heating an area it's better to run pipes through tiles than through atmosphere. In both cases the equation for "Building and the cells it occupies" is used which multiplies both Thermal conductivities, and in general, gases have a much lower thermal conductivity than liquids, which have lower conductivity than solids.
- However, if drastic cooling is desired, then Steam Turbines and Aquatuners will have to be involved, which means a cavity filled with Steam will have to be used.
- Since Insulated Tiles have a factor of 1/16256, and pipes a factor of 1/32, much less heat is transferred if a regular pipe goes through an insulated tile than when an insulated pipe goes through a regular Tile. Though, of course, insulating both has an even better insulating effect.
- Even though Insulite has a lower thermal conductivity than any Insulated Tile, the change in formula from to makes insulated tiles much more practical insulators than a regular Tile made from Insulite. Indeed, they are so good that even using regular rock is often sufficient to shut down heat transfer completely, or to practically unnoticeable levels.
References
https://forums.kleientertainment.com/forums/topic/84275-decrypting-heat-transfer/