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Understanding & Optimizing Heat Transfer


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Been diving into heat exchangers for a minute and want to get a sanity check here on my optimizations. First from the wiki we have some formulas.

Scenario Heat Transfer Formula
Cell to cell {\displaystyle q=k_{geom}*\Delta T*\Delta t*M*1000m}
Entity inside of a cell {\displaystyle q=k_{lowest}*\Delta T*\Delta t*1000m}
Debris on top of a solid cell {\displaystyle q=k_{lowest}*\Delta T*\Delta t*62.5m}
Building and the cells it occupies {\displaystyle q=k_{building}*k_{tile}*\Delta T*\Delta t*C*0.5{\frac {m^{2}s\ ^{\circ }C^{2}}{DTU^{2}}}}
Insulated pipe and its contents {\displaystyle q=k_{lowest}*\Delta T*\Delta t*50m}
Other pipes and their contents {\displaystyle q=k_{average}*\Delta T*\Delta t*50m}

Heat transfer (q) in general is *mostly* governed by k - the thermal conductivity of one of the two materials, typically the lower of the two.

Consider a heat exchanger counterflowing material on a rail against material in a pipe through a single tile. Let's walk through a specific example I'm working on. Wood vs Ethanol.

Ethanol to pipe uses the average of the thermal conductivity, so for the most efficient transfer I want a high TC material for the pipe.

Pipe to tile uses the either lower of the two or their product (entity inside cell or building & cell it occupies?). In the worst case the tile's TC only needs to greater the pipe's if the transfer uses k-low.

The next transfer is from tile to material if I understand correctly (not tile to rail then to material). That's limited by the lower of the thermal conductivity of the two. Lumber's TC is 0.6 (genetic ooze). The tile material should be greater than 0.6 to prevent slowing this transfer down.

Since the fastest heat can flow from hot ethanol to cool lumber is limited to the least conductive material, in this case Genetic Ooze slows everything down. To optimize the heat transfer I only need to choose tile materials with TC of at least 0.6 and pipe TC at least 1.029 (average ethanol + pipe > 0.6).

Taking specific heat capacity into consideration (minimizes the heat-up time) obsidian and sedimentary rock (TC 2, SHC 0.2) are good choices for blocks and pipes. Using radiant pipe and metal tile only speeds up part of the energy movement. When it tries to go from tile to lumber it gets limited by the lower thermal conductivity. As long as everything else goes faster than that I have the fastest system possible for these two materials.

How am I doing so far?

 

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19 minutes ago, occamrazor said:

Pipe to tile uses the either lower of the two or their product (entity inside cell or building & cell it occupies?). In the worst case the tile's TC only needs to greater the pipe's if the transfer uses k-low.

Pipe to tile should use the "Building and the cells it occupies" equation above which is similar to a geometric mean of the conductivities.  But it also includes the heat capacity of the hotter entity which adds a "fun" twist on thermodynamics.

 

23 minutes ago, occamrazor said:

Since the fastest heat can flow from hot ethanol to cool lumber is limited to the least conductive material, in this case Genetic Ooze slows everything down. To optimize the heat transfer I only need to choose tile materials with TC of at least 0.6 and pipe TC at least 1.029 (average ethanol + pipe > 0.6).

To optimize total heat flow in ONI (and real life) you have to optimize the conductivity of all steps.  There's no single rate limiting step.  (As with most engineering) a circuit analogy works well.  Voltage is temperature, heat flow is current, and resistance is the reciprocal of conductivity.  The total flow is inversely proportional to the sum of the resistances of each step.

Now, the wood to tile step will have the highest resistance and will probably dominate.  But you to truly optimize, as in determine the singular optimum, you have to consider the other steps as well.

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12 hours ago, occamrazor said:

Heat transfer (q) in general is *mostly* governed by k - the thermal conductivity of one of the two materials, typically the lower of the two.

It is typically the geometric mean of the two.  It is only the lower of the two if one of them is insulated.

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