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

Heat Transfer $q$, in DTU, is mainly a product of:

• $\Delta T$, the temperature difference in °C
• $\Delta t$, the time interval, which is always one tick, $0.2\text{ s}$, and
• $k$, the applicable thermal conductivity in DTU/m/s/°C
  • $k_{\text{min}}$ is the lower of the two: $\min (k_1,k2)$
  • $k_{\text{geom}}$ is the geometric mean of the two: $\sqrt{k_1\cdot k_2}$
  • $k_{\text{avg}}$ the arithmetic average of the two: $(k_1+k_2)/2$
  • $k_{\text{mult}}$ the product of the two, halved: $k_1\cdot k_2/2$

In some cases, heat flow depends on the thermal mass of the hotter of the two objects:

• $C_{\text{th max}}=\{\begin{array}{cc}\frac{m_{\text{hot}}c}{5A}& \text{if the object is a building}\\ \frac{m_{\text{hot}}c}{A}& \text{otherwise}\end{array}$

where $m_{\text{hot}}$ is mass of the hotter object, $c$ is is specific heat capacity (SHC), $A$ is its area (1 for single cells), divided by 5 if the hotter object is a building.

Equations

Scenario	Formula
Cell ↔ adjacent Cell
Solid ↔ Solid	$q=\Delta T\cdot \Delta t\cdot k_{\text{geom}}\cdot 1000$
Solid ↔ Liquid
Gas ↔ Liquid
Gas ↔ Gas
Solid ↔ Gas	$q=\Delta T\cdot \Delta t\cdot k_{\text{geom}}\cdot 1000\cdot 25$
Liquid ↔ Liquid	$q=\Delta T\cdot \Delta t\cdot k_{\text{geom}}\cdot 1000\cdot 625$
Entity lying on a Solid	$q=\Delta T\cdot \Delta t\cdot k_{\text{min}}\cdot 62.5$
Building ↔ Solid tile below it	$N/A$
pipe ↔ adjacent pipe	$N/A$
Inside a Cell
Entity ↔ Cell	$q=\Delta T\cdot \Delta t\cdot k_{\text{min}}\cdot 1000$
Building ↔ Cell	$q=\Delta T\cdot \Delta t\cdot k_{\text{mult}}\cdot C_{\text{th max}}$
Building ↔ Building	$N/A$
Building ↔ Conduction Panel	$q=\Delta T\cdot \Delta t\cdot k_{\text{mult}}\cdot C_{\text{th max}}\cdot 5\cdot 1000\cdot 10^{-6}$
Building ↔ Entity	$N/A$
Building's Contents
pipe ↔ pipe contents	$q=\Delta T\cdot \Delta t\cdot k_{\text{avg}}\cdot 50$
Insulated pipe ↔ contents	$q=\Delta T\cdot \Delta t\cdot k_{\text{min}}\cdot 50$
pipe contents ↔ Conduction Panel	$q=\Delta T\cdot k_{\text{avg}}\cdot 50$ (heat transfer occurs when piped contents flow which occurs at most once per second)
Cell ↔ pipe contents	$N/A$: transfers through the pipe instead
pipe bridge ↔ bridge contents	$N/A$: bridges teleport elements, NO contents
Building ↔ building contents	$N/A$
Building's Cell of Interest ↔ building contents	see Cell↔Entity

Thermal Element Categories

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 $(\frac{255}{2}{)}^2$ (not correctly reflected under Properties)
• Insulated Liquid Pipe and Insulated Gas Pipe: divide by 32
• Power Wires: divide by 20
• Some background automation buildings: divide by 20
  • AND Gate
  • OR Gate
  • XOR Gate
  • NOT Gate
  • FILTER Gate
  • BUFFER Gate
  • Signal Distributor
  • Signal Selector
• 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 3×3 area 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 -- debris, animals, plants -- 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 and Compost act as normal buildings, but their 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 Cell 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.

Insulated Tiles reduce the thermal conductivity of their building material by (255/2)² (or 16 256) instead of 100 as stated in the game. It also uses $k_{\text{min}}$instead of $k_{\text{geom}}$for the purpose of cell to cell conductivity, which is mostly going to be the insulated tile conductivity. Solid to gas multiplier still applies.

