# Heat transfer math help needed

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Does anybody know how to properly calculate length of heat-exchanging pipe or duration of this process (their values are the same I suppose) using thermal conductivity (TC)?

My suppositions are:

1. TCs of heat-exchanging pipes (copper/golden/steel/etc) can be ignored because of they're much bigger than TCs of mediums.

Then, we have several simplified formulas (indexes 1 and 2 represent two mediums):

1. F=Q/(K•T) - the length of pipe (in m) or duration (in s), where Q - amount of heat (in DTE) and both K and T are:
2. T=|dti-dto|/ln(dto/dti) - Logarithmic Mean Temperature Difference (LMTD), where dti=|t1input-t2input|, dto=|t1output-t2output|; or, in brief, differences between input temperatures and output temperatures of mediums.
3. K=1/(1/k1+1/k2), where k1 and k2 are TCs of mediums.

WAIDW?

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I don't have any complex pipelength math for you, but iirc, the transferrate is the average of the 2 materials, only if one of them has the "insulation" property, then it is using the smaller one, so the material of the radiant pipes are relevant

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31 minutes ago, GemeinerJack said:

I don't have any complex pipelength math for you, but iirc, the transferrate is the average of the 2 materials, only if one of them has the "insulation" property, then it is using the smaller one, so the material of the radiant pipes are relevant

You mean: K=kmin, where  kmin is the smallest TC between two mediums - right? Sounds reasonable.

But what about T? The in-game description of TC contains words about the difference between current temperatures of mediums. And this difference is being changed (lowered) every single second of heat-exchanging.

Reasons for this post are my love to engineering (going hand by hand with poor remembering of school physics lessons) and absence of desire to rebuild my systems again and again in survival.

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As i understand it:

Iron radiant pipe TC: 110, Water 0.609, so the actual TC between them is 55,3045 per degree difference, so the radiant pipes boost the TC a lot, even more extrem in the case of a thermium radiant pipe with a TC of 440, so that the TC of the "hot" and "cold" mediums are more or less no longer relevant...

The radiant pipes, most of the time, are giving more then 90% of the transfer capacity of the "radiator" design

So it is like the complete opposit of your suppostion

But if you use for example a "Insulation" insulated pipe, thanks to the insulation property of the pipe, the TC would be the 0 from the insulated pipe

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Wow, thanks GemeinerJack! Didn't know it...

But the question about math stays opened. And it looks like the answer becomes more complex because of radiant tubes' parameters.

In general, right now I'm just trying to calculate the length of a pipe to boil crude oil into petroleum using polluted O2 (I've got these sources one next to another on my map).

EDIT: ...and find out if it's enough to have 8-tiled heat-exchanger to cool gasses in my setup (uses pwater).

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1 hour ago, GemeinerJack said:

As i understand it:

Iron radiant pipe TC: 110, Water 0.609, so the actual TC between them is 55,3045

Most of your answer is correct, but it´s not (always) the arithmetic mean.

(In our lovely forum should be a couple threads talking about how the average is calculated)

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Iirc it`s not an arithmetic average but a logarythmic average:

This is an equation i found. It seems to be used for caculating a heat exchanger. T1 and T2 are the temperatures on two sides of the exchanger. I`m not sure if it`s the same one used in the game. Probably you need to replace the temperature with thermal conductivity to get the right value if it is.