Thermal Conductivity - I don't get the math

[Karlex]

Hey there,

i searched a lot on google and still here, but i really don't get it.

So basicly, I know how to do the math to get the required energy to heat/cool something (Example Water: Thermal Capacity 4.179 J/g/K; Cool 10kg down from 100°C to 90°C (delta 10°C); 4.179 J/g/K * 10,000g * 10K = 417,900J)

But now i'm trying to figure out, how long this 10kg water has to be in a pipe out of Granit in a stable Hydrogenroom (2kg) with constant -50°C, till it reaches the 90°C (the Hydron and Pipe wont change their temperature, cuz wheeze cool it down)

 

In Debug mode i figured out in a Vaacum Room with 1 Pipe tile (granit) and the rest is isulated, from 100°C Water in a 0°C Pipe, it always heats the Pipe 1.6°C up (1kg or 10kg Water does no difference, only the temperature that the Water loos is different)

 

So my question mainly is, whats the math behind the conductivity. How do I get this 1.6°C loos of the Pipe and the around 0.2°C (i think that was the number of the 10kg Water) loss of the Water that gone trough that Pipe?

[Tobruk]

I'm not good at math, but I can help you through a different suggestion - do an in-pipe sensor measuring if the water is above >90 and then liquid shutoff to some designated place

[Karlex]

Ya i know that I can do a koop till it reaches the Temperature that i want

But then this stops the nicly flow and also not Real Good calculated Systems because it drains for sure more temperature that it needs, this takes more Energy, this Maybe **** up the System cus there are Not enough wheeze

[erso]

The termal conductivity can be calculated with:

A (Water): 0.609 (W/m)/K
B (Granite): 3.39 (W/m)/K

X = (A - B) / (LN(A) - LN(B)) = 1.61991 (W/m)/K

However, this value basically describes the termal conductivity from 1g to 1g. Usually you have 100kg pipe and about 10kg of liquid and thus still some calculation to do.

 

[Coolthulhu]

8 hours ago, erso said:

X = (A - B) / (LN(A) - LN(B))

This obviously can't be true. Proof: see what happens when A = B

[Grimgaw]

4 minutes ago, Coolthulhu said:

This obviously can't be true. Proof: see what happens when A = B

It is though, the missing constrains are X=0 if A=0 or B=0, X=A=B if A=B.

https://en.wikipedia.org/wiki/Logarithmic_mean 

[Yunru]

16 minutes ago, Coolthulhu said:

This obviously can't be true. Proof: see what happens when A = B

Pulease. There's like only two cases where 0/0=1 doesn't work. Including 0^0 (which is 1).

It's one of the dumbest things I learned in Numerical Methods: that it's not acknowledged.

[Karlex]

8 hours ago, erso said:

The termal conductivity can be calculated with:

A (Water): 0.609 (W/m)/K
B (Granite): 3.39 (W/m)/K

X = (A - B) / (LN(A) - LN(B)) = 1.61991 (W/m)/K

However, this value basically describes the termal conductivity from 1g to 1g. Usually you have 100kg pipe and about 10kg of liquid and thus still some calculation to do.

 

So you do mass x A W/m/K and mass x B W/m/K and start after that with the Formular ?

[erso]

14 hours ago, Karlex said:

So you do mass x A W/m/K and mass x B W/m/K and start after that with the Formular ?

I always use termal conductivity between elements as an indicator of whether transfer is good or bad. It is certainly possible to calc out the whole thing, but it exceeds my knowledge. (Usually you just want to know if heat is well isolated or transfered.)

To my knowledge, in order to calculate it exactly, one would have to include the respective specifiy heat capacity and mass in relation to each other. Whether the calculation is done in the same way in the game is then another topic.

[Ilmu011]

I was so happy, when I finished highschool, because I wouldn't have physics lessons anymore, where I constantly calculated **** like that. 

Now I am doing it all the time for a video game. Damn...

[Karlex]

1 hour ago, Ilmu011 said:

I was so happy, when I finished highschool, because I wouldn't have physics lessons anymore, where I constantly calculated **** like that. 

Now I am doing it all the time for a video game. Damn...

Then you should play minecraft

I Love games with little physics and Automation (like Space Engineers too)

Specially included with survival Mode, where ONI is alot better then SE

Okay i See, there is only the way to Test Everything in the Debug mode to check if the length of a pipe is enough....

[Ilmu011]

On 28.8.2018 at 12:47 PM, Karlex said:

Then you should play minecraft

I Love games with little physics and Automation (like Space Engineers too)

Specially included with survival Mode, where ONI is alot better then SE

Okay i See, there is only the way to Test Everything in the Debug mode to check if the length of a pipe is enough....

I think I have 2000 hours total playtime in my lifetime in Minecraft so far and not even once needed any kind of formulas or calculations...

[KittenIsAGeek]

There are two thermal transfers that are going on: One is the gas in the room to the pipe.  The next is the pipe to the liquid inside.  So you need to run your calculations for each interaction.    

Here's an example where I'm keeping my bristle blooms at about 17c using 50g packets of constantly moving -3c polluted water.

Spoiler