Recap of Cell-to-Cell multipliers

				Gas	Liquid	Solid
Gas				1	1	25
Liquid				1	625	1
Solid				25	1	1

Because of the gas-to-solid ×25 multiplier, it's recommended to use a double layer of tiles or a single layer of tiles plus a thin liquid layer when trying to insulate between two rooms, to instead get a ×1 multiplier.

Special cases for surface area multipliers

Neutronium has a ×0 multiplier on all cells (separate from the fact that it has 0 thermal conductivity and 0 specific heat capacity).

Thermium has an additional ×2 multiplier on cell-to-cell multipliers. This implies that Thermium -to-Thermium has a combined multiplier of ×4, and Thermium -to-gas has a combined multiplier of ×50.

Snow , Crushed Ice , Packed Snow has a ×1000 multipler on solid-to-gas (on top of the ×25 for gas-to-solid already). This includes the Snow Tile, which makes it a subpar insulator against gas despite its relatively low 0.545 DTU/m/s/K thermal conductivity. (Indeed, this is actually one of the most thermally conductive element interaction in the game)

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 1 g

Upper Limits

Heat transfer between cells is capped by the following upper bound:

If the calculated heat transfer would result in a temperature jump of more than one fourth of their temperature difference $(T_1-T_2)/4$ in either material, then the heat flow is limited to $\max (\frac{T_1-T_2}{4}\cdot m_1\cdot c_1,\frac{T_1-T_2}{4}\cdot m_2\cdot c_2)$ DTU per tick.

Simply said: if the temperature difference is 40 °C, each object's temperature can change by 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:

$T_{\text{eq}}=\frac{T_{\text{building}}\cdot C_{\text{building}}+T_{\text{cell}}\cdot C_{\text{cell}}\cdot A}{C_{\text{building}}+C_{\text{cell}}\cdot A}$

The maximum permitted heat transfer per cell is the difference between the building's temperature and the equilibrium temperature divided by the building's area.

$q_{\text{max}}=C_{\text{building}}\cdot \frac{T_{\text{building}}-T_{\text{eq}}}{A}$

If the thermal mass of the cell is very large relative to the building, then the maximum temperature change can be approximated as simply $\frac{\Delta T}{A}$

Floating-Point Calculation Limits

While the above limits are deliberately implemented, it is also possible for heat exchange to fail 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 small changes to be lost. For example, using 32-bit floats, 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 a large tile, especially an unnaturally large tile, from infinitely dumping heat/cold into a smaller tile without itself changing temperature.

Floating Point Calculation Limits In Insulated Tiles

Main article: Insulated Tile

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 / 68 °F, will not exchange heat with a solid or liquid tile unless the temperature difference is at least 248.05 °C, and won't exchange heat with a gas tile unless the temperature difference is at least 9.92 °C. This makes it quite easy to achieve actually zero heat transfer without resorting to Insulite or Vacuum . The exact formulas governing this are: $\Delta T_{\text{ignorable}}=2^{\lfloor {\log }_2(T)-24\rfloor }$ and $q_{\text{max}}=\Delta T_{\text{ignorable}}\cdot m\cdot c$, where temperature $T$, mass $m$, and SHC $c$ are for the cell holding everything constant, and $q_{\text{max}}$ is the relevant heat-exchange function between the two cells, which can be reversed to find $\Delta T_{\text{max}}$.

It is also readily observed with liquid tiles, that Magma and Water can have immense thermal masses which means that 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 their masses are are sufficiently low. 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 / 32 °F 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 four thermal descriptors in the game, and they are applied to elements whose thermal characteristics reach a certain threshold. These descriptors do not affect the element any further.

• Thermally Reactive: Elements with a specific heat capacity less than or equal to 0.2
• Slow heating: Elements with a specific heat capacity greater than or equal to 1.0
• Insulator: Elements with a thermal conductivity less than or equal to 1.0
• High Thermal Conductivity: Elements with a thermal conductivity greater than or equal to 10.0

Pipes list

Liquid Pipes

Liquid Pipes

Pipe	Material	Thermal Conductivity
Insulated Liquid Pipe	Insulite	0.0000003125
Liquid Pipe	Insulite	0.00001
Insulated Liquid Pipe	Ceramic	0.019375
Insulated Liquid Pipe	Shale	0.05625
Insulated Liquid Pipe	Obsidian	0.0625
Insulated Liquid Pipe	Igneous Rock	0.0625
Insulated Liquid Pipe	Sedimentary Rock	0.0625
Insulated Liquid Pipe	Sandstone	0.090625
Insulated Liquid Pipe	Granite	0.1059375
Insulated Liquid Pipe	Wolframite	0.46875
Insulated Liquid Pipe	Tungsten	0.46875
Liquid Pipe	Ceramic	0.62
Liquid Pipe	Shale	1.8
Liquid Pipe	Obsidian	2
Liquid Pipe	Igneous Rock	2
Liquid Pipe	Sedimentary Rock	2
Liquid Pipe	Sandstone	2.9
Liquid Pipe	Granite	3.39
Insulated Liquid Pipe	Thermium	6.875
Liquid Pipe	Wolframite	15
Liquid Pipe	Tungsten	60
Radiant Liquid Pipe	Lead	70
Radiant Liquid Pipe	Niobium	108
Radiant Liquid Pipe	Steel	108
Radiant Liquid Pipe	Iron	110
Radiant Liquid Pipe	Copper	120
Radiant Liquid Pipe	Tungsten	120
Radiant Liquid Pipe	Gold	120
Radiant Liquid Pipe	Nickel	182
Radiant Liquid Pipe	Cobalt	200
Liquid Pipe	Thermium	220
Radiant Liquid Pipe	Iridium	340
Radiant Liquid Pipe	Aluminum	410
Radiant Liquid Pipe	Thermium	440

Gas 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	Shale	0.05625
Insulated Gas Pipe	Obsidian	0.0625
Insulated Gas Pipe	Igneous Rock	0.0625
Insulated Gas Pipe	Sedimentary Rock	0.0625
Insulated Gas Pipe	Fossil	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	Shale	1.8
Gas Pipe	Obsidian	2
Gas Pipe	Igneous Rock	2
Gas Pipe	Sedimentary Rock	2
Gas Pipe	Fossil	2
Gas Pipe	Sandstone	2.9
Gas Pipe	Granite	3.39
Radiant Gas Pipe	Gold Amalgam	4
Radiant Gas Pipe	Nickel Ore	6
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	Iridium	340
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 $\frac{base}{100}$, but the actual value used by calculations (and shown here) is $base\cdot (\frac{2}{255}{)}^2$.

Tiles

Tile	Material	Thermal Conductivity
Insulated Tile	Insulite	6.15e-10
Tile Carpeted Tile	Insulite	0.00001
Insulated Tile	Ceramic	0.0000381
Insulated Tile	Mafic Rock	0.0000615
Insulated Tile	Shale	0.000111
Insulated Tile	Fossil	0.000123
Insulated Tile	Igneous Rock	0.000123
Insulated Tile	Obsidian	0.000123
Insulated Tile	Sedimentary Rock	0.000123
Insulated Tile	Sandstone	0.000178
Insulated Tile	Granite	0.000209
Plastic Tile	Plastic	0.150
Wood Tile	Wood	0.220
Plastic Tile	Plastium	0.250
Plastic Tile	Solid Visco-Gel	0.450
Tile Carpeted Tile	Ceramic	0.620
Window Tile	Glass	1.110
Tile Carpeted Tile	Mafic Rock	1.000
Tile Carpeted Tile	Shale	1.800
Tile Carpeted Tile	Fossil	2.000
Tile Carpeted Tile	Igneous Rock	2.000
Tile Carpeted Tile	Obsidian	2.000
Tile Carpeted Tile	Sedimentary Rock	2.000
Tile Carpeted Tile	Sandstone	2.900
Tile Carpeted Tile	Granite	3.390
Metal Tile	Depleted Uranium	20
Metal Tile	Lead	35
Metal Tile Bunker Tile	Steel	54
Metal Tile	Niobium	54
Metal Tile	Iron	55
Metal Tile	Copper	60
Metal Tile	Gold	60
Metal Tile	Tungsten	60
Window Tile	Diamond	80
Metal Tile	Nickel	91
Metal Tile	Cobalt	100
Metal Tile	Iridium	170
Metal Tile	Aluminum	205
Metal Tile	Thermium	220

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. 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 $k_{geom}$ to $k_{min}$ 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